Revisiting scalable modular multiplication over GF(2/sup m/) for elliptic curve cryptography

A new unbalanced exponent modular reduction over GF(2m) is proposed. The algorithm can achieve high efficiency when computing on a certain class of fields generated by f(x) = x^m + T(x) where deg[T(x)] Lt C m. The algorithm is applied in modular multiplication on the basis of scalable polynomial basis(SPB) to form scalable modular multiplication. Most of irreducible polynomials used in elliptic curve cryptography(ECC) fulfil the characteristic mentioned above well. So the scalable algorithm is implemented in ECC computation with high flexibility and efficiency both in theoretic calculation and application