Efficient Construction of CGL Hash Function Using Legendre Curves

Modern Hash Function Construction

This paper discusses modern hash function construction using the NIST SHA-3 competition as a survey of modern hash function construction properties. Three primary hash function designs are identified based on the designs of SHA-3 candidates submitted as part of the NIST SHA-3 competition. These designs are Widepipe, Sponge, and HAsh Iterated FrAmework (HAIFA). Keywordscryptography; hashing; has...

Legendre Transformations of Curves

In a recent paper of Wintner [l ], an extension is made of a classical theorem on the Legendre transformation of a convex function (for details of the proof, see [3], and for related results, cf. [4; 5]). His assumptions are that the function be strictly convex and of class C1. Here we shall prove a more general result which eliminates both of these restrictions and shows that, in a sense, they...

An Indifferentiable Hash Function into Elliptic Curves

We provide the first construction of a hash function into an elliptic curve that is indifferentiable from a random oracle. Our construction can be based on any efficient encoding into an elliptic-curve, for example Icart’s function or the Shallue-Woestijne-Ulas (SWU) algorithm.

An Improved Hash Function Based on the Tillich-Zémor Hash Function

Using the idea behind the Tillich-Zémor hash function, we propose a new hash function. Our hash function is parallelizable and its collision resistance is implied by a hardness assumption on a mathematical problem. Also, it is secure against the known attacks. It is the most secure variant of the Tillich-Zémor hash function until now.

Efficient Construction of Cryptographically Strong Elliptic Curves