Efficient signature schemes based on polynomial equations
Proceedings of CRYPTO 84 on Advances in cryptology
Perfectly one-way probabilistic hash functions (preliminary version)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of Block Ciphers with Overdefined Systems of Equations
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Solving Underdefined Systems of Multivariate Quadratic Equations
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
A New Interactive Hashing Theorem
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Higher order correlation attacks, XL algorithm and cryptanalysis of Toyocrypt
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
About the XL algorithm over GF(2)
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
On building hash functions from multivariate quadratic equations
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
A family of fast syndrome based cryptographic hash functions
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
Computational bounds on hierarchical data processing with applications to information security
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
New proofs for NMAC and HMAC: security without collision-resistance
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
QUAD: a practical stream cipher with provable security
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
VSH, an efficient and provable collision-resistant hash function
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
IEEE Transactions on Information Theory
Multivariates Polynomials for Hashing
Information Security and Cryptology
Secure PRNGs from Specialized Polynomial Maps over Any $\mathbb{F}_{q}$
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Security Analysis of Multivariate Polynomials for Hashing
Information Security and Cryptology
Interpreting hash function security proofs
ProvSec'10 Proceedings of the 4th international conference on Provable security
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We analyse the security of new hash functions whose compression function is explicitly defined as a sequence of multivariate equations. First we prove non-universality of certain proposals with sparse equations, and deduce trivial collisions holding with high probability. Then we introduce a method inspired from coding theory for solving underdefined systems with a low density of non-linear monomials, and apply it to find collisions in certain functions. We also study the security of message authentication codes HMAC and NMAC built on multivariate hash functions, and demonstrate that families of low-degree functions over GF(2) are neither pseudo-random nor unpredictable.