Awesome Crypto Papers

A curated list of cryptography papers, articles, tutorials and howtos for non-cryptographers.

Notes

The goal of this list is to provide educational reading material for different levels of cryptographic knowledge. I started it because my day job onboarding engineers at Cossack Labs includes educating them in cryptographic matters and giving advise what to read on specific topics, and that involves finding the same materials repeatedly. Hopefully, it will be useful for someone else as well.

It is aimed at people who are using cryptography in higher-level security systems to implement database encryption, secure sharing, end-to-end encryption in various schemes, and should understand how it works, how it fails and how it is attacked. It is not a list of notable / important / historically important papers (although many of them are here). It is not aimed at academics (who have better grasp of what they need anyway), nor it is aimed for systematic study of wanna-be cryptographers (who better follow structured approach under professional guidance).

It will be extended gradually as I find something of “must-have” value. Pull requests are very welcome.

Introducing people to data security and cryptography.
- Simple: cryptography for non-engineers.
- Brief engineer-oriented introductions.
Specific topics.
- Hashing - important bits on modern and classic hashes.
- Secret key cryptography - all things symmetric encryption.
- Cryptanalysis - attacking cryptosystems.
- Public key cryptography: General and DLP - RSA, DH and other classic techniques.
- Public key cryptography: Elliptic-curve crypto - ECC, with focus on pratcial cryptosystems.
- Zero Knowledge Proofs - Proofs of knowledge and other non-revealing cryptosystems.
- Math - useful math materials in cryptographic context.
- Post-quantum cryptography - Cryptography in post-quantum period.
Books.
Lectures and educational courses.
Online crypto challenges.

The list

Introducing people to data security and cryptography

Simple: cryptography for non-engineers

Nuts and Bolts of Encryption: A Primer for Policymakers.
Keys under Doormats - Or why cryptography shouldn’t be backdoored, by a all-star committee of crypto researches from around the world.

Brief introductions

An Overview of Cryptography - By Gary C. Kessler.
Using Encryption for Authentication in Large Networks - By Needham, Schroeder: this is were crypto-based auth starts.
Communication Theory of Secrecy Systems - Fundamental cryptography paper by Claude Shannon.

General cryptographic interest

Another Look at “Provable Security” - Inquiries into formalism and naive intuition behind security proofs, by Neal Koblitz et al.
The security impact of a new cryptographic library - Introductory paper on NaCl, discussing important aspects of implementing cryptography and using it as a larger building block in security systems, by Daniel J. Bernstein, Tanja Lange, Peter Schwabe.

Specific topics

Hashing

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.
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.

Secret key cryptography

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.

Cryptanalysis

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.

Public key cryptography: General and DLP

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.
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.
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.

Public key cryptography: Elliptic-curve crypto

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)
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.

Zero Knowledge Proofs

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.

Key Management

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.

Math

PRIMES is in P - Unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite.

Post-quantum cryptography

Kyber and Dilithium - These lectures describe Kyber (ML-KEM) and Dilithium (ML-DSA), the quantum-safe lattice-based key encapsulation and signature schemes that were standardized in August 2024 by the National Institute of Standards and Technology (NIST).
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.

Books

That seems somewhat out of scope, isn’t it? But these are books only fully available online for free. Read them as a sequence of papers if you will.

A Graduate Course in Applied Cryptography - By Dan Boneh and Victor Shoup. A well-balanced introductory course into cryptography, a bit of cryptanalysis and cryptography-related security.
Analysis and design of cryptographic hash functions, MAC algorithms and block ciphers - Broad overview of design and cryptanalysis of various ciphers and hash functions, by Bart Van Rompay.
CrypTool book - Predominantly mathematically oriented information on learning, using and experimenting cryptographic procedures.
Handbook of Applied Cryptography - By Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone. Good classical introduction into cryptography and ciphers.
The joy of Cryptography - By Mike Rosulek. A lot of basic stuff covered really well. No ECC.
A Computational Introduction to Number Theory and Algebra - By Victor Shoup, excellent starters book on math universally used in cryptography.

Lectures and educational courses

Understanding cryptography: A textbook for Students and Practitioners - Textbook, great lectures and problems to solve.
Crypto101 - Crypto 101 is an introductory course on cryptography, freely available for programmers of all ages and skill levels.
A Course in Cryptography - Lecture notes by Rafael Pass, Abhi Shelat.
Lecture Notes on Cryptography - Famous set of lectures on cryptography by Shafi Goldwasser (MIT), M. Bellare (University of California).
Introduction to Cryptography by Christof Paar - Video course by Christof Paar (University of Bochum in Germany). In english.
Cryptography I - Stanford University course on Coursera, taught by prof. Dan Boneh. Cryptography II is still in development.

Online crypto challenges

Not exactly papers, but crypto challenges are awesome educational material.

CryptoHack
Cryptopals crypto challenges.
id0-rsa crypto challenges.
MTC3 - xipher contest with more than 200 challenges of different levels, a moderated forum, and a hall-of-fame.

License

To the extent possible under law, author has waived all copyright and related or neighboring rights to this work.

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