The first efficient generic-point parallel scalar multiplication method is presented here. The novelty of the proposed method is that the precomputation overhead can be replaced by postcomputations that can be parallelised. This method will be very attractive for use in high-performance end servers that employ parallel elliptic curve cryptoprocessors.

We report the discovery of a new factor for each of the Fermat numbers F13, F15, F16. These new factors have 27, 33 and 27 decimal digits respectively. Each factor was found by the elliptic curve method. After division by the new factors and previously known factors, the remaining cofactors are seen to be composite numbers with 2391, 9808 and 19694 decimal digits respectively.

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Public key cryptography systems are based on sound mathematical foundations that are designed to make the problem hard for an intruder to break into the system. The major approaches that since 1976 have withstood intruder attacks, are the discrete logarithm Mr. Raja Ghosal PhD Student, Auto-ID Lab, ADELAIDE School of Electrical and Electronics Engineering, The University of Adelaide Prof. Peter...

Formalizing a mathematical theory is a necessary first step to proving the correctness of programs that refer to that theory in their specification. This paper demonstrates how the mathematical theory of elliptic curves and their application to cryptography can be formalized in higher order logic. This formal development is mechanized using the HOL4 theorem prover, resulting in a collection of ...

In this paper, we propose an elliptic curve key generation processor over GF(2 163 ) scheme based on the Montgomery scalar multiplication algorithm. The new architecture is performed using polynomial basis. The Finite Field operations use a cellular automata multiplier and Fermat algorithm for inversion. For real time implementation, the architecture has been tested on an ISE 9.1 Software using...

The strength of public key cryptography utilizing Elliptic Curves relies on the difficulty of computing discrete logarithms in a finite field. Diffie-Hellman key exchange algorithm also relies on the same fact. There are two flavors of this algorithm, one using Elliptic Curves and another without using Elliptic Curves. Both flavors of the algorithm rely on the difficulty of computing discrete l...

Public-key cryptography is based on the intractability of certain mathematical problems. Early public-key systems, such as the RSA algorithm, are secure assuming that it is difficult to factor a large integer composed of two or more large prime factors. For elliptic-curve-based protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publ...

In 1987 Neil Koblitz first suggested the use of Elliptic curves for Public Key Cryptosystems. This has triggered publications about ECC (Elliptic Curve Cryptography) in recent years as well as the appearance of first University textbooks about that topic. Some Mathematicians and Computer Scientists have focused their studies of Elliptic curves on efficiency and security of ECC. Questions arise ...

This paper covers relatively new and emerging subject of the elliptic curve crypto systems whose fundamental security is based on the algorithmically hard discrete logarithm problem. Work includes the study of the following issues: mathematical background of the elliptic curve crypto systems, discrete logarithm problem, practical use cases in the industry, common implementation mistakes, perfor...