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awesome-crypto-papers

A curated list of cryptography papers, articles, tutorials and howtos.
https://github.com/pFarb/awesome-crypto-papers

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      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • FIPS 198-1: HMACs - The Keyed-Hash Message Authentication Code FIPS document.
      • FIPS 202: SHA3 - SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions.
      • Birthday problem - The best simple explanation of math behind [birthday attack](https://en.wikipedia.org/wiki/Birthday_attack).
      • On the Security of HMAC and NMAC Based on HAVAL, MD4, MD5, SHA-0 and SHA-1 - Security analysis of different legacy HMAC schemes by Jongsung Kim et al.
      • On the Security of Randomized CBC-MAC Beyond the Birthday Paradox Limit - Security of randomized CBC-MACs and a new construction that resists birthday paradox attacks and provably reaches full security, by E. Jaulmes et al.
      • FIPS 197 - AES FIPS document.
      • List of proposed operation modes of AES - Maintained by NIST.
      • Recomendation for Block Cipher modes of operation: Methods and Techniques
      • Stick figure guide to AES - If stuff above was a bit hard or you're looking for a good laugh.
      • Cache timing attacks on AES - Example of designing great practical attack on cipher implementation, by Daniel J. Bernstein.
      • Cache Attacks and Countermeasures: the Case of AES - Side channel attacks on AES, another view, by Dag Arne Osvik, Adi Shamir and Eran Tromer.
      • Salsa20 family of stream ciphers - Broad explanation of Salsa20 security cipher by Daniel J. Bernstein.
      • New Features of Latin Dances: Analysis of Salsa, ChaCha, and Rumba - Analysis of Salsa20 family of ciphers, by Jean-Philippe Aumasson et al.
      • ChaCha20-Poly1305 Cipher Suites for Transport Layer Security (TLS) - IETF Draft of ciphersuite family, by Adam Langley et al.
      • AES submission document on Rijndael - Original Rijndael proposal by Joan Daemen and Vincent Rijmen.
      • Ongoing Research Areas in Symmetric Cryptography - Overview of ongoing research in secret key crypto and hashes by ECRYPT Network of Excellence in Cryptology.
      • The Galois/Counter Mode of Operation (GCM) - Original paper introducing GCM, by by David A. McGrew and John Viega.
      • The Security and Performance of the Galois/Counter Mode (GCM) of Operation - Design, analysis and security of GCM, and, more specifically, AES GCM mode, by David A. McGrew and John Viega.
      • GCM Security Bounds Reconsidered - An analysis and algorithm for nonce generation for AES GCM with higher counter-collision probability, by Yuichi Niwa, Keisuke Ohashi, Kazuhiko Minematsu, Tetsu Iwata.
      • Proxy-Mediated Searchable Encryption in SQL Databases Using Blind Indexes - An overview of existing searchable encryption schemes, and analysis of scheme built on AES-GCM, blind index and bloom filter by Eugene Pilyankevich, Dmytro Kornieiev, Artem Storozhuk.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Differential Cryptanalysis of Salsa20/8 - A great example of stream cipher cryptanalysis, by Yukiyasu Tsunoo et al.
      • Slide Attacks on a Class of Hash Functions - Applying slide attacks (typical cryptanalysis technique for block ciphers) to hash functions, M. Gorski et al.
      • Self-Study Course in Block Cipher Cryptanalysis - Attempt to organize the existing literature of block-cipher cryptanalysis in a way that students can use to learn cryptanalytic techniques and ways to break new algorithms, by Bruce Schneier.
      • Statistical Cryptanalysis of Block Ciphers - By Pascal Junod.
      • Cryptanalysis of block ciphers and protocols - By Elad Pinhas Barkan.
      • Too much crypto - Analysis of number of rounds for symmetric cryptography primitives, and suggestions to do fewer rounds, by Jean-Philippe Aumasson.
      • How to Break MD5 and Other Hash Functions - A 2005 paper about modular differential collision attack on MD5, MD4 and other hash functions, by Xiaoyun Wang and Hongbo Yu.
      • New attacks on Keccak-224 and Keccak-256 - A 2012 paper about using the combination of differential and algebraic techniques for collision attacks on SHA-3, by Itai Dinur, Orr Dunkelman, Adi Shamir.
      • A Single-Key Attack on the Full GOST Block Cipher - An attack ("Reflection-Meet-inthe-Middle Attack") on GOST block cipher that allows to recover key with 2^225 computations and 2^32 known plaintexts, by Takanori Isobe.
      • Intro to Linear & Differential Cryptanalysis - A beginner-friendly paper explaining and demonstrating techniques for linear and differential cryptanalysis.
      • MEGA: Malleable Encryption Goes Awry - Proof-of-concept versions of attacks on MEGA data storage. Showcasing their practicality and exploitability. [Official webpage](https://mega-awry.io/).
      • New Directions in Cryptography - Seminal paper by Diffie and Hellman, introducing public key cryptography and key exchange/agreement protocol.
      • RFC 2631: Diffie-Hellman Key Agreement - An explanation of the Diffie-Hellman methon in more engineering terms.
      • A Method for Obtaining Digital Signatures and Public-Key Cryptosystems - Original paper introducing RSA algorithm.
      • RSA Algorithm - Rather education explanation of every bit behind RSA.
      • How to Share a Secret - A safe method for sharing secrets.
      • Twenty Years of Attacks on the RSA Cryptosystem - Great inquiry into attacking RSA and it's internals, by Dan Boneh.
      • Remote timing attacks are practical - An example in attacking practical crypto implementationby D. Boneh, D. Brumley.
      • The Equivalence Between the DHP and DLP for Elliptic Curves Used in Practical Applications, Revisited - by K. Bentahar.
      • SoK: Password-Authenticated Key Exchange – Theory, Practice, Standardization and Real-World Lessons - History and classification of the PAKE algorithms.
      • RSA, DH and DSA in the Wild - Collection of implementation mistakes which lead to exploits of assymetric cryptography.
      • Elliptic Curve cryptography: A gentle introduction
      • Explain me like I'm 5: How digital signatures actually work - EdDSA explained with ease and elegance.
      • Elliptic Curve Cryptography: finite fields and discrete logarithms
      • Detailed Elliptic Curve cryptography tutorial
      • Elliptic Curve Cryptography: ECDH and ECDSA
      • Elliptic Curve Cryptography: breaking security and a comparison with RSA
      • Elliptic Curve Cryptography: the serpentine course of a paradigm shift - Historic inquiry into development of ECC and it's adoption.
      • Let's construct an elliptic curve: Introducing Crackpot2065 - Fine example of building up ECC from scratch.
      • Explicit-Formulas Database - For many elliptic curve representation forms.
      • Curve25519: new Diffie-Hellman speed records - Paper on Curve25519.
      • Software implementation of the NIST elliptic curves over prime fields - Pracitcal example of implementing elliptic curve crypto, by M. Brown et al.
      • High-speed high-security signatures - Seminal paper on EdDSA signatures on ed25519 curve by Daniel J. Bernstein et al.
      • Recommendations for Discrete Logarithm-Based Cryptography: Elliptic Curve Domain Parameters (NIST SP 800-186) - Official NIST guide how securely implement elliptic curves. It also includes math shortcuts, optimizations and possible security risk of wrong algorithm implementation. [(February 2023)](https://csrc.nist.gov/pubs/sp/800/186/final)
      • Biased Nonce Sense: Lattice Attacks against Weak ECDSA Signatures in Cryptocurrencies - Computing private keys by analyzing and exploiting biases in ECDSA nonces.
      • Minerva: The curse of ECDSA nonces - Exploiting timing/bit-length leaks for recovering private keys from ECDSA signatures
      • LadderLeak: Breaking ECDSA With Less Than One Bit Of Nonce Leakage - Breaking 160-bit curve ECDSA using less than one bit leakage.
      • Proofs of knowledge - A pair of papers which investigate the notions of proof of knowledge and proof of computational ability, M. Bellare and O. Goldreich.
      • How to construct zero-knowledge proof systems for NP - Classic paper by Goldreich, Micali and Wigderson.
      • Proofs that yield nothing but their validity and a Methodology of Cryptographic protocol design - By Goldreich, Micali and Wigderson, a relative to the above.
      • A Survey of Noninteractive Zero Knowledge Proof System and Its Applications
      • How to Prove a Theorem So No One Else Can Claim It - By Manuel Blum.
      • Information Theoretic Reductions among Disclosure Problems - Brassau et al.
      • Knowledge complexity of interactive proof systems - By GoldWasser, Micali and Rackoff. Defining computational complexity of "knowledge" within zero knowledge proofs.
      • A Survey of Zero-Knowledge Proofs with Applications to Cryptography - Great intro on original ZKP protocols.
      • Zero Knowledge Protocols and Small Systems - A good intro into Zero knowledge protocols.
      • Multi-Theorem Preprocessing NIZKs from Lattices - Construction of non-interactive zero-knowledge (NIZK) proofs using lattice-based preprocessing models, by Sam Kim and David J. Wu.
      • Recommendation for Key Management – Part 1: General - Methodologically very relevant document on goals and procedures of key management.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • PRIMES is in P - Unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite.
      • Post-quantum cryptography - dealing with the fallout of physics success - Brief observation of mathematical tasks that can be used to build cryptosystems secure against attacks by post-quantum computers.
      • Post-quantum cryptography - Introduction to post-quantum cryptography.
      • Post-quantum RSA - Daniel Bernshtein's insight how to save RSA in post-quantum period.
      • MAYO: Practical Post-Quantum Signatures from Oil-and-Vinegar Maps - The Oil and Vinegar signature scheme, proposed in 1997 by Patarin, is one of the oldest and best-understood multivariate quadratic signature schemes. It has excellent performance and signature sizes. This paper is about enhancing this algorithm in usage in the post-quantum era. [Official website](https://pqmayo.org/).
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • Secure Communications Over Insecure Channels - Paper by R. Merkle, predated "New directions in cryptography" though it was published after it. The Diffie-Hellman key exchange is an implementation of such a Merkle system.
      • On the Security of Public Key Protocols - Dolev-Yao model is a formal model, used to prove properties of interactive cryptographic protocols.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Cryptanalysis of block ciphers and protocols - By Elad Pinhas Barkan.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Elliptic Curve Cryptography: the serpentine course of a paradigm shift - Historic inquiry into development of ECC and it's adoption.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Proofs that yield nothing but their validity and a Methodology of Cryptographic protocol design - By Goldreich, Micali and Wigderson, a relative to the above.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • Cache Attacks and Countermeasures: the Case of AES - Side channel attacks on AES, another view, by Dag Arne Osvik, Adi Shamir and Eran Tromer.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • A Method for Obtaining Digital Signatures and Public-Key Cryptosystems - Original paper introducing RSA algorithm.
      • On the Security of Public Key Protocols - Dolev-Yao model is a formal model, used to prove properties of interactive cryptographic protocols.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • On the Security of Public Key Protocols - Dolev-Yao model is a formal model, used to prove properties of interactive cryptographic protocols.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.
      • DES is not a group - Old but gold mathematical proof that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. That means that multiple DES encryption is not equivalent to single DES encryption and means that the size of the subgroup generated by the set of DES permutations is greater than 10^2499, which is too large for potential attacks on DES, which would exploit a small subgroup.
      • Selecting Cryptographic Key Sizes - Classic paper from 1999 with guidelines for the determination of key sizes for symmetric cryptosystems, RSA, ECC, by Arjen K. Lenstra and Eric R. Verheul.

    • Introducing people to data security and cryptography

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