论文信息 - The Implementation of Elliptic Curve Cryptosystems

The Implementation of Elliptic Curve Cryptosystems

In this chapter we explore the feasibility of efficient implementation of an arithmetic processor for performing elliptic curve computations over finite fields. For a secure system, it is evident from the results of Chapter 5 that the curve and underlying field should be judiciously chosen. However we should point out that for a given underlying field there are a large number of suitable elliptic curve to choose from. If the logarithm problem in supersingular curves is indeed as hard as the logarithm problem in finite fields, and/or if the logarithm problem in non-supersingular curves is indeed intractable, then the systems discussed here are both efficient and secure and very attractive for practical usage.

Alfred Menezes | Scott A. Vanstone | A. Menezes | S. Vanstone

[1] P. L. Montgomery. Speeding the Pollard and elliptic curve methods of factorization , 1987 .

[2] Joseph H. Silverman,et al. The arithmetic of elliptic curves , 1986, Graduate texts in mathematics.

[3] Johan Håstad,et al. On Using RSA with Low Exponent in a Public Key Network , 1985, CRYPTO.

[4] J. Hastd,et al. "On using RSA with low exponent in a public key network," Proc. of Crypto'85 , 1985 .

[5] T. Elgamal. A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[6] N. Koblitz. Elliptic curve cryptosystems , 1987 .

[7] Ronald C. Mullin,et al. Optimal normal bases in GF(pn) , 1989, Discret. Appl. Math..

[8] N. Koblitz. A Course in Number Theory and Cryptography , 1987 .

[9] Ian F. Blake,et al. Low complexity normal bases , 1989, Discret. Appl. Math..

[10] Whitfield Diffie,et al. New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[11] T. Rosati. A high speed data encryption processor for public key cryptography , 1989, 1989 Proceedings of the IEEE Custom Integrated Circuits Conference.

[12] Victor S. Miller,et al. Use of Elliptic Curves in Cryptography , 1985, CRYPTO.