Chien-Yuan Chen

A high-speed division algorithm in residue number system using parity-checking technique

The residue number system (RNS) has computational advantages for large integer arithmetic because of its parallel, carry free, and high-speed arithmetic nature. However, overflow detection, sign detection, relative-magnitude detection, and division are highly time-consuming operations in RNS. Among them, the most interesting one is division because it can apply to modular arithmetic. To speed up the operation, Hiasat and Abdel-Aty-Zohdy proposed a high-speed division algorithm for RNS in 1997. Hiasat and Abdel-Aty-Zohdys algorithm computes a temporal quotient according to the highest power of 2 in the dividend and the divisor. Nevertheless, the temporal quotient is underestimated such that the algorithm has redundant execution rounds. In this article, we improve Hiasat and Abdel-Aty-Zohdys division algorithm by using parity checking. Our improvement can reduce the number of execution rounds by 50%. cychen@isu.edu.tw E-mail: jenho@cs.ccu.edu.tw

A Conference Key Distribution Scheme Using Interpolating Polynomials

Conference keys are secret keys used by a group of users commonly with which they can encipher (or decipher) messages such that communications are secure. Based on Diffie and Hellmans PKDS, a conference key distribution scheme is presented in this paper. A sealed lock is used to lock the conference key in such a way that only the private keys of the invited members are matched. Then the sealed lock is thus made public or distributed to all the users, only legitimate users can disclose it and obtain the conference key. In our scheme, the construction of a sealed lock is simple and the revelation of a conference key is efficient as well.

A fast modular multiplication algorithm for calculating the product AB modulo N

Abstract In this paper, we propose a fast iterative modular multiplication algorithm for calculating the product AB modulo N , where N is a large modulus in number-theoretic cryptosystems, such as RSA cryptosystems. Our algorithm requires ( 5 3 − 1 4 k ) n k + 5 3 4 k − 1 3 2 k − 17 6 additions on average for an n -bit modulus if k carry bits are dealt with in each loop. For a 512 -bit modulus, the known fastest modular multiplication algorithm, Chen and Lius algorithm, requires 517 additions on average. However, compared to Chen and Lius algorithm, our algorithm reduces the number of additions by 26 % for a 512 -bit modulus.

Cryptanalysis of short secret exponents modulo RSA primes

In this manuscript, one way to attack on the short secret exponent dq modulo a larger RSA prime q is presented. When dq < (2p/3q)½ and e < (pq)½, dq can be discovered from the continued fraction of e/pq, where e and pq denote the public exponent and the modulus, correspondingly. Furthermore, the same way to attack on an unbalanced RSA is also discussed. According to cryptanalysis presented in this study, the unbalanced RSA will be resolved if dq < (2/3)½ q4/9.

An improved Chen's parity detection technique for the two-moduli set

This paper improved Chens residue number system (RNS) parity detection technique such that the original two-moduli set {2 h −1, 2 h +1} is extended to {2p−1, 2p+1}, where h and p are positive integers. Given an RNS number X=(x 1, x 2) based on the extended two-moduli set, it is found that the parity of X is (p mod 2)·y 0 ⊕ y 1 if x 1≥x 2, where y 1 y 0 denotes the binary representation of x 1+x 2 mod 4. On the contrary, if x 1<x 2, the parity of X is . Obviously, our parity technique, compared with Lu and Chiangs, can discover the parity of an RNS number without the table lookup and fractional number approaches.

A fast modular multiplication method using Yacobi's algorithm

Summary form only given. A fast modular multiplication method is presented. The known fastest modular multiplication method by Su and Hwang requires n+11 additions on average for an n-bit modulus. In Su and Hwangs method, the computed values are not stored for use again. In our method, the computed values can be stored by Yacobis algorithm. According to our analysis, our method is faster than Su and Hwangs when n/spl ges/512. Furthermore, our method only requires 0.6718 n additions on average as n approaches the limit infinity.

A new subliminal channel based on fiat‐Shamir's signature scheme

Abstract This paper constructs a subliminal channel in a RSA‐like variant of the Fiat‐Shamir signature scheme to transfer any secret information. The proposed subliminal channel, unlike that in El‐Gamal signature scheme, can avoid the serious shortcoming that a subliminal receiver can undetectably forge a signers signature. In addition, our channel also overcomes almost all shortcomings from which the subliminal channel in El‐Gamal signature scheme suffer.