A Montgomery Representation of Elements in GF(25) for Efficient Arithmetic to Use in Elliptic Curve Cryptography

Elliptic curve calculation was not introduced to cryptography until 1985. Compared with RSA, the advantage of elliptic curve cryptography lies in its ensuring the same security while the length of key of elliptic curve cryptography is much less than RSA cryptography and its lessening operation load. In this article a change of representation for elements in GF(2⁵) is proposed to use in elliptic curve cryptography. The proposed representation is useful for architectures that implement Montgomery multiplication in the finite field GF(2⁵). In fact, it needs virtually no cost in terms of conversion operations from a standard multiplication into a Montgomery multiplication.