METHOD AND APPARATUS FOR CONSTRUCTING EFFICIENT ELLIPTIC CURVE CRYPTOSYSTEMS

摘要

METHOD AND APPARATUS FOR CONSTRUCTING EFFICIENT ELLIPTIC CURVE CRYPTOSYSTEMS[err]Abstract: Methods and apparatus to construct finite fields over which efficient elliptic curve cryptosystems can be set up. Given a security parameter k, the said methods and apparatus consist of devices for carrying out operations in a small k[err]-bit field k[err] and methods to successively build extension fields K[err] ; K[err], ..., K[err], where the extension K[err]/K[err] has degree 2 or 3 and the other extensions K[err]/K[err] are quadratic,K[err] is the final field over which elliptic curves are defined, and K[err] has size k[err]2[err] or 3k[err]2[err] just exceeding the said security parameter k.