Publication
Using cyclotomic polynomials to construct efficient discrete logarithm cryptosystems over finite fields
Related publications (39)
Practical Cryptography in High Dimensional Tori
At Crypto 2004, van Dijk and Woodruff introduced a new way of using the algebraic tori in cryptography, and obtained an asymptotically optimal savings in bandwidth and storage for a number of cryptographic applications. However, the compu ...
Springer Berlin Heidelberg2005Function Field Sieve in Characteristic Three
In this paper we investigate the efficiency of the function field sieve to compute discrete logarithms in the finite fields . Motivated by attacks on identity based encryption systems using supersingular elliptic curves, we pay special at ...
Springer Berlin Heidelberg2004Computing the performance of unitary space-time group codes from their character table
Multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment. Their success, however, depends on the design of cedes that achieve these promises. It is well known that unitary matrices can be ...
2002Selecting cryptographic key sizes
In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm-based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based ...
Springer Verlag2001The XTR public key system
This paper introduces the XTR public key system. XTR is based on a new method for representing elements of a subgroup of a multiplicative group of a finite field. Application of XTR in cryptographic protocols leads to substantial savings both in communicat ...
2000Efficient identity based parameter selection for elliptic curve cryptosystems
A method is proposed that allows each individual party to an elliptic curve cryptosystem to quickly determine its own unique pair of finite field and Weierstrass equation, in such a way that the resulting pair provides adequate security. Although the choic ...
1999Deciding properties of number fields without factoring
The polynomial time algorithm of Lenstra, Lenstra, and Lovász [15] for factoring integer polynomials and variants thereof have been widely used to show that various computational problems in number theory have polynomial time solutions. Among them is the p ...
1997Optimal algorithms for multiplication in certain finite fields using elliptic curves
Using the results given in [D,. V. Chudnovsky and G. V Chudnovsky, Proc. Nat. Acad. Sci. USA, 84 (1987), pp. 1739-1743] and [W. C. Waterhouse, Ann. Sci. École Norm. Sup., 4 (1969), pp. 521560], it is proven that the rank (= bilinear complexity of multipli ...
1992Efficient randomized generation of optimal algorithms for multiplication in certain finite fields
Let denote the maximum number of points of an elliptic curve over . Given a prime power and an integern satisfying , we present an algorithm which on inputq andn produces an optimal bilinear ...
1992