Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents

This contribution describes a new class of arithmetic architectures for Galois fields GF (2k). The main applications of the architecture are public-key systems which are based on the discrete logarithm problem for elliptic curves. The architectures use a representation of the field GF (2k) as GF ((2n)m), where k = n · m. The approach explores bit parallel arithmetic in the subfield GF (2n), and serial processing for the extension field arithmetic. This mixed parallel-serial (hybrid) approach can lead to fast implementations. As the core module, a hybrid multiplier is introduced and several ∗This paper is an extension of [1]. The bit parallel squarer architectures have been completely revised.