Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Journal of the ACM (JACM)
A new identification scheme based on syndrome decoding
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Trapdoor one-way permutations and multivariate polynominals
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
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
Practical and Provably-Secure Commitment Schemes from Collision-Free Hashing
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
EUROCRYPT'96 Proceedings of the 15th 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
Unbalanced oil and vinegar signature schemes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Public-key identification schemes based on multivariate quadratic polynomials
CRYPTO'11 Proceedings of the 31st annual 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
Public-Key identification schemes based on multivariate cubic polynomials
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
| Hi-index | 0.00 |
In [15] a protocol ZK(2) using zero-knowledge argument of knowledge was designed from a solution of a set of multivariate quadratic equations over a finite field (i.e. from MQ problem). In this paper, we propose a new scheme ZK(d) which is a generalization of ZK(2), i.e. we consider systems of polynomials of degree d. The key idea of the scheme ZK(d) is to use a polarization identity that allows to get a d-linear function and then use a cut-and-choose technique. We also observe that the scheme $\tilde{ZK}(d)$, which is the natural generalization of the protocol based on the MQ problem to higher degree, is more efficient in terms of computations whereas the ZK(d) scheme is better in terms of bits to be sent. Moreover these properties are still true for all kinds of polynomials: for example if the polynomials are sparse or dense. Finally, we will present two examples of applications: with Brent equations, or with morphisms of polynomials.