New Forms of Defining the Hidden Discrete Logarithm Problem

The new protocol blind digital signature based on the discrete logarithm problem on elliptic curve

In recent years it has been trying that with regard to the question of computational complexity of discrete logarithm more strength and less in the elliptic curve than other hard issues, applications such as elliptic curve cryptography, a blind  digital signature method, other methods such as encryption replacement DLP. In this paper, a new blind digital signature scheme based on elliptic curve...

Hidden Signature Schemes Based on the Discrete Logarithm Problem and Related Concepts Hidden Signature Schemes Based on the Discrete Logarithm Problem and Related Concepts

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Problem 3 : The Discrete Logarithm

New algorithm for the discrete logarithm problem on elliptic curves

A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of Boolean equations. Under a first fall degree assumption the regularity degree of the system is at most 4. Extensive experimental data which supports the assu...

A Kilobit Hidden SNFS Discrete Logarithm Computation

We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields. This computation took a little over two months of calendar time on an academic cluster using the open-source CADO-NFS software. Our chosen prime p looks random, and p−1 has a 160-bit pri...