Analysis of a public key approach based on polynomial substitution
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Efficient signature schemes based on birational permutations
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Cryptoanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'88
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Cryptanalysis of HFEv and internal perturbation of HFE
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Differential cryptanalysis for multivariate schemes
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Cryptanalysis of HFE with internal perturbation
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Key recovery on hidden monomial multivariate schemes
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Inverting HFE is quasipolynomial
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Secure variants of the square encryption scheme
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Proxy signature scheme based on isomorphisms of polynomials
NSS'12 Proceedings of the 6th international conference on Network and System Security
Performance analysis of multivariate cryptosystem schemes for wireless sensor network
Computers and Electrical Engineering
Towards provably secure proxy signature scheme based on Isomorphisms of Polynomials
Future Generation Computer Systems
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The HFE cryptosystem was the subject of several cryptanalytic studies, sometimes successful, but always heuristic. To contrast with this trend, this work goes back to the beginnning and achieves in a provable way a first step of cryptanalysis which consists in distinguishing HFE public keys from random systems of quadratic equations. We provide two distinguishers: the first one has polynomial complexity and subexponential advantage; the second has subexponential complexity and advantage close to one. These distinguishers are built on the differential methodology introduced at Eurocrypt'05 by Fouque & al. Their rigorous study makes extensive use of combinatorics in binary vector spaces. This combinatorial approach is novel in the context of multivariate schemes. We believe that the alliance of both techniques provides a powerful framework for the mathematical analysis of multivariate schemes