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
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
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
An efficient provable distinguisher for HFE
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
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
Inverting HFE is quasipolynomial
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Complexity estimates for the F4 attack on the perturbed Matsumoto-Imai cryptosystem
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Square-Vinegar Signature Scheme
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum 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
Proposal of a signature scheme based on STS trapdoor
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Feasibility of position-based multivariate cryptosystems for WSN
International Journal of Internet Technology and Secured Transactions
Performance analysis of multivariate cryptosystem schemes for wireless sensor network
Computers and Electrical Engineering
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Multivariate Cryptography has been an active line of research for almost twenty years. While most multivariate cryptosystems have been under attack, variations of the basic schemes came up as potential repairs. In this paper, we study the Internal Perturbation variation of HFE recently proposed by Ding and Schmidt. Although several results indicate that HFE is vulnerable against algebraic attacks for moderate size parameters, Ding and Schmidt claim that the cryptosystem with internal perturbation should be immune against them. However in this paper, we apply the recently discovered method of differential analysis to the Internal Perturbation of HFE and we find a subtle property which allows to disclose the kernel of the perturbation. Once this has been achieved, the public key can be inverted by attacking the underlying HFE provided the parameters were taken low enough to make the perturbed scheme of competitive performance.