Efficient arithmetic in finite fields of odd characteristic on binary hardware

摘要

A method and apparatus for processing binary data representing field elements of an odd-characteristic finite field GF(p^k). Binary data representing at least a portion of a field element of an odd-characteristic finite field GF(p^k) is stored in a register, p being an odd prime number. The field element includes k coefficients in accordance with a polynomial-basis representation. The binary data includes plural groups of data bits, wherein each group of data bits represents an associated one of the k coefficients. At least one operation on contents of the register such that the plural groups of data bits are processed in parallel.