Hyperelliptic Curve Crypto-Coprocessor over Affine and Projective Coordinates

Genus Two Hyperelliptic Curve Coprocessor

Hyperelliptic curve cryptography with genus larger than one has not been seriously considered for cryptographic purposes because many existing implementations are significantly slower than elliptic curve versions with the same level of security. In this paper, the first ever complete hardware implementation of a hyperelliptic curve coprocessor is described. This coprocessor is designed for genu...

Fault Attacks on Projective-to-Affine Coordinates Conversion

Operations of Points on Elliptic Curve in Projective Coordinates

In this article, we formalize operations of points on an elliptic curve over GF(p). Elliptic curve cryptography [7], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security. We prove that the two operations of points: compell ProjCo and addell ProjCo are unary and binary operations of a point over the elliptic curve. The te...

Set of Points on Elliptic Curve in Projective Coordinates

For simplicity, we use the following convention: x is a set, i, j are integers, n, n1, n2 are natural numbers, and K, K1, K2 are fields. Let K be a field. A field is called a subfield of K if it satisfies the conditions (Def. 1). (Def. 1)(i) The carrier of it ⊆ the carrier of K, (ii) the addition of it = (the addition of K) (the carrier of it), (iii) the multiplication of it = (the multiplicati...

Increasing the Bitlength of a Crypto-Coprocessor

We present a novel technique which allows a virtual increase of the bitlength of a crypto-coprocessor in an efficient and elegant way. The proposed algorithms assume that the coprocessor is equipped with a special modular multiplication instruction. This instruction, called MultModDiv(A,B,N) computes A ∗ B mod N and (A ∗B)/N . In addition to the doubling algorithm, we also present two conceivab...