How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
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
A New \mathcal{NP}-Complete Problem and Public-Key Identification
Designs, Codes and Cryptography
Asymmetric cryptography with S-Boxes
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Trapdoor one-way permutations and multivariate polynominals
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Cryptanalysis of ``2 R'' Schemes
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
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Compact FPGA implementations of QUAD
ASIACCS '07 Proceedings of the 2nd ACM symposium on Information, computer and communications security
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Symposium on Theory of Computing Conference (co-located with FCRC 2007 Conference)
An efficient parallel repetition theorem for Arthur-Merlin games
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Multivariates Polynomials for Hashing
Information Security and Cryptology
Security Proofs for Identity-Based Identification and Signature Schemes
Journal of Cryptology
Security Analysis of Multivariate Polynomials for Hashing
Information Security and 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
Fast exhaustive search for polynomial systems in F2
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
A zero-knowledge identification scheme based on the q-ary syndrome decoding problem
SAC'10 Proceedings of the 17th international conference on Selected areas in cryptography
Public-key identification schemes based on multivariate quadratic polynomials
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
CRYPTO'06 Proceedings of the 26th annual international 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
A new paradigm for public key identification
IEEE Transactions on Information Theory - Part 1
Zero-Knowledge for multivariate polynomials
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
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Solving a system of multivariate polynomials over a finite field is a promising problem in cryptography. Recently, Sakumoto et al. proposed public-key identification schemes based on the quadratic version of the problem, which is called the MQ problem. However, it is still an open question whether or not it is able to build efficient constructions of public-key identification based on multivariate polynomials of degree greater than two. In this paper, we tackle the cubic case of this question and construct public-key identification schemes based on the cubic version of the problem, which is called the MC problem. The MQ problem is a special case of the MC problem. Our schemes consist of a protocol which is zero-knowledge argument of knowledge for the MC problem under the assumption of the existence of a non-interactive commitment scheme. For a practical parameter choice, the efficiency of our scheme is highly comparable to that of the schemes based on the MQ problem. Furthermore, the parallel version of our scheme also achieves the security under active attack with some additional cost.