FPGA realization of normal basis modular multiplication in GF (2~(233));

Design and Realization of Fast Modular Multiplication Based on Normal Basis of TypeⅡ;

This paper analyzes the point multiplication in EC and educes the modular multiplication formula in GF(2m)for systolic implementation with partial-parallelism in MSB mode.

The size and speed of the modular multiplier hinders the implementation of public key cryptography RSA applications for smart cards.

A novel systolic array modular multiplier is presented based on the modified Montgomery algorithm which is ideally suitable for hardware-inplementation.

A new VLSI architecture of high-radix modular multiplier to compute RSA public-key cryptosystem using our modified Montgomery algorithm is proposed.

This paper presents several popular algorithms of producing large prime numbes,and gives a algorithm which bases on Miller-Rabin prime detection algorithm and modular exponentiation algorithm based on Montgomery Modular Multiplication algorithm to rapidly generate large prime numbers.

Montgomery modular multiplication(MMM) plays a crucial role in the implementation of modular exponentiations of public-key cryptography.

Through a research on the property of Montgomery modular multiplication,the Pollard Phro、(P-1) and P+1 algorithms are modified respectively so that the classic modular multiplication can be replaced by Montgomery modular multiplication.

Novel systolic implementation of modular multiplication for large operands;

The modular multiplication over finite field GF(2m) is the most fundamental operation in elliptic curve cryptography, and accelerating the modular multiplication is the key to improving the performances of ECC algorithms over GF(2m).

With the help of word-based modular multiplication algorithm,the proposed multiplier is able to work with any precision of the input operands.