How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
An observation on the security of McEliece's public-key cryptosystem
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
A (non-practical) three-pass identification protocol using coding theory
AUSCRYPT '90 Proceedings of the international conference on cryptology on Advances in cryptology
Efficient signature schemes based on birational permutations
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
A new identification scheme based on syndrome decoding
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Attacks on the birational permutation signature schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
QUARTZ, 128-Bit Long Digital Signatures
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
The Security of Hidden Field Equations (HFE)
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
An Efficient Identification Scheme Based on Permuted Kernels (Extended Abstract)
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Designing Identification Schemes with Keys of Short Size
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Zero-Knowledge Proofs for Finite Field Arithmetic; or: Can Zero-Knowledge be for Free?
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
The Cryptographic Security of the Syndrome Decoding Problem for Rank Distance Codes
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Cryptanalysis of the TTM Cryptosystem
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A New Identification Algorithm
Proceedings of the International Conference on Cryptography: Policy and Algorithms
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Ideals over a non-commutative ring and their application in cryptology
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
A new identification scheme based on the perceptrons problem
EUROCRYPT'95 Proceedings of the 14th 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
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Solving Structured Polynomial Systems and Applications to Cryptology
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Cryptanalysis of multivariate and odd-characteristic HFE variants
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
BGN authentication and its extension to convey message commitments
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
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A Zero-knowledge protocol provides provably secure entity authentication based on a hard computational problem. Among many schemes proposed since 1984, the most practical rely on factoring and discrete log, but still they are practical schemes based on NP-hard problems. Among them, the problem SD of decoding linear codes is in spite of some 30y ears of research effort, still exponential. We study a more general problem called MinRank that generalizes SD and contains also other well known hard problems. MinRank is also used in cryptanalysis of several public key cryptosystems such as birational schemes (Crypto'93), HFE (Crypto'99), GPT cryptosystem (Eurocrypt'91), TTM (Asiacrypt'2000) and Chen's authentication scheme (1996). We propose a new Zero-knowledge scheme based on MinRank. We prove it to be Zero-knowledge by black-box simulation. An adversary able to fraud for a given MinRank instance is either able to solve it, or is able to compute a collision on a given hash function. MinRank is one of the most efficient schemes based on NP-complete problems. It can be used to prove in Zero-knowledge a solution to any problem described by multivariate equations. We also present a version with a public key shared by a few users, that allows anonymous group signatures (a.k.a. ring signatures).