The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Cryptanalysis of cryptosystems based on non-commutative skew polynomials
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
A novel group signature scheme based on MPKC
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
Public-key identification schemes based on multivariate quadratic polynomials
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
MQQ-SIG: an ultra-fast and provably CMA resistant digital signature scheme
INTRUST'11 Proceedings of the Third international conference on Trusted Systems
Proxy signature scheme based on isomorphisms of polynomials
NSS'12 Proceedings of the 6th international conference on Network and System Security
Towards provably secure proxy signature scheme based on Isomorphisms of Polynomials
Future Generation Computer Systems
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At Eurocrypt'96, Patarin proposed [9] new cryptographic schemes based on the Isomorphism of Polynomials with one Secret problem (IP1S) [9]. We study in this paper a restriction of IP1S called Polynomial Linear Equivalence problem (PLE) [7]. We show that PLE is in fact not a restriction of IP1S, in the sense that any algorithm solving PLE can be efficiently transformed into an algorithm for solving IP1S. Motivated by the cryptanalysis of schemes based on IP1S, we present a new efficient algorithm for solving PLE. This algorithm is mainly based on a differential property of PLE. The main advantage of this approach is to translate PLE into a simple linear algebra problem. The performances of our algorithm evidence that, with the parameters proposed in [9], schemes based on IP1S are far from achieving the security level required for cryptographic applications.