Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
General fault attacks on multivariate public key cryptosystems
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
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It is widely believed to take exponential time to find a solution of a system of random multivariate polynomials because of the NP-completeness of such a task. On the other hand, in most of multivariate public key cryptosystems proposed so far, the computational complexity of cryptanalysis is polynomial time due to the trapdoor structure. In this paper, we introduce a new concept, piece in hand (soldiers in hand) matrix, which brings the computational complexity of cryptanalysis of multivariate public key cryptosystems close to exponential time by adding random polynomial terms to original cryptosystems. This is a general concept which can be applicable to any type of multivariate public key cryptosystems for the purpose of enhancing their security. As an implementation of the concept, we propose the linear PH matrix method with random variables. In 2003 Faugère and Joux broke the first HFE challenge (80 bits), where HFE is one of the major variants of multivariate public key cryptosystem, by computing a Gröbner basis of the public key of the cryptosystem. We show, in an experimental manner, that the linear PH matrix method with random variables can enhance the security of HFE even against the Gröbner basis attack. In what follows, we consider the strength of the linear PH matrix method against other possible attacks.