Computer algebra: symbolic and algebraic computation (2nd ed.)
Computer algebra: symbolic and algebraic computation (2nd ed.)
Does co-NP have short interactive proofs?
Information Processing Letters
Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Attacking the Affine Parts of SFLASH
Proceedings of the 8th IMA International Conference on Cryptography and Coding
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
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
A toolbox for cryptanalysis: linear and affine equivalence algorithms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Interactions between computer algebra (Gröbner bases) and cryptology
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Cryptanalysis of the Square Cryptosystems
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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
Cryptanalysis of the TRMS signature scheme of PKC'05
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
New differential-algebraic attacks and reparametrization of rainbow
ACNS'08 Proceedings of the 6th international conference on Applied cryptography and network security
Total break of the l-IC signature scheme
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
FGb: a library for computing Gröbner bases
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Algebraic cryptanalysis of curry and flurry using correlated messages
Inscrypt'09 Proceedings of the 5th international conference on Information security and cryptology
A novel group signature scheme based on MPKC
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
Protecting white-box AES with dual ciphers
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
Efficient algorithms for some special cases of the polynomial equivalence problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
MQQ-SIG: an ultra-fast and provably CMA resistant digital signature scheme
INTRUST'11 Proceedings of the Third international conference on Trusted Systems
On polynomial systems arising from a weil descent
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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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The Isomorphism of Polynomials (IP) [28], which is the main concern of this paper, originally corresponds to the problem of recovering the secret key of a C* scheme [26]. Besides, the security of various other schemes (signature, authentication [28], traitor tracing [5], ...) also depends on the practical hardness of IP. Due to its numerous applications, the Isomorphism of Polynomials is thus one of the most fundamental problems in multivariate cryptography. In this paper, we address two complementary aspects of IP, namely its theoretical and practical difficulty. We present an upper bound on the theoretical complexity of “IP-like” problems, i.e. a problem consisting in recovering a particular transformation between two sets of multivariate polynomials. We prove that these problems are not NP-Hard (provided that the polynomial hierarchy does not collapse). Concerning the practical aspect, we present a new algorithm for solving IP. In a nutshell, the idea is to generate a suitable algebraic system of equations whose zeroes correspond to a solution of IP. From a practical point of view, we employed a fast Gröbner basis algorithm, namely F5 [17], for solving this system. This approach is efficient in practice and obliges to modify the current security criteria for IP. We have indeed broken several challenges proposed in literature [28, 29, 5]. For instance, we solved a challenge proposed by O. Billet and H. Gilbert at Asiacrypt'03 [5] in less than one second.