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Strong cryptography
Strong cryptography
Strong cryptography
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Strong cryptography or cryptographically strong are general terms used to designate the cryptographic algorithms that, when used correctly, provide a very high (usually insurmountable) level of protection against any eavesdropper, including the government agencies.[1] There is no precise definition of the boundary line between the strong cryptography and (breakable) weak cryptography, as this border constantly shifts due to improvements in hardware and cryptanalysis techniques.[2] These improvements eventually place the capabilities once available only to the NSA within the reach of a skilled individual,[3] so in practice there are only two levels of cryptographic security, "cryptography that will stop your kid sister from reading your files, and cryptography that will stop major governments from reading your files" (Bruce Schneier).[2]

The strong cryptography algorithms have high security strength, for practical purposes usually defined as a number of bits in the key. For example, the United States government, when dealing with export control of encryption, considered as of 1999 any implementation of the symmetric encryption algorithm with the key length above 56 bits or its public key equivalent[4] to be strong and thus potentially a subject to the export licensing.[5] To be strong, an algorithm needs to have a sufficiently long key and be free of known mathematical weaknesses, as exploitation of these effectively reduces the key size. At the beginning of the 21st century, the typical security strength of the strong symmetrical encryption algorithms is 128 bits (slightly lower values still can be strong, but usually there is little technical gain in using smaller key sizes).[5][needs update]

Demonstrating the resistance of any cryptographic scheme to attack is a complex matter, requiring extensive testing and reviews, preferably in a public forum. Good algorithms and protocols are required (similarly, good materials are required to construct a strong building), but good system design and implementation is needed as well: "it is possible to build a cryptographically weak system using strong algorithms and protocols" (just like the use of good materials in construction does not guarantee a solid structure). Many real-life systems turn out to be weak when the strong cryptography is not used properly, for example, random nonces are reused[6] A successful attack might not even involve algorithm at all, for example, if the key is generated from a password, guessing a weak password is easy and does not depend on the strength of the cryptographic primitives.[7] A user can become the weakest link in the overall picture, for example, by sharing passwords and hardware tokens with the colleagues.[8]

Background

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The level of expense required for strong cryptography originally restricted its use to the government and military agencies,[9] until the middle of the 20th century the process of encryption required a lot of human labor and errors (preventing the decryption) were very common, so only a small share of written information could have been encrypted.[10] US government, in particular, was able to keep a monopoly on the development and use of cryptography in the US into the 1960s.[11] In the 1970, the increased availability of powerful computers and unclassified research breakthroughs (Data Encryption Standard, the Diffie-Hellman and RSA algorithms) made strong cryptography available for civilian use.[12] Mid-1990s saw the worldwide proliferation of knowledge and tools for strong cryptography.[12] By the 21st century the technical limitations were gone, although the majority of the communication were still unencrypted.[10] At the same the cost of building and running systems with strong cryptography became roughly the same as the one for the weak cryptography.[13]

The use of computers changed the process of cryptanalysis, famously with Bletchley Park's Colossus. But just as the development of digital computers and electronics helped in cryptanalysis, it also made possible much more complex ciphers. It is typically the case that use of a quality cipher is very efficient, while breaking it requires an effort many orders of magnitude larger - making cryptanalysis so inefficient and impractical as to be effectively impossible.

Cryptographically strong algorithms

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This term "cryptographically strong" is often used to describe an encryption algorithm, and implies, in comparison to some other algorithm (which is thus cryptographically weak), greater resistance to attack. But it can also be used to describe hashing and unique identifier and filename creation algorithms. See for example the description of the Microsoft .NET runtime library function Path.GetRandomFileName.[14] In this usage, the term means "difficult to guess".

An encryption algorithm is intended to be unbreakable (in which case it is as strong as it can ever be), but might be breakable (in which case it is as weak as it can ever be) so there is not, in principle, a continuum of strength as the idiom would seem to imply: Algorithm A is stronger than Algorithm B which is stronger than Algorithm C, and so on. The situation is made more complex, and less subsumable into a single strength metric, by the fact that there are many types of cryptanalytic attack and that any given algorithm is likely to force the attacker to do more work to break it when using one attack than another.

There is only one known unbreakable cryptographic system, the one-time pad, which is not generally possible to use because of the difficulties involved in exchanging one-time pads without them being compromised. So any encryption algorithm can be compared to the perfect algorithm, the one-time pad.

The usual sense in which this term is (loosely) used, is in reference to a particular attack, brute force key search — especially in explanations for newcomers to the field. Indeed, with this attack (always assuming keys to have been randomly chosen), there is a continuum of resistance depending on the length of the key used. But even so there are two major problems: many algorithms allow use of different length keys at different times, and any algorithm can forgo use of the full key length possible. Thus, Blowfish and RC5 are block cipher algorithms whose design specifically allowed for several key lengths, and who cannot therefore be said to have any particular strength with respect to brute force key search. Furthermore, US export regulations restrict key length for exportable cryptographic products and in several cases in the 1980s and 1990s (e.g., famously in the case of Lotus Notes' export approval) only partial keys were used, decreasing 'strength' against brute force attack for those (export) versions. More or less the same thing happened outside the US as well, as for example in the case of more than one of the cryptographic algorithms in the GSM cellular telephone standard.

The term is commonly used to convey that some algorithm is suitable for some task in cryptography or information security, but also resists cryptanalysis and has no, or fewer, security weaknesses. Tasks are varied, and might include:

Cryptographically strong would seem to mean that the described method has some kind of maturity, perhaps even approved for use against different kinds of systematic attacks in theory and/or practice. Indeed, that the method may resist those attacks long enough to protect the information carried (and what stands behind the information) for a useful length of time. But due to the complexity and subtlety of the field, neither is almost ever the case. Since such assurances are not actually available in real practice, sleight of hand in language which implies that they are will generally be misleading.

There will always be uncertainty as advances (e.g., in cryptanalytic theory or merely affordable computer capacity) may reduce the effort needed to successfully use some attack method against an algorithm.

In addition, actual use of cryptographic algorithms requires their encapsulation in a cryptosystem, and doing so often introduces vulnerabilities which are not due to faults in an algorithm. For example, essentially all algorithms require random choice of keys, and any cryptosystem which does not provide such keys will be subject to attack regardless of any attack resistant qualities of the encryption algorithm(s) used.

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See also: Cryptography § Forced disclosure of encryption keys

Widespread use of encryption increases the costs of surveillance, so the government policies aim to regulate the use of the strong cryptography.[15] In the 2000s, the effect of encryption on the surveillance capabilities was limited by the ever-increasing share of communications going through the global social media platforms, that did not use the strong encryption and provided governments with the requested data.[16] Murphy talks about a legislative balance that needs to be struck between the power of the government that are broad enough to be able to follow the quickly-evolving technology, yet sufficiently narrow for the public and overseeing agencies to understand the future use of the legislation.[17]

USA

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The initial response of the US government to the expanded availability of cryptography was to treat the cryptographic research in the same way the atomic energy research is, i.e., "born classified", with the government exercising the legal control of dissemination of research results. This had quickly found to be impossible, and the efforts were switched to the control over deployment (export, as prohibition on the deployment of cryptography within the US was not seriously considered).[18]

Main article: Export of cryptography from the United States

The export control in the US historically uses two tracks:[19]

  • military items (designated as "munitions", although in practice the items on the United States Munitions List do not match the common meaning of this word). The export of munitions is controlled ty the Department of State. The restrictions for the munitions are very tight, with individual export licenses specifying the product and the actual customer;
  • dual-use items ("commodities") need to be commercially available without excessive paperwork, so, depending on the destination, broad permissions can be granted for sales to civilian customers. The licensing for the dual-use items is provided by the Department of Commerce. The process of moving an item from the munition list to commodity status is handled by the Department of State.

Since the original applications of cryptography were almost exclusively military, it was placed on the munitions list. With the growth of the civilian uses, the dual-use cryptography was defined by cryptographic strength, with the strong encryption remaining a munition in a similar way to the guns (small arms are dual-use while artillery is of purely military value).[20] This classification had its obvious drawbacks: a major bank is arguably just as systemically important as a military installation,[20] and restriction on publishing the strong cryptography code run against the First Amendment, so after experimenting in 1993 with the Clipper chip (where the US government kept special decryption keys in escrow), in 1996 almost all cryptographic items were transferred to the Department of Commerce.[21]

EU

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The position of the EU, in comparison to the US, had always been tilting more towards privacy. In particular, EU had rejected the key escrow idea as early as 1997. European Union Agency for Cybersecurity (ENISA) holds the opinion that the backdoors are not efficient for the legitimate surveillance, yet pose great danger to the general digital security.[15]

Five Eyes

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The Five Eyes (post-Brexit) represent a group of states with similar views one the issues of security and privacy. The group might have enough heft to drive the global agenda on the lawful interception. The efforts of this group are not entirely coordinated: for example, the 2019 demand for Facebook not to implement end-to-end encryption was not supported by either Canada or New Zealand, and did not result in a regulation.[17]

Russia

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President and government of Russia in 90s has issued a few decrees formally banning uncertified cryptosystems from use by government agencies. Presidential decree of 1995 also attempted to ban individuals from producing and selling cryptography systems without having appropriate license, but it wasn't enforced in any way as it was suspected to be contradictory the Russian Constitution of 1993 and wasn't a law per se.[22][23][24][note 1] The decree of No.313 issued in 2012 further amended previous ones allowing to produce and distribute products with embedded cryptosystems and requiring no license as such, even though it declares some restrictions.[25][26] France had quite strict regulations in this field, but has relaxed them in recent years.[citation needed]

Examples

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Strong

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  • PGP is generally considered an example of strong cryptography, with versions running under most popular operating systems and on various hardware platforms. The open source standard for PGP operations is OpenPGP, and GnuPG is an implementation of that standard from the FSF. However, the IDEA signature key in classical PGP is only 64 bits long, therefore no longer immune to collision attacks. OpenPGP therefore uses the SHA-2 hash function and AES cryptography.
  • The AES algorithm is considered strong after being selected in a lengthy selection process that was open and involved numerous tests.
  • Elliptic curve cryptography is another system which is based on a graphical geometrical function.
  • The latest version of TLS protocol (version 1.3), used to secure Internet transactions, is generally considered strong. Several vulnerabilities exist in previous versions, including demonstrated attacks such as POODLE. Worse, some cipher-suites are deliberately weakened to use a 40-bit effective key to allow export under pre-1996 U.S. regulations.

Weak

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Examples that are not considered cryptographically strong include:

  • The DES, whose 56-bit keys allow attacks via exhaustive search.
  • Triple-DES (3DES / EDE3-DES) can be subject of the "SWEET32 Birthday attack"[27]
  • Wired Equivalent Privacy which is subject to a number of attacks due to flaws in its design.
  • SSL v2 and v3. TLS 1.0 and TLS 1.1 are also deprecated now [see RFC7525] because of irreversible flaws which are still present by design and because they do not provide elliptical handshake (EC) for ciphers, no modern cryptography, no CCM/GCM ciphermodes. TLS1.x are also announced off by the PCIDSS 3.2 for commercial business/banking implementations on web frontends. Only TLS1.2 and TLS 1.3 are allowed and recommended, modern ciphers, handshakes and ciphermodes must be used exclusively.
  • The MD5 and SHA-1 hash functions, no longer immune to collision attacks.
  • The RC4 stream cipher.
  • The 40-bit Content Scramble System used to encrypt most DVD-Video discs.
  • Almost all classical ciphers.
  • Most rotary ciphers, such as the Enigma machine.
  • DHE/EDHE is guessable/weak when using/re-using known default prime values on the server

Notes

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References

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Sources

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See also

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Strong cryptography

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Strong cryptography refers to the deployment of algorithms and protocols based on industry-tested, accepted designs with key lengths providing at least 112 bits of effective security strength, rendering unauthorized decryption computationally infeasible using current or anticipated technology. These methods prioritize symmetric ciphers like AES-256 or asymmetric schemes such as RSA with 2048-bit or larger keys, alongside robust hash functions, to protect data , , and authenticity against cryptanalytic exploits. Central to strong cryptography are principles of open scrutiny and empirical validation, where algorithms undergo extensive and real-world to identify flaws before widespread adoption, distinguishing them from proprietary or unvetted alternatives prone to hidden weaknesses. practices, including secure generation, distribution, and rotation of keys, are equally critical, as even the strongest fail without them. Its defining achievements include underpinning secure protocols like TLS, which safeguard global and communications, and enabling privacy-preserving technologies amid rising pressures. Notable controversies arise from conflicts between unbreakable encryption and state demands for access, exemplified by historical U.S. restrictions on strong crypto in the —later repealed—and ongoing debates over mandated backdoors, which cryptographers argue inevitably weaken overall system security for all users. Implementation pitfalls, such as side-channel leaks or poor , have compromised otherwise strong systems in practice, underscoring that cryptographic strength alone does not secure weak surrounding architectures. Recent advancements address quantum threats via NIST-standardized post-quantum algorithms, extending strong cryptography's resilience into an era of advanced computational adversaries.

Definition and Principles

Core Definition

Strong cryptography refers to the use of cryptographic algorithms, protocols, and systems engineered to withstand attacks from computationally bounded adversaries, even those equipped with extensive resources such as clusters or specialized hardware like . These systems achieve security through computational hardness assumptions, where decryption or key recovery demands infeasible amounts of time or energy—typically on the order of billions of years with current technology—rather than relying solely on of the algorithm or perfect implementation. Unlike information-theoretically secure schemes (e.g., the ), strong cryptography provides practical security predicated on the difficulty of solving specific mathematical problems, such as factoring large integers or computing discrete logarithms, assuming no efficient quantum or classical algorithms exist beyond exhaustive search. The strength of such cryptography is quantified by metrics like bits of , derived from the minimum operations required for the most efficient known attack; for example, a 128-bit secure system resists brute-force attacks needing roughly 2^128 trials, far exceeding the estimated 10^18 operations per second of the world's fastest supercomputers as of 2023. directly influences this: symmetric ciphers like AES-256 offer 256 bits of security against brute force, while asymmetric systems like RSA-3072 provide approximately 128 bits, per evaluations balancing against attack complexity. NIST guidelines emphasize that strong cryptography must employ approved algorithms from (FIPS), such as AES or elliptic curve variants, with key strengths migrating upward to counter advances in computing power and —e.g., deprecating 80-bit security levels by 2030. Critically, "strong" status is not static; algorithms once deemed robust, such as DES with its 56-bit key (breakable via exhaustive search in hours today using off-the-shelf hardware since 1998), have been relegated to historical use due to and parallelization advances. Strong cryptography thus demands ongoing scrutiny, including resistance to side-channel attacks (e.g., timing or ) and implementation flaws, with peer-reviewed validation ensuring no structural weaknesses like those exposed in older systems such as or SHA-1. Adoption requires not only algorithm selection but also secure and , as poor can undermine even the strongest primitives.

Security Metrics and Strength Evaluation

The security strength of cryptographic algorithms is quantified primarily through the of bit-security, which estimates the exponent of 2 representing the minimum number of operations (e.g., bit operations or modular exponentiations) an adversary must perform to achieve a successful attack with non-negligible probability. For symmetric ciphers, this is often bounded by the key length kk, with exhaustive search requiring up to 2k2^k trials, though meet-in-the-middle attacks can reduce effective security to approximately k/2k/2 bits in some cases; NIST equates AES-128's strength to 128 bits against brute force, assuming no structural weaknesses. Public-key systems derive strength from the computational hardness of problems like or discrete logarithms, where equivalent security levels demand larger parameters—e.g., 3072-bit RSA moduli or 256-bit keys for 128-bit security—calibrated against generic attacks like Pollard's rho or number field sieve. Evaluation of strength incorporates both theoretical metrics and empirical testing. Key theoretical metrics include attack complexity (time and space requirements), such as the data complexity of differential (measured by the number of plaintext-ciphertext pairs needed) or the bias in linear approximations, alongside provable reductions to hard problems under standard models like the model. Practical evaluation relies on to identify weaknesses, with strength affirmed by the absence of feasible breaks despite extensive scrutiny; for instance, AES has withstood over two decades of public analysis without sub-128-bit attacks. NIST guidelines mandate transitioning to at least 128-bit security by 2030, deprecating weaker options like 80-bit equivalents, while post-quantum algorithms are benchmarked against classical symmetric strengths to ensure resilience against Grover's or Shor's algorithms. No metric guarantees absolute , as algorithms are designed under computational assumptions vulnerable to advances in computing power or novel attacks; thus, strength assessment demands conservative margins, ongoing , and diversification across to mitigate single-point failures. Side-channel resistance, while implementation-specific, factors into overall via metrics like leakage success rates, but algorithmic strength prioritizes black-box resistance assuming ideal implementations. In practice, competitions and peer-reviewed challenges, such as NIST's post-quantum standardization process completed in 2024, validate candidates through community-vetted metrics balancing evidence against efficiency.

Historical Development

Pre-Modern Foundations

The earliest documented cryptographic device was the , employed by Spartan military forces as early as the for secure transmission of orders during campaigns. This involved wrapping a narrow strip of around a cylindrical baton of fixed diameter, inscribing the plaintext message along the length in sequential columns, then unwrapping the strip to produce a jumbled that appeared incoherent without the matching baton to realign it. The method's security derived from its physical key—the baton's precise dimensions—ensuring only authorized recipients could reconstruct the message, though it offered limited resistance to an adversary possessing a rod of identical specifications. In , utilized a rudimentary monoalphabetic around 58–51 BC to communicate confidential directives to generals, shifting each letter by a fixed offset of three positions in the Latin alphabet (e.g., A to D). Described by in De vita Caesarum, this "Caesar shift" provided basic obscurity against casual interception but was inherently weak, as its 25 possible shifts (for a 26-letter alphabet) could be brute-forced exhaustively, and letter frequencies remained preserved. Despite these vulnerabilities, it established substitution as a core principle, influencing subsequent ciphers by demonstrating how key-controlled letter mapping could obscure meaning without altering message length or structure. Advancements in emerged in the AD with , an Arab scholar whose treatise Manuscript on Deciphering Cryptographic Messages introduced systematic to break monoalphabetic substitutions. Observing that letter frequencies (e.g., alif appearing most often) were consistent across texts, al-Kindi advocated tallying symbols' occurrences and mapping them to the most probable equivalents, enabling decryption of simple ciphers like the Caesar variant without the key. This method underscored the limitations of frequency-preserving encryptions, compelling later cryptographers to seek designs that flattened statistical patterns, such as polyalphabetic schemes, and highlighted as an adversarial force driving cryptographic evolution. During the , polyalphabetic ciphers addressed vulnerabilities; devised one in 1553, later popularized by in 1586 as a tableau-based system using a repeating keyword to select shifting alphabets for each letter. proceeded by adding the keyword letter's position (modulo 26) to the letter's, yielding output resistant to single-alphabet counts since each position drew from a different substitution. Considered indecipherable for centuries—earning the la cifra indéchiffrable—it withstood attacks until Friedrich Kasiski's method exploited repeated plaintext-keyword alignments, yet its key-dependent multiple alphabets prefigured modern notions of and key space expansion for strength. These pre-modern innovations collectively laid groundwork for strong cryptography by introducing transposition, substitution, statistical countermeasures, and the key- interplay, though computational constraints limited their scalability against determined manual .

20th Century Advances and World Wars

The advent of radio communication in the early necessitated more robust cryptographic methods to secure wireless transmissions, leading to the development of mechanical cipher devices. In 1917, American inventor Edward Hebern patented the first , an electromechanical device employing rotating disks to implement polyalphabetic substitution, which increased key variability and resistance to compared to manual ciphers. This innovation marked a shift toward automated systems capable of handling higher volumes of traffic securely, though early models like Hebern's were not widely adopted militarily until later refinements. During , belligerents relied on a mix of manual codes and ciphers, with radio interception driving advances in both and . The German , introduced in March 1918, combined and double transposition to disrupt statistical patterns, making it one of the era's most complex field ciphers and initially resistant to manual breaking; it was only solved by French cryptanalyst Georges Painvin in June 1918 through exhaustive analysis of captured messages. British Naval Intelligence's exploited German procedural errors to decrypt the Zimmermann Telegram in January 1917, revealing a proposed Mexican alliance and contributing to U.S. entry into the war, underscoring how human factors often undermined even advanced systems. These efforts highlighted the limitations of pen-and-paper methods against industrialized warfare's scale, spurring interwar experimentation with machines. In the interwar period, rotor-based systems proliferated, with patenting the in 1918, initially for commercial use before military adaptation by in the 1920s. By , Enigma's three (later four) rotors and plugboard provided approximately 10^23 possible settings, enabling daily key changes and securing much of German command traffic, though its security relied on operator discipline and was ultimately compromised by Polish and British cryptanalysts exploiting reuse patterns. For high-level communications, employed the Lorenz SZ40/42 from 1941, using 12 wheels for irregular stepping and addition modulo 2, which offered greater complexity than Enigma but was broken at via the , the world's first programmable electronic digital machine, by December 1942. Allied powers prioritized unbreakable designs, exemplified by the U.S. (ECM Mark II), developed in the 1930s and fielded from 1940, featuring 15 rotors with non-uniform stepping and separate key streams for rotors and brushes, yielding an effective key space exceeding 10^30 and resisting all wartime cryptanalytic attempts due to its deliberate avoidance of Enigma-like regularities. Britain's , introduced in 1937, similarly enhanced rotor wiring and reflector designs for superior diffusion, securing diplomatic and military links without successful Axis breaks. Japan's (Red/Purple), deployed from 1939, used stepping switches for substitution but was vulnerable to U.S. attacks by September 1940, aided by mathematical modeling of its 25x25 state matrix. These systems demonstrated that strong cryptography in wartime demanded not only vast key spaces but also resistance to known-plaintext attacks and implementation flaws, with 's unbreached record validating irregular rotor motion as a key principle. The wars' cryptanalytic successes, including over 10% of German traffic decrypted via Enigma breaks from 1941, informed post-war emphasis on provable security metrics.

Post-1970s Standardization and Adoption

The publication of the Diffie-Hellman key exchange method in 1976 marked a pivotal advancement in enabling secure key distribution without prior shared secrets, laying groundwork for systems. This was followed in 1977 by the U.S. National Bureau of Standards (NBS, predecessor to NIST) adopting the (DES) as Federal Information Processing Standard (FIPS) 46, a symmetric with a 56-bit key designed for federal use in protecting unclassified data. DES, originally developed by as a refinement of the algorithm, underwent public scrutiny and validation, including analysis by the Diffie-Hellman team, before standardization, though its relatively short key length later prompted concerns over brute-force feasibility with advancing computing power. In the same year, Ron Rivest, Adi Shamir, and Leonard Adleman publicly described the RSA algorithm, a public-key system based on the difficulty of factoring large semiprimes, which facilitated asymmetric encryption and digital signatures. Standardization efforts accelerated through the 1980s and 1990s via bodies like NIST, ANSI, and ISO, incorporating RSA into standards such as PKCS #1 for encryption and ANSI X9.31 for signatures. DES variants like Triple DES (3DES), mandating three iterations for enhanced effective key length of 168 bits, were endorsed in FIPS 46-3 in 1999 to extend its viability amid growing computational threats. By the late 1990s, DES's vulnerabilities—demonstrated by practical breaks using distributed computing resources—led NIST to initiate the Advanced Encryption Standard (AES) process in 1997, soliciting submissions for a successor with 128-, 192-, or 256-bit keys. Rijndael, submitted by Joan Daemen and , was selected as AES in 2000 after rigorous public competition and , with FIPS 197 published on November 26, 2001, establishing it as the symmetric standard for U.S. government systems. AES's adoption was bolstered by its efficiency in both hardware and software, supporting block sizes of 128 bits and resistance to known attacks at the time of selection. Complementary standards emerged for , such as FIPS 186 for digital signatures using RSA or DSA, and SP 800-56 for key establishment incorporating Diffie-Hellman. Adoption extended beyond government mandates into commercial and internet applications, driven by protocols integrating these primitives. (PGP), released in 1991 by , popularized for email using RSA and symmetric ciphers like IDEA, enabling civilian secure communication despite export restrictions on strong crypto. Netscape's Secure Sockets Layer (SSL) protocol, introduced in 1995, combined public-key handshakes (RSA or Diffie-Hellman) with symmetric (initially , later AES) to secure web transactions, evolving into Transport Layer Security (TLS) standardized by the IETF, which by the 2000s underpinned for widespread e-commerce and data protection. validation for cryptographic modules further promoted implementation reliability in federal and enterprise systems, with AES and RSA becoming de facto standards in VPNs, , and secure communications by the early 2010s.

Cryptographic Primitives and Algorithms

Symmetric-Key Algorithms

Symmetric-key algorithms, also termed secret-key algorithms, require the same cryptographic key for both encryption of and decryption of , enabling efficient bulk data protection when keys are managed securely and possess adequate length to withstand exhaustive search. These algorithms form the core of many secure systems due to their computational speed compared to asymmetric counterparts, but their strength hinges on resistance to differential and , as well as sufficient key to deter brute-force attacks estimated at 2^128 operations or more for modern hardware. Block ciphers dominate symmetric encryption in strong cryptography, processing data in fixed-size blocks—typically 128 bits—via substitution, , and key mixing over multiple rounds. The Advanced Encryption Standard (AES), formalized in FIPS 197 on November 26, 2001, exemplifies this category, adopting the Rijndael algorithm selected by NIST after a 1997 public competition evaluating resistance to known attacks. encrypts 128-bit blocks using keys of 128, 192, or 256 bits across 10, 12, or 14 rounds, respectively, with NIST affirming all variants suitable for U.S. government classified data protection due to their design margins against cryptanalytic advances as of certification. Secure block cipher usage demands modes of operation to handle variable-length data and provide additional properties like . Galois/Counter Mode (GCM), detailed in NIST SP 800-38D, combines counter mode for with Galois field multiplication for , yielding with associated data (AEAD) in a single pass, preferred over Cipher Block Chaining (CBC)—specified in SP 800-38A—which offers but no built-in and risks attacks without separate verification. GCM with AES-128 or AES-256 achieves 128-bit levels, balancing performance and for protocols like TLS. Stream ciphers, generating pseudorandom keystreams XORed with plaintext, suit real-time applications requiring low latency. ChaCha20, a 256-bit key stream cipher designed by Daniel J. Bernstein in 2008, resists timing attacks better than older RC4 and matches AES-256 security while excelling in software on mobile devices due to simple arithmetic operations over 32-bit words in 20 rounds. It pairs with Poly1305 for AEAD, as in RFC 7539, and is integrated into standards like TLS 1.3 for robust symmetric protection. Deprecated symmetric algorithms underscore evolution toward strength: the Data Encryption Standard (DES), with its 56-bit key, succumbed to brute-force by 1998 via distributed efforts exhausting 2^56 possibilities, while Triple DES (3DES)—applying DES thrice for nominal 168-bit keys—yields only ~112 bits effective security, vulnerable to attacks like Sweet32 (CVE-2016-2183) exploiting birthday collisions over 2^32 blocks. NIST deprecated 3DES in 2017, prohibiting new implementations post-2023 due to these limitations and superior alternatives like AES.

Public-Key Algorithms

Public-key algorithms, or asymmetric cryptographic algorithms, rely on mathematical pairs of keys—a publicly shareable key and a corresponding private key—to enable , digital signatures, and without prior shared secrets. The public key can encrypt data or verify signatures, while only the private key holder can decrypt or sign, providing and authenticity resistant to classical computing attacks when using sufficiently large parameters. Security derives from computationally hard problems, such as or discrete logarithms, with strength evaluated by resistance to known algorithms like the general number field sieve for . The Rivest–Shamir–Adleman (RSA) algorithm, introduced in 1977, bases its security on the difficulty of factoring the product of two large prime numbers. For strong cryptography, RSA requires at least 2048-bit keys for 112-bit security levels acceptable through 2030, with 3072-bit or larger recommended for extended protection against advances in factoring methods. RSA supports , decryption, and digital signatures, but its larger key sizes make it computationally intensive compared to alternatives. Elliptic curve cryptography (ECC) leverages the elliptic curve discrete logarithm problem, allowing equivalent security to RSA with much smaller keys—e.g., a 256-bit ECC key provides approximately 128-bit security, comparable to a 3072-bit RSA key. NIST-approved ECC variants include ECDSA for signatures and ECDH for key agreement, using standardized curves like NIST P-256 or , which resist known attacks through rigorous parameter selection and avoid vulnerable curves like those with anomalous properties. ECC's efficiency suits resource-constrained devices, though curve selection must avoid implementations susceptible to side-channel attacks. Diffie–Hellman (DH) key exchange, extended to elliptic curves as ECDH, enables secure shared secret generation over insecure channels by exploiting hardness. Finite-field DH with 2048-bit moduli or ECDH with 256-bit curves meets current strong security thresholds, but both classical RSA/ECC and DH are vulnerable to quantum attacks via , necessitating hybrid or post-quantum transitions. Post-quantum public-key algorithms, standardized by NIST to counter quantum threats, include module-lattice-based key encapsulation (ML-KEM, derived from ) in FIPS 203 for encryption/key exchange, module-lattice-based signatures (ML-DSA, from ) in FIPS 204, and hash-based signatures (SLH-DSA, from Sphincs+) in FIPS 205, finalized in August 2024. These provide at least 128-bit security against quantum adversaries using Grover's and Shor's algorithms, with additional code-based KEM HQC selected in March 2025 for standardization. Deployment emphasizes hybrid modes combining classical and post-quantum primitives during transition to mitigate risks from "" threats.

Hash Functions and Message Authentication

Cryptographic hash functions are mathematical algorithms that map data of arbitrary size to a fixed-length output, known as a hash value or digest, designed to be computationally infeasible to invert or find collisions under strong security assumptions. For strength in cryptography, these functions must exhibit preimage resistance (difficulty in finding an input producing a given output), second-preimage resistance (difficulty in finding a different input with the same output as a given input), and (difficulty in finding two distinct inputs with the same output), properties formalized in standards like NIST FIPS 180-4, which specifies algorithms such as the family including SHA-256. These properties ensure the hash serves as a reliable for , with providing approximately 128 bits of security for 256-bit outputs like SHA-256, meaning 2^128 operations are required for a success probability exceeding 50%. The SHA-2 family, standardized by NIST in 2002 and updated in FIPS 180-4 (2015), includes , which produces a 256-bit digest and remains unbroken against practical attacks as of 2025, with no known preimage or collision vulnerabilities exploitable by classical computing. , approved in FIPS 202 (2015), uses a construction for diversity against potential weaknesses in Merkle-Damgård designs like SHA-2, offering equivalent security levels while resisting length-extension attacks without keyed variants. NIST recommends and for new applications, deprecating due to practical collision attacks demonstrated in 2017, with full transition from SHA-1 required by December 31, 2030, for FIPS-validated modules. Weaknesses in older hashes like , broken for collisions since 2004, underscore the need for functions with provable margins against differential cryptanalysis, as SHA-256 withstands reduced-round attacks but remains secure in full rounds. Message authentication codes (MACs) leverage s to verify both and origin authenticity, typically by incorporating a secret key. The HMAC construction, defined in RFC 2104 (1997) and endorsed by NIST, applies a twice with inner and outer key padding: HMAC(K, m) = H((K ⊕ opad) || H((K ⊕ ipad) || m)), providing security reducible to the underlying hash's compression function strength. NIST SP 800-107 (2009, revised) guidelines affirm -SHA-256's resistance to key-recovery and forgery attacks when using approved hashes, recommending key lengths at least as long as the hash output (e.g., 256 bits) and warning against truncation below half the digest size to maintain full security. In practice, ensures existential unforgeability under chosen-message attacks, with empirical validation showing no breaks for -SHA-256 despite extensive analysis, making it integral to protocols like TLS 1.3 for secure data transmission. Alternatives like CMAC (for block ciphers) exist, but hash-based MACs predominate due to efficiency and broad hardware support.

Criteria for Cryptographic Strength

Resistance to Known Attacks

Resistance to known attacks constitutes a primary measure of cryptographic strength, requiring that algorithms remain secure against established cryptanalytic techniques under standard adversary models, such as chosen-plaintext or adaptive chosen-ciphertext scenarios, without practical key recovery or decryption feasible with current or near-future computational resources. This criterion demands extensive peer-reviewed analysis, including differential, linear, , and algebraic attacks, where the algorithm's design—such as sufficient rounds and diffusion properties—ensures attack complexities approach or exceed exhaustive key search. For symmetric ciphers, this typically translates to security margins where the best theoretical attacks on full-round implementations demand exponential resources, e.g., exceeding 2^{100} operations, far beyond brute-force alternatives. In practice, resistance is validated through open competitions and continuous scrutiny by the global cryptographic community, as exemplified by the NIST Advanced Encryption Standard (AES) selection process from 1997 to 2001, where candidate algorithms endured thousands of attack attempts without viable breaks on the full cipher. AES-128, for instance, resists differential cryptanalysis with probabilities bounded by 2^{-99} or lower due to its wide-trail strategy, and linear approximations are thwarted by non-linear S-boxes providing high nonlinearity (around 112 for 8-bit boxes). No practical full-round attacks exist in the single-key model; related-key boomerang attacks on AES-256 require 2^{99.5} time and specific key relations unlikely in real deployments, underscoring that deviations from standard models do not compromise core security. Similarly, hash functions like SHA-256 maintain collision resistance against differential paths, with the best attacks on reduced rounds (e.g., 42 rounds) still impractical at 2^{46} time, preserving full 128-bit security against known methods. Public-key algorithms achieve resistance via hard mathematical problems; for example, 2048-bit RSA withstands the general number field sieve (GNFS) factoring attack, estimated at 2^{112} operations as of hardware, with no superior general-purpose methods known. variants like secp256r1 resist Pollard's rho attack at 2^{128} complexity, verified through exhaustive searches for weak curves excluded during . However, this resistance presumes proper implementation; known attacks often exploit protocol flaws or side-channels rather than core primitives, emphasizing that algorithm strength alone does not guarantee system security. Ongoing evaluations, such as NIST's lightweight cryptography project, confirm candidates like SKINNY resist standard attacks like up to full rounds. Algorithms failing these tests, such as those vulnerable to practical differential distinguishers, are deprecated, reinforcing that true strength emerges from unbroken performance under adversarial scrutiny over time.

Key Length and Computational Security

Computational security in cryptography refers to the property that breaking a cryptosystem requires computational resources infeasible for any adversary with realistic constraints on time, cost, and hardware. Key length, expressed in bits, fundamentally determines resistance to brute-force attacks, which involve exhaustively searching the key space of size 2^k for a k-bit key, requiring an average of 2^{k-1} trials. This exponential growth ensures that sufficiently long keys render exhaustive search impractical, even assuming massive parallelism and optimized hardware. For instance, a 128-bit key demands on the order of 10^{38} operations, far exceeding the capabilities of global computing infrastructure, which might achieve 10^{18} to 10^{20} operations per second in aggregate supercomputing efforts. In symmetric cryptography, such as block ciphers, key length directly equates to the security level in bits against brute-force attacks, assuming no structural weaknesses. NIST recommends symmetric keys of at least 112 bits as minimally acceptable through 2030, but 128 bits or more— as in AES-128—provide robust 128-bit security suitable for protecting sensitive data against classical adversaries for decades. Longer keys, like AES-256's 256 bits, offer margins against potential advances in or parallelization, with brute-force efforts projected to remain infeasible even if computational power doubles every two years per historical trends. Deprecation of keys below 112 bits is advised by 2030 to align with rising threats. Asymmetric algorithms require disproportionately longer keys to achieve comparable security, as their hardness relies on problems like (RSA) or discrete logarithms (Diffie-Hellman), which admit sub-exponential but still computationally intensive attacks beyond pure brute force. A 2048-bit RSA modulus yields approximately 112 bits of security, deemed sufficient by NIST for most uses until at least 2030, but 3072 bits or more are needed for 128-bit equivalence. variants (ECC) are more efficient, with 256-bit keys providing 128-bit security due to the elliptic curve problem's resistance. These lengths ensure that the best-known classical attacks, including number field sieve variants, demand resources equivalent to brute-forcing a symmetric key of matching bit strength.
Cryptosystem TypeExample AlgorithmMinimum Key Length for 128-bit SecurityNotes on Brute-Force Resistance
SymmetricAES128 bitsDirect 2^{128} key space; infeasible classically.
RSARSA3072 bitsFactoring attack complexity calibrated to ~2^{128} effort.
ECCECDSA/ECDH256 bitsDiscrete log security matches symmetric levels efficiently.
Emerging quantum threats, via algorithms like Grover's, effectively halve symmetric (e.g., AES-128 to 64 bits), underscoring the need for 256-bit symmetric keys for post-quantum computational , though classical brute-force remains the baseline metric. Standards bodies like NIST emphasize that key length alone does not guarantee strength—algorithm design and must also withstand side-channel and analytical attacks—but it sets the irreducible computational barrier.

Implementation and Usage Best Practices

Implementing strong cryptography demands rigorous adherence to established standards to mitigate risks from flawed code, misconfigurations, or environmental exposures, as even robust algorithms can fail under poor . NIST Special Publication 800-57 emphasizes pre-implementation evaluation to ensure cryptographic techniques are correctly applied, warning that strong primitives may be undermined by inadequate software practices such as improper error handling or predictable . Developers should prioritize validated cryptographic modules compliant with , which certifies hardware and software for secure key operations, over custom implementations that risk introducing subtle vulnerabilities like buffer overflows or integer underflows. Key generation must employ cryptographically secure pseudorandom number generators (CSPRNGs) with high sources, such as those approved by NIST in SP 800-90A, to avoid predictability that could enable key recovery attacks observed in historical breaches like the 2010 vulnerability where reduced collapsed the key space. Keys should be generated at sufficient lengths—e.g., at least 256 bits for symmetric algorithms like AES—to provide computational security exceeding 2^128 operations against brute-force, with rotation policies limiting lifetime based on usage and threat models, as recommended in NIST SP 800-57 Part 1. Storage requires protection against unauthorized access, favoring hardware security modules (HSMs) for high-value keys or encrypted vaults with access controls, while avoiding hardcoded keys in , which OWASP identifies as a common vector for exposure in systems. Secure coding practices are essential to counter side-channel attacks, including timing discrepancies, , and ; implementations should use constant-time algorithms to prevent information leakage through execution variability, as demonstrated in the 2003 timing attack on RSA decryption. For protocols like TLS, enforce via ephemeral keys (e.g., ECDHE) and disable deprecated ciphersuites such as CBC modes without proper to avert padding oracle exploits like in 2014. Message authentication must integrate integrity checks using constructs like with SHA-256, avoiding homegrown MACs that fail under length-extension attacks inherent to plain hashes. Regular auditing, including code reviews, , and penetration testing, is critical to detect implementation flaws, with tools applied where feasible for high-assurance systems. Compliance with guidelines like those in CISA's practices ensures keys remain protected against modification and disclosure throughout their lifecycle, including secure destruction via overwriting or physical means to prevent forensic recovery. In resource-constrained environments, balance performance with security by selecting optimized yet vetted libraries like or Bouncy Castle, subjected to ongoing patches for discovered issues.

Examples of Strong Cryptography

Approved Algorithms (e.g., AES, SHA-256)

The Advanced Encryption Standard (AES), formalized in Federal Information Processing Standard (FIPS) PUB 197 in 2001, serves as the primary approved symmetric-key block cipher for encrypting electronic data in federal systems and beyond. AES, based on the Rijndael algorithm submitted by Joan Daemen and Vincent Rijmen, operates on 128-bit blocks with variable key sizes of 128, 192, or 256 bits, achieving corresponding security margins against exhaustive key search. It has withstood over two decades of cryptanalytic scrutiny without practical breaks, rendering it suitable for high-security applications like file encryption and secure communications, provided implementations avoid side-channel vulnerabilities. NIST continues to endorse AES without planned deprecation for symmetric encryption, even amid quantum computing advances, as Grover's algorithm reduces effective security by only a square root factor (e.g., 256-bit keys retain 128-bit post-quantum security). For hashing and message authentication, the , including SHA-256, remains approved under FIPS 180-4, offering fixed-length outputs resistant to preimage, second-preimage, and collision attacks. SHA-256 produces a 256-bit digest from inputs up to 2^64 - 1 bits, designed by the and published by NIST in 2002 as successors to . These functions underpin digital signatures, constructs, and integrity checks in protocols like TLS, with no known weaknesses compromising their core security when used with adequate input lengths; NIST recommends transitioning from SHA-1 entirely by 2030 but affirms SHA-2's longevity. Approved public-key algorithms include RSA and Elliptic Curve Cryptography (ECC) variants, as specified in FIPS 186-5 for digital signatures and key establishment. RSA, with moduli of at least 2048 bits (providing ~112-bit security), relies on the problem's hardness, while ECC (e.g., ECDSA or ECDH over NIST P-256 curves) achieves equivalent security with smaller 256-bit keys due to elliptic curve complexity. Both are validated for use in modules but face eventual quantum obsolescence via ; NIST mandates migration planning to post-quantum alternatives by 2030-2035 for vulnerable systems, yet they constitute strong cryptography against classical adversaries.
AlgorithmTypeStandardSecurity ParameterApproval Basis
AES-128/192/256Symmetric FIPS 197128/192/256-bit keysBrute-force resistance; no practical cryptanalytic breaks
SHA-256FIPS 180-4256-bit output >2^128 operations
RSA (2048-bit)Public-Key (Signatures/)FIPS 186-52048-bit modulusFactorization hardness
ECC (P-256)Public-Key (ECDSA/ECDH)FIPS 186-5256-bit curveDiscrete log hardness; efficient key sizes
These algorithms form the core of strong cryptography when paired with secure and , as validated through NIST's Cryptographic Algorithm Validation Program.

Secure Protocols and Systems

(TLS) version 1.3, specified in RFC 8446 published by the IETF in August 2018, exemplifies a secure protocol for application-layer communications such as . It enforces with associated data (AEAD) using ciphers like AES-256-GCM or , paired with elliptic curve Diffie-Hellman ephemeral (ECDHE) key exchanges to achieve perfect , ensuring that compromised long-term keys do not expose prior session data. TLS 1.3 removes insecure mechanisms from prior versions, including static RSA key transport, hashing, and support for weak cipher suites, thereby mitigating risks from attacks like Logjam and . NIST Special Publication 800-52 Revision 2, issued in August 2019, recommends TLS 1.3 for federal systems due to its enhanced privacy through early handshake encryption and resistance to downgrade attacks. IPsec, a suite of protocols for network-layer , secures IP packet exchanges in virtual private networks (VPNs) and site-to-site connections. As detailed in NIST Special Publication 800-77 Revision 1 from June 2020, IPsec employs the Encapsulating Payload (ESP) for and via AES in GCM mode, with optional Authentication Header (AH) for anti-replay protection using SHA-256. It supports version 2 (IKEv2) for and key establishment, often with , providing resilience against , modification, and replay attacks even in untrusted networks. Proper configuration avoids deprecated algorithms like 3DES, ensuring computational against brute-force efforts exceeding billions of years with current hardware. Secure Shell (SSH) version 2 facilitates encrypted remote command execution and file transfers, integrating with symmetric session . It mandates algorithms like Curve25519-sha256 or ECDH with SHA-256, followed by ciphers such as AES-256-GCTR and message via HMAC-SHA-256, as per IETF standards in RFC 4253. This design resists man-in-the-middle interception when host keys are verified, with NIST endorsing its use in secure remote access guidelines for avoiding weak Diffie-Hellman groups or CBC modes vulnerable to exploits. End-to-end encryption systems like the Signal Protocol, used in applications such as Signal and WhatsApp, extend strong cryptography to messaging. It employs the Extended Triple Diffie-Hellman (X3DH) for asynchronous key agreement with Curve25519, the Double Ratchet for per-message forward secrecy, and AES-256-GCM with HMAC-SHA-256 for payload protection, enabling deniability and post-compromise recovery without central key escrow. Audits confirm its robustness against known cryptanalytic attacks, though implementation flaws in client software remain a deployment risk.

Examples of Weak or Deprecated Cryptography

Vulnerable Algorithms (e.g., DES, MD5)

The Data Encryption Standard (DES), standardized by the National Bureau of Standards (now NIST) as FIPS PUB 46 in 1977, uses a symmetric block cipher with a 56-bit effective key length, processing 64-bit blocks. This key size yields approximately 7.2 × 10^16 possible keys, enabling brute-force attacks feasible with mid-1990s hardware; for instance, in 1997, a distributed effort under the RSA DES Challenges recovered keys in months using thousands of idle computers. By July 1998, the Electronic Frontier Foundation's specialized DES Cracker hardware, costing under $250,000, exhaustively searched the key space in 56 hours. A January 1999 collaboration between distributed.net and the EFF further reduced this to 22 hours and 15 minutes via parallel computing. NIST retired validation testing for DES in its Cryptographic Algorithm Validation Program, reflecting its obsolescence against modern computational power, where attacks now require seconds on contemporary hardware. MD5 (Message-Digest Algorithm 5), designed by Ronald Rivest and published in 1992 as RFC 1321, produces a 128-bit hash value and was intended for applications like digital signatures and integrity checks. Its vulnerability stems from structural flaws allowing collision attacks, where distinct inputs yield identical outputs; the first such collisions were constructed and published on August 17, 2004, by Xiaoyun Wang and colleagues, requiring about 2^39 operations—practical on 2000s-era clusters. By December 2008, chosen-prefix collisions, more dangerous for forging certificates, were demonstrated in under 2^39 MD5 compressions, enabling real-world exploits like rogue certificates. NIST's policy on hash functions explicitly discourages MD5 for security purposes, favoring variants due to these breaks eroding essential for cryptographic integrity. Other notable vulnerable algorithms include , a 160-bit hash from 1995, where full collisions were achieved in 2017 by Google's Project SHAttered team using custom hardware equivalent to 6,500 years of 2017 CPU time, prompting NIST's 2022 retirement announcement with a phase-out by December 31, 2030. , a from 1987, exhibits key-stream biases exploitable since 2001 analyses, leading to practical decryption attacks by 2013 and deprecation in protocols like TLS 1.2 per IETF guidance. These examples illustrate how aging designs fail under advancing and hardware, underscoring the need for algorithms resisting at least 2^128 operations for foreseeable security.

Historical Failures and Lessons

The , used by during , exemplified early cryptographic overconfidence in mechanical complexity without sufficient resistance to systematic . Polish cryptologists , Jerzy Różycki, and exploited fixed rotor wirings and daily key settings to reconstruct the machine's internals by 1932, enabling initial breaks. British efforts at , led by , further advanced machines that automated crib-based attacks, decoding millions of messages by 1945 despite operator errors like repeating phrases. This failure underscored the necessity of designs resistant to known-plaintext attacks and human procedural lapses, reinforcing Kerckhoffs' principle that security should rely on key secrecy alone, not algorithmic obscurity. The , adopted by NIST in 1977 with a 56-bit key, initially withstood theoretical scrutiny but proved computationally vulnerable as hardware advanced. In 1998, the Electronic Frontier Foundation's DES Cracker machine recovered a key in 56 hours using custom costing $250,000, demonstrating brute-force feasibility against mid-1990s technology. This prompted the AES competition, culminating in Rijndael's selection in 2001, and highlighted the critical need for key lengths providing margins against exponential compute growth, ideally exceeding 128 bits for symmetric ciphers. Designers must anticipate Moore's Law-like scaling, as DES's effective 56-bit security fell to adversaries within two decades. Hash function MD5, published by Ronald Rivest in 1991, suffered a practical in 2004 by Xiaoyun Wang and colleagues, who generated differing inputs yielding identical 128-bit outputs in hours using differential cryptanalysis. This enabled attacks like forged certificates in 2008, eroding trust in MD5 for digital signatures and integrity checks. The incident illustrated that hash algorithms require provable under foreseeable advances; MD5's design flaws, including weak compression, necessitated deprecation in favor of SHA-256, emphasizing proactive retirement of functions showing partial breaks. Dual_EC_DRBG, standardized by NIST in 2006 as an , contained a suspected backdoor via non-random curve points P and Q, allegedly influenced by the NSA. Edward Snowden's leaks revealed NSA payments to RSA for prioritizing it in products, allowing efficient prediction of outputs if the was known, compromising downstream encryption. NIST withdrew it in , teaching that government-influenced standards demand independent verification of parameters and preference for transparent, community-vetted alternatives like Hash_DRBG to mitigate hidden weaknesses. U.S. export controls in the classified strong cryptography as munitions, mandating weakened 40-bit keys for international versions, which were routinely cracked—e.g., Netscape's export-grade SSL in days by university teams. This policy stifled global adoption of robust systems, benefiting foreign adversaries who faced no such limits, and contributed to breaches until liberalization in 2000. Similarly, the 1993 initiative proposed Skipjack encryption with escrowed keys split between users and government, but exposed flaws like a 1994 key-recovery and public rejection over privacy risks led to its abandonment by 1996. These underscore that regulatory mandates for backdoors or weakened exports undermine security incentives, fostering distrust and suboptimal implementations. Collectively, these failures reveal causal pitfalls in strong cryptography: insufficient margins against compute escalation, reliance on over open , to institutional influence, and policy distortions prioritizing access over resilience. Empirical evidence demands algorithms vetted through adversarial , with implementations audited for side-channels, and policies enabling widespread strong crypto deployment without compromise.

Export Controls and Historical Restrictions

The United States classified strong cryptographic technologies as munitions under the Arms Export Control Act and International Traffic in Arms Regulations (ITAR), administered by the Department of State, subjecting exports to rigorous licensing from the 1970s onward, with roots in earlier Cold War-era controls via the Coordinating Committee on Multilateral Export Controls (CoCom), which restricted dual-use items to NATO allies and like-minded nations. This framework intensified in the 1990s amid the rise of public-key cryptography, limiting commercial exports to weak variants like 40-bit keys while requiring case-by-case approvals for stronger systems, driven by national security concerns over potential use by adversaries or terrorists. A prominent case involved Phil Zimmermann's 1991 release of Pretty Good Privacy (PGP), an open-source tool using 1024-bit RSA keys; its online availability was deemed an unauthorized export, prompting a federal grand jury investigation from 1993 to 1996, which ended without indictment after public and industry backlash highlighted the policy's overreach. Policy began liberalizing in 1996 when President Clinton's Executive Order 13026 allowed exports of 56-bit (DES) to most countries, responding to technology sector arguments that restrictions disadvantaged U.S. firms against unrestricted foreign competitors like RSA Laboratories' international operations. Further easing occurred in 1998–1999, permitting retail sales of stronger products after review periods, culminating on January 14, 2000, when the Bureau of Export Administration transferred commercial encryption from ITAR's U.S. Munitions List to the less stringent () under the Department of Commerce, enabling license exceptions for many items below specified key lengths (e.g., 56 bits symmetric, 1024 bits asymmetric) to non-prohibited destinations. These shifts reflected recognition that source code publication and overseas development rendered controls ineffective for preventing strong cryptography's global diffusion, though mass-market exemptions still mandated self-classification and reporting. Internationally, historical restrictions aligned with multilateral regimes, including CoCom's 1949–1994 oversight of cryptographic hardware and software as dual-use, succeeded by the 1996 —a voluntary pact among 42 states to control Category 5 ( and ) items, including unlimited-strength "non-designed for" commercial crypto but requiring notifications for high-performance systems. aimed to curb destabilizing accumulations without outright bans, influencing national implementations like the European Union's dual-use regulations, though U.S. in the 1990s often exceeded these baselines, prompting allied divergences and economic critiques. Post-2000, controls persist under updates, focusing on "cryptographic equipment" with exceptions for published source code, but embargoed nations (e.g., , ) face ongoing prohibitions.

Debates on Government Access and Backdoors

The debate over government access to strongly encrypted data centers on the tension between enabling investigations and preserving the integrity of cryptographic systems designed to protect against unauthorized intrusion. Proponents, including U.S. agencies, argue that hinders access to evidence in criminal and cases, creating a "going dark" problem where vital communications become inaccessible despite valid warrants. The FBI maintains that it supports "responsibly managed encryption" allowing decryption for lawful purposes, without mandating universal backdoors, to balance privacy with needs such as preventing attacks. Critics, including cryptographers and technology firms, counter that any mandated access mechanism inherently weakens encryption by introducing exploitable vulnerabilities, as no implementation can guarantee exclusivity to authorized entities. Historical efforts to impose government access illustrate the challenges and failures of such policies. In 1993, the U.S. government proposed the , an NSA-developed encryption device with a "law enforcement access field" enabling decryption via escrowed keys held by federal agencies, intended for voluntary use in secure communications. The initiative faced widespread opposition from advocates and industry, who demonstrated key recovery flaws and argued it would stifle innovation and export markets; it was abandoned by 1996 after public demonstrations of vulnerabilities and legal challenges. Revelations from in 2013 further eroded trust, exposing NSA efforts to undermine commercial encryption standards like those in NIST algorithms, prompting companies such as Apple and to adopt default and fueling global policy backlash against backdoor mandates. A prominent modern case arose in 2016 following the San Bernardino shooting, where the FBI sought a compelling Apple to create software bypassing the passcode on an used by one perpetrator, arguing it was necessary to access potential evidence. Apple refused, contending that such a tool would set a undermining device for all users and violate engineering principles by requiring disablement of security features like after failed attempts. The dispute ended when the FBI accessed the device via a third-party exploit from an undisclosed vendor, avoiding resolution on the broader legal question but highlighting technical alternatives to compelled backdoors. From a technical standpoint, cryptographers emphasize that strong encryption's derives from mathematical indistinguishability of from random data without the key; inserting access points, whether via or exceptional access, reduces effective key strength and invites attacks, as adversaries could reverse-engineer or compromise the mechanism. supports this: past proposals like suffered from implementation flaws, and simulations show that even "secure" backdoors increase systemic risk, as seen in vulnerabilities exploited in weakened protocols. advocates respond that targeted access, limited by warrants and oversight, enhances by enabling prevention of threats like child exploitation or , without broadly compromising algorithms. However, no peer-reviewed framework has demonstrated a backdoor resistant to or leakage, and international examples, such as Crypto AG's secret NSA/CIA backdoor compromising allies' communications for decades, underscore risks to diplomatic and . As of 2025, U.S. policy has not enacted broad backdoor requirements, with FBI Director Christopher Wray reiterating calls for lawful access tools amid rising encrypted device encounters in investigations—over 7,000 in 2023 alone—while legislative efforts like the Lawful Access to Encrypted Data Act remain stalled due to industry opposition. The consensus among security experts is that mandating access erodes trust in digital infrastructure, potentially benefiting state actors like or who already deploy their own tools, rather than democratic . This ongoing contention reflects causal trade-offs: while access aids specific probes, it predictably amplifies vulnerabilities in an era where nation-state threats exploit any weakness.

International Policy Variations

Policies on strong cryptography exhibit significant international variations, driven by differing priorities between , capabilities, and economic innovation. In liberal democracies, strong is often promoted as essential for and cybersecurity, though tempered by law enforcement demands, whereas authoritarian states impose stringent controls to ensure state oversight, including mandatory approvals and state-vetted algorithms. These divergences stem from multilateral frameworks like the , which harmonizes export controls among 42 participating states but allows domestic policy flexibility, leading to inconsistent implementation. In the , strong encryption is endorsed as a cornerstone of data protection under the General Data Protection Regulation (GDPR), which mandates robust safeguards for , implicitly favoring algorithms like AES-256. However, ongoing debates reflect tensions, with the European Commission's 2025 roadmap for lawful access to data proposing enhanced tools without explicit backdoors, while proposals like the Child Sexual Abuse Regulation (Chat Control) have raised concerns over client-side scanning of encrypted communications, potentially undermining in messaging apps. The EU's 2024 Europol report on encryption emphasizes "security through encryption" alongside "security despite encryption," advocating technical solutions for access rather than weakening standards. China's approach contrasts sharply, prioritizing state control through the Cryptography Law effective January 1, 2020, which categorizes encryption into "core" (for national security, using state-approved algorithms like SM2 and SM4) and "commercial" varieties, the latter requiring licensing from the State Cryptography Administration for production, sale, import, and export. Commercial encryption must undergo security assessments, and foreign products face barriers unless compliant with domestic standards, reflecting a policy blending commercial development with political oversight to prevent unmonitored communications. As of 2025, China has advanced indigenous post-quantum standards, bypassing Western-led efforts. Russia mandates regulatory clearance for the import, export, and domestic use of -based products under Federal Law No. 152-FZ and related decrees, requiring operators to notify the and obtain approvals for strong cryptographic means, with exemptions for certain low-risk items but prohibitions on unlicensed strong in . This framework, updated as of 2023, enables FSB access to keys in some cases, aligning with priorities amid geopolitical tensions. India imposes restrictions via Section 84A of the (amended 2021), empowering the government to prescribe standards and methods, effectively limiting bulk deployment by service providers without approval and regulating VPNs to prevent . The 2021 Intermediary Guidelines further enable of messages for serious crimes, signaling a tilt toward over unrestricted strong cryptography, though no outright ban on algorithms like AES exists.
Country/RegionKey Policy FeaturesStrength of Restrictions
GDPR-mandated strong ; proposals for LE access without weakening standardsMinimal to moderate
State-approved core/commercial categories; licensing for import/export/useSignificant
FSB approval for imports/uses; key access provisionsSignificant
Govt-prescribed standards; traceability mandatesWidespread

Controversies and Societal Impacts

Privacy Rights vs. Law Enforcement Needs

The debate over strong cryptography pits individual privacy rights against law enforcement's capacity to investigate crimes and threats, with proponents of robust encryption arguing it safeguards against unauthorized surveillance and data breaches, while authorities contend it enables criminals to evade detection. End-to-end encryption, as implemented in systems like Signal and Apple's iMessage, renders communications inaccessible even to service providers, aligning with privacy protections under frameworks such as the Fourth Amendment in the U.S., which requires warrants for searches but does not compel weakening of security features. Law enforcement agencies, including the FBI, have invoked the "going dark" phenomenon—coined in a 2014 speech by then-Director James Comey—to describe barriers to accessing encrypted data, citing instances where such tools allegedly impeded probes into terrorism and child exploitation. However, empirical analyses have revealed overstatements in these claims; for example, a 2018 DOJ Inspector General review found the FBI inflated "going dark" case counts by including non-encryption-related phone locks, with actual encryption-denied accesses comprising only about 7.4% of attempted unlocks in fiscal year 2017, not the higher figures initially reported. A pivotal case illustrating this tension occurred in 2016 following the December 2, 2015, San Bernardino shooting, where attackers Syed Farook and Tashfeen Malik killed 14 people; the FBI sought a compelling Apple to create software bypassing the 5C's passcode protections and disable security features like auto-erase after 10 failed attempts. Apple CEO refused in a public letter, warning that such a "backdoor" would undermine device security for all users by introducing exploitable vulnerabilities, potentially accessible to hackers or foreign adversaries, and set a eroding trust in encrypted products. The dispute, rooted in the of 1789, was rendered moot when the FBI accessed the device via a third-party tool from an undisclosed vendor (later identified as involving techniques similar to those from firms like ), yielding minimal evidentiary value. This episode highlighted causal risks of mandated access: engineering deliberate weaknesses in cryptographic systems, such as or exceptional access mechanisms, inevitably expands attack surfaces, as no implementation can guarantee exclusivity to authorized entities—evidenced by historical failures like the 1990s initiative, abandoned due to demonstrated flaws and export concerns. Critics of law enforcement demands emphasize that alternatives like forensic tools (e.g., GrayKey or Magnet Forensics) already enable access to many encrypted devices without systemic backdoors, with reports indicating U.S. agencies successfully unlocked over 90% of targeted iOS and Android devices in recent years through commercial vendors or user errors like weak passcodes. Proponents of privacy, including organizations like the Electronic Frontier Foundation, argue from first-principles that encryption's mathematical strength—rooted in algorithms like AES-256—provides indiscriminate protection, benefiting dissidents in authoritarian regimes as much as criminals, and that weakening it for exceptional cases invites broader exploitation, as seen in vulnerabilities like the 2016 Juniper Networks backdoor tied to alleged state actors. Conversely, agencies assert that unbreachable encryption shields serious offenders, with FBI data from 2021 operations like the ANOM sting—where a deliberately flawed encrypted phone network infiltrated over 300 syndicates—demonstrating targeted weaknesses can yield investigative gains, though such operations require substantial resources and do not scale to general policy. Empirical trade-offs reveal no zero-sum resolution: while privacy erosion risks mass surveillance creep, as critiqued in National Academies analyses, overreliance on decryption mandates could stifle innovation in secure systems essential for economic and national security.

Economic and National Security Implications

Strong cryptography underpins the security of digital economies by safeguarding financial transactions, , and consumer data against unauthorized access, thereby reducing the economic fallout from cyber incidents. According to the Cost of a Report for 2025, organizations employing mitigate breach costs by an average of over $200,000 per incident compared to those without it, as limits the usability of stolen data for attackers. The U.S. National Institute of Standards and Technology (NIST) estimates that the (AES), a cornerstone of strong cryptography, has delivered at least $250 billion in economic benefits to the U.S. economy since its adoption in 2001, primarily through enhanced trust in secure communications and . Globally, damages—often exacerbated by weak or absent —are projected to reach $10.5 trillion annually by 2025, underscoring how robust prevents losses from data theft and by rendering compromised information indecipherable. Mandating weakened encryption or backdoors, conversely, would erode economic productivity by diminishing trust in digital systems, leading to higher compliance costs and reduced investment in innovation. A 2021 analysis by the projects that laws undermining could depress in the , forcing firms to allocate additional resources to alternative security measures and potentially stifling sectors like and . For small- and medium-sized enterprises, which comprise a significant portion of economic activity, such policies risk amplifying breach vulnerabilities, as evidenced by modeling in a report indicating substantial compliance burdens and lost revenue from eroded customer confidence. Empirical data from historical weak standards, such as the deprecated (DES), further illustrate that inadequate cryptography correlates with elevated vulnerability to economic , contrasting with the protective role of strong alternatives. From a national security standpoint, strong cryptography fortifies defenses against foreign adversaries by protecting military communications, critical infrastructure, and intelligence data from state-sponsored hacking. End-to-end encryption has proven essential in countering threats from actors like China and Russia, enabling secure data flows that underpin U.S. technological superiority and alliances, as argued in analyses emphasizing its role in shielding against digital repression and espionage. Weakening encryption, however, invites exploitation by these same adversaries, who could leverage backdoors intended for domestic law enforcement, thereby compromising broader national defenses—a risk highlighted in reports warning that such measures threaten America's edge in cybersecurity. While critics, including some law enforcement voices, contend that unbreakable encryption impedes counter-terrorism efforts, evidence suggests alternative investigative tools like metadata analysis and human intelligence suffice for most cases, without the systemic vulnerabilities introduced by deliberate flaws. Thus, prioritizing strong cryptography aligns with causal realities of asymmetric threats, where protection against advanced persistent threats outweighs selective access demands.

Criticisms of Regulatory Overreach

Critics argue that regulatory efforts to mandate access mechanisms in strong cryptographic systems, such as or backdoors, fundamentally compromise the mathematical integrity of , creating exploitable vulnerabilities that adversaries can leverage more readily than can control. Technologists emphasize that no backdoor can be engineered to distinguish between authorized use and unauthorized access by criminals or foreign , as evidenced by inherent design flaws in proposed systems where a single weakness propagates system-wide risks. Such mandates, proponents of strong cryptography contend, prioritize short-term investigative access over long-term , ignoring first-principles of where relies on the impossibility of efficient key recovery without exhaustive search. The U.S. initiative of 1993 exemplifies regulatory overreach, as the Agency's proposal required hardware-based for voice , allowing government decryption via split keys held by agents. Despite initial executive endorsement, the program faced immediate backlash for its technical vulnerabilities—a 1994 flaw exposed the 80-bit unit key via side-channel analysis—and for burdening manufacturers with uncompetitive compliance, leading to zero commercial adoption by 1996. Critics, including industry groups and the , highlighted how the chip's failure demonstrated that coerced weakening of standards erodes public trust and stifles innovation, as users rejected escrowed systems in favor of open, uncompromised alternatives like software. In the 2016 Apple-FBI dispute over an from the San Bernardino attack, a federal magistrate ordered Apple to develop disabling passcode limits and safeguards, which CEO decried as creating a "master key" potentially applicable to millions of devices and undermining global user confidence in U.S. technology. Apple's refusal, upheld when the FBI accessed the device via a third-party exploit on March 28, 2016, underscored criticisms that such orders exceed judicial authority under the and set precedents for eroding , with security experts warning of cascading effects on Secure Enclave protections. Export controls on strong cryptography, relaxed only in 2000 after years of restriction under the and U.S. munitions list classifications, inflicted measurable economic harm on the software sector, with a 1998 U.S. Department of Commerce assessment estimating losses of up to $5 billion in annual exports and thousands of jobs due to foreign competitors offering unrestricted alternatives. These controls treated as a , compelling firms like to deploy weakened 40-bit keys abroad, which were trivially broken—demonstrating via 1995 that reduced key lengths invite brute-force attacks—while failing to curb proliferation of strong foreign crypto like RSAREF. Post-relaxation analyses confirm that liberalization boosted U.S. market share without commensurate security risks, validating arguments that overregulation hampers competitiveness against non-compliant actors. Ongoing proposals for "lawful access" in jurisdictions like the and draw similar rebukes for ignoring that backdoors amplify risks from state actors and cybercriminals, as seen in the 2015-2016 Yahoo scanner mandate yielding data to Russian FSB. Libertarian-leaning analyses further contend that such overreach disproportionately burdens democratic societies reliant on strong crypto for and , while adversaries like advance their own uncompromised systems, tilting global tech leadership. Overall, detractors maintain that regulatory pursuits of universal access defy causal realities of decentralized threat landscapes, where compliant entities weaken themselves against non-compliant foes.

Recent Developments and Future Challenges

Post-Quantum Cryptography Initiatives

The National Institute of Standards and Technology (NIST) launched its (PQC) standardization process in December 2016, soliciting proposals for quantum-resistant public-key algorithms to replace vulnerable standards like RSA and . The initiative progressed through multiple evaluation rounds, with 82 initial submissions narrowed down; by July 2022, NIST advanced four algorithms—CRYSTALS- for key encapsulation, CRYSTALS- and for digital signatures, and SPHINCS+ for hash-based signatures—to final standardization. On August 13, 2024, NIST published the first three (FIPS): FIPS 203 specifying ML-DSA (derived from ) for signatures, FIPS 204 specifying ML-KEM (from ) for key encapsulation, and FIPS 205 specifying SLH-DSA (from SPHINCS+) for signatures. In March 2025, NIST selected Hamming Quasi-Cyclic (HQC) as an additional key-encapsulation mechanism to provide diversity against potential lattice-based weaknesses, with ongoing work toward its standardization. NIST's migration roadmap urges immediate inventorying of cryptographic assets and hybrid implementations, deprecating algorithms with security below 112 bits by 2030 and mandating full PQC adoption for new systems by 2035 to mitigate "" risks from quantum advances. Complementing NIST, U.S. agencies have initiated coordinated efforts: the (CISA) established a PQC Initiative in 2022 to guide federal and transitions through interagency collaboration and risk assessments. The (NSA) endorses NIST standards while emphasizing quantum-resistant transitions in its Commercial Algorithm Suite 2.0, updated in 2022 to include PQC candidates. In May 2025, federal procurement policies began requiring PQC considerations for protecting sensitive data against quantum threats. Internationally, the has pursued harmonized PQC adoption, with a 2025 recommendation directing member states to transition to quantum-resistant encryption by 2030, aligning with NIST standards while exploring hybrids via the EuroQCI initiative. The collaborates with the U.S. on accelerated PQC migration to ensure , as outlined in joint policy briefs emphasizing empirical testing of algorithm performance. China's State Cryptography Administration has developed indigenous PQC proposals, including lattice-based schemes tested in national standards since 2020, though details remain limited to state publications prioritizing domestic quantum networks. These efforts underscore a global push for crypto-agility, with organizations like ETSI evaluating NIST-selected algorithms for broader telecommunications standards.

Quantum Computing Threats

Quantum computers pose a fundamental threat to asymmetric cryptographic systems, such as RSA and (ECC), primarily through , which efficiently solves and problems intractable for classical computers. Developed by in 1994, the algorithm leverages and entanglement to factor large numbers in polynomial time, potentially rendering current public-key infrastructures vulnerable to key recovery attacks. This capability endangers protocols reliant on these primitives, including secure key exchange in TLS/SSL, digital signatures, and certificate authorities. Symmetric ciphers like AES face a lesser but non-negligible risk from , introduced in 1996, which provides a quadratic speedup for unstructured search problems, effectively reducing the security level of an n-bit key to n/2 bits against brute-force attacks. For instance, AES-256 would offer only 128-bit security in a quantum setting, necessitating larger keys or alternatives for sustained protection. However, symmetric systems remain more resilient overall, as the exponential scaling of classical security is not fully overturned. As of 2025, no quantum computer can break cryptographically relevant keys; demonstrations have factored only small integers, such as 48-bit or 50-bit RSA moduli using experimental systems with tens of qubits. Recent analyses estimate that cracking RSA-2048 would require approximately one million logical qubits, with optimizations potentially enabling this by 2030 if scaling trends persist, though error-corrected qubits remain scarce. Claims of breakthroughs, such as those from Chinese researchers, involve trivial key sizes and do not approach operational threats. The primary near-term concern is "" attacks, where adversaries collect encrypted data today—such as long-lived secrets in or financial records—for future quantum decryption, amplifying risks to data with extended confidentiality needs. U.S. agencies, including the NSA via Commercial National Security Algorithm Suite 2.0 (2022) and Memorandum 10 (2022), classify this as a strategic , urging migration to quantum-resistant algorithms despite the threat's timeline extending decades. Independent assessments, like those from , affirm quantum as a long-term warranting proactive preparation rather than immediate .

Crypto-Agility and Migration Strategies

Cryptographic agility, also known as crypto-agility, refers to the capability of systems, protocols, applications, software, hardware, and embedded components to efficiently replace or adapt cryptographic algorithms and parameters in response to emerging vulnerabilities or evolving standards, without requiring extensive redesign or redeployment. This property is essential for maintaining security in dynamic threat landscapes, such as the anticipated advent of cryptographically relevant quantum computers capable of breaking widely used public-key algorithms like RSA and (ECC). NIST emphasizes that crypto-agility mitigates risks from algorithm weaknesses discovered post-deployment, enabling timely transitions to stronger primitives, as demonstrated by historical shifts from to SHA-256 in response to collision vulnerabilities identified in 2004. Achieving crypto-agility involves architectural principles such as modular design with abstraction layers that decouple cryptographic operations from application logic, allowing algorithm swaps via configuration changes or software updates. NIST's Cybersecurity White Paper 39 outlines considerations including the use of standardized interfaces (e.g., or protocol-level extensibility in TLS), dynamic systems, and automated inventory tools to track algorithm usage across enterprises. For instance, hybrid cryptographic schemes combining classical and post-quantum algorithms—such as pairing (now ML-KEM) with ECDH in TLS handshakes—facilitate gradual migration while preserving compatibility, as standardized by NIST in August 2024 for initial post-quantum algorithms including ML-KEM, ML-DSA, and SLH-DSA. Migration strategies prioritize comprehensive crypto inventories to identify vulnerable assets, followed by phased implementation: assessing risk based on data sensitivity and exposure timelines (e.g., prioritizing long-lived keys in certificates valid for years), prototyping hybrid modes, and deploying monitoring for impacts, which can increase signature sizes by factors of 10-20 for lattice-based schemes like . The Coalition's 2025 roadmap recommends organizational alignment through governance frameworks, including stakeholder mapping and metrics for agility maturity, such as the proportion of systems supporting algorithm parameter negotiation. Automated tools for discovery and inventory, as outlined in CISA's September 2024 strategy, enable scalable transitions by detecting non-compliant in legacy environments, reducing manual burdens that historically delayed responses to threats like the 2013 SHAMOW breakthrough against SHA-1. Challenges in migration include issues with non- endpoints, computational overhead from larger post-quantum keys (e.g., ML-KEM-768 public keys at 1,184 bytes versus 32 bytes for X25519), and dependencies on hardware supporting new instructions, as seen in limited initial adoption of ARM's Crypto Extensions for PQC. Best practices advocate for forward-thinking protocol designs, like those in the IETF's TLS 1.3 extensions for post-quantum , and regular agility assessments to avoid "crypto-lock-in" from embedded, non-updatable . Organizations like AWS have outlined multi-year plans involving service-by-service audits and hybrid rollouts, targeting full PQC readiness by 2030 to counter "" attacks where adversaries store encrypted data for future quantum decryption.

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