Elliptic Curve Cryptography and Coding Theory

Software Elliptic Curve Cryptography

In this thesis, we study the software implementation of the NIST-recommended elliptic curves over prime fields. Our implementation goals are to achieve a fast, small, and portable cryptographic library, which supports elliptic curve digital signature generation and verification. The implementation results are presented on a Pentium I1 448.81 MHz. We also consider the sliding window algorithm (S...

Elliptic Curve Cryptography

There is a re-emerging demand for low-end devices such as 8-bit processors, driven by needs for pervasive applications like sensor networks and RF-ID tags. Security in pervasive applications, however, has been a major concern for their widespread acceptance. Public-key cryptosystems (PKC) like RSA and DSA generally involve computation-intensive arithmetic operations with operand sizes of 1024 −...

Elliptic Curve Cryptography

Elliptic Curve Cryptography

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...

Formalized Elliptic Curve Cryptography

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 ...