Toshiya Itoh

A fast algorithm for computing multiplicative inverses in GF(2 m ) using normal bases

Abstract This paper proposes a fast algorithm for computing multiplicative inverses in GF(2 m ) using normal bases. Normal bases have the following useful property: In the case that an element x in GF(2 m ) is represented by normal bases, 2 k power operation of an element x in GF(2 m ) can be carried out by k times cyclic shift of its vector representation. C. C. Wang et al. proposed an algorithm for computing multiplicative inverses using normal bases, which requires ( m − 2) multiplications in GF(2 m ) and ( m − 1) cyclic shifts. The fast algorithm proposed in this paper also uses normal bases, and computes multiplicative inverses iterating multiplications in GF(2 m ). It requires at most 2[log 2 ( m − 1)] multiplications in GF(2 m ) and ( m − 1) cyclic shifts, which are much less than those required in the Wangs method. The same idea of the proposed fast algorithm is applicable to the general power operation in GF(2 m ) and the computation of multiplicative inverses in GF( q m ) ( q = 2 n ).

Structure of parallel multipliers for a class of fields GF(2 m )

Abstract This paper presents a configuration of parallel multipliers for GF (2 m ) based on canonical bases. The possible parallel multipliers by the proposed configuration are limited to a class of fields GF (2 m ). However they can be constructed by O(m 2 ) AND-gates and O(m 2 ) EOR-gates with the structural modularity (this is a desirable feature for the hardware implementation), and their operation time is about (log m ) T , where m is the dimension of GF (2 m ) and T is the delay time of an EOR-gate. In order to construct such parallel multipliers, we define two types of polynomials of special form over GF (2), one is called all one polynomial (denoted by AOP) and the other is called equally spaced polynomial (denoted by ESP). Furthermore, we show a necessary and sufficient condition for ESPs to be irreducible over GF (2) and the uniqueness of the irreducible ESPs over GF (2). Finally, we propose the configuration of parallel multipliers for a class of fields GF (2 m ) based on irreducible AOPs and ESPs over GF (2).

An ID-based cryptosystem based on the discrete logarithm problem

In a modern network system, data security technologies such as cryptosystems, signature schemes, etc., are indispensable for reliable data transmission. In particular, for a large-scale network, ID-based systems such as the ID-based cryptosystem, the ID-based signature scheme, or the ID-based key distribution system are among the better countermeasures for establishing efficient and secure data transmission systems. The concept of an ID-based cryptosystem has been proposed by A. S?hamir (1985), and it is advantageous to public-key cryptosystems because a large public-key file is not required for such a system. An ID-based cryptosystem based on the discrete logarithm problem is proposed which is one of the earliest realizations in Shamirs sense. The security against a conspiracy of some entities in the proposed system is considered, along with the possibility of establishing a more secure system. >

A language-dependent cryptographic primitive

In this paper we provide a new cryptographic primitive that generalizes several existing zero-knowledge proofs and show that if a languageL induces the primitive, then there exists a perfect zero-knowledge proof forL. In addition, we present several kinds of languages inducing the primitive, some of which are not known to have a perfect zero-knowledge proof.

Improved Constructions for Query-Efficient Locally Decodable Codes of Subexponential Length

A (k, δ, e)-locally decodable code

A Progress Report on Subliminal-Free Channels

C:{\bf F}_{q}^{n} \ ightarrow {\bf F}_{q}^{N}

On the Complexity of Constant Round ZKIP of Possession of Knowledge

is an error-correcting code that encodes

Competitive Analysis of Multi-Queue Preemptive QoS Algorithms for General Priorities*Supported in part by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research on Priority Areas, 16092205, 2005.

\vec{x}=(x_{1},x_{2},\ldots,x_{n}) \in {\bf F}_{q}^{n}

On the sample size of k -restricted min-wise independent permutations and other k -wise distributions

to

A public-key cryptosystem based on the difficulty of solving a system of nonlinear equations

C(\vec{x}) \in {\bf F}_{q}^{N}