Conference: MINI SYMPOSIUM on CRYPTOGRAPHY


Elliptic curve cryptography on FPGA

Jamshid Shokrollahi's talk
Date: 23.06.05   Time: 11.00 - 12.00   Room: Y36M24

This talk consists of two parts:

- In the first part we consider and analyze different possibilities to implement scalar multiplication of points on elliptic curves over finite fields of characteristic 2 on FPGA platforms. The study will be divided into three levels of finite field arithmetic, point addition, and scalar multiplication. This part will be concluded with the datapath structures and benchmark results for an implemented elliptic curve coprocessor in GF(2^191) on a XCV2000E FPGA.

- The second part is about the factorization of the change of basis matrix from optimal normal bases of type II to some kind of polynomial basis. Using this factorization which resembles the FFT factorizations of the DFT matrix, multiplication of elements of GF(2^n) which are represented by an optimal normal basis of type II can be done in M(n)+O(n log n) bit operations, where M(n) is the cost of multiplying two n-bit polynomials over GF(2).