Ryou Fujita

Proposal of a signature scheme based on STS trapdoor

A New digital signature scheme based on Stepwise Triangular Scheme (STS) is proposed. The proposed trapdoor has resolved the vulnerability of STS and secure against both Grobner Bases and Rank Attacks. In addition, as a basic trapdoor, it is more efficient than the existing systems. With the efficient implementation, the Multivariate Public Key Cryptosystems (MPKC) signature public key has the signature longer than the message by less than 25 %, for example.

Proposal for Piece in Hand Matrix: General Concept for Enhancing Security of Multivariate Public Key Cryptosystems

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 Faugere 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 Grobner 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 Grobner basis attack. In what follows, we consider the strength of the linear PH matrix method against other possible attacks.

Privacy Preserving Data Processing with Collaboration of Homomorphic Cryptosystems

We propose a privacy-preserving data processing system using homomorphic cryptosystem. Proposed system consists of several functionalities corresponding to addition and multiplication of plaintexts encrypted in ciphertexts. Using these functionalities repeatedly, any multivariate polynomial evaluation of secret inputs can be achieved. We clarify the role and the function of each organization participating in the process — custodians of personal data, processing center of cryptographic function, and computing center. The cooperation of several entities makes arbitrary times of the calculations, which is a requirement of fully homomorphic encryption, more efficient. We give security proofs of the scheme and show the result of implementation of the scheme.