Implementation of SEA Algorithm on the Windows Platforms

Abstract

In FIPS 186-2, NIST (National Institute of Standards and Technology) recommends five elliptic curve parameters over prime field for building up secure elliptic curve cryptosystem. If the user can randomly produce elliptic curve parameters over prime field, the cryptosystem will be more secure. One of the important steps is to count the number of rational points on an elliptic curve over prime field and find the curve of prime order. Because SEA algorithm is an effective algorithm for counting points on elliptic curve over prime field, we can build up secure elliptic curve cryptosystem by using it to search for curve of prime order. The study uses MIRACL as embedded function library, C++ Builder to design the graphic user’s interface, and the computer with Pentium 2.80G CPU, 2G memory, and Windows server 2003 platforms for experiment. On average, it takes individually 610, 1386, 2093, 24514, and 100203 seconds to search out elliptic curve of prime order for cryptosystem; it takes 32, 69, 108, 751, and 3413 seconds individually to count the number of points on elliptic curve on the basis of 192, 224, 256, 384, and 521 bits of underlying field.