Hardware Implementation Of Elliptic Curve Cryptosystems Over GF(2～n)

We describe a cryptographic processor for Elliptic Curve Cryptography(ECC). ECC is evolving as an attractive alternative to other public-key cryptosystems such as the Rivest-Shamir-Adleman algorithm( RSA) by offering the smallest key size and the highest strength per bit. Multiplication over finite field is the most time consuming operation in implementing ECC, Actually multiplication over finite field is modular multiplication, The cryptographic processor performs multiplication over finite field GF(2~n) for ECC. In contrast to other designs that only support fixed field and fixed irreducible polynomials, our multiplier can support every finite field GF(2~n) which n from 160 to 256 and irreducible polynomials recommended by the National Institute for Standards and Technology(NIST). Our processor has high scalability and flexibility between speed, hardware area and operand size.When operand size is 32 bit, The processor performs 256 bit multiplication by only 18 clock, the clock frequency is above 66 MHz and the area is 0.98cm~2 ;When operand size is 16 bit, The processor performs 256 bit multiplication by 34 clock, the clock frequency is 100 MHz and the area is 0.67cm~2.