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...

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 provides a methodology for obtaining high-speed, efficient, and scalable implementations of network security protocols. In this paper, we describe in detail three protocols based on elliptic curve cryptographic techniques, and the results of our implementation of the elliptic curve cryptography over the Galois field GF (2k), where k is a composite number. 1 Elliptic ...

As computing and communication devices are equipped with increasingly versatile wireless connection capabilities, the demand for security increases. Cryptography provides a method for securing and authenticating the transmission of information over the insecure channels. Elliptic Curve [EC] Cryptography is a public key cryptography which replaces RSA because of its increased security with lesse...

Elliptic Curve Cryptography (ECC) can be considered an approach to public-key cryptography based on the arithmetic of elliptic curves and the Elliptic Curve Discrete Logarithm Problem (ECDLP). Regarding encryption, the best-known scheme based on ECC is the Elliptic Curve Integrated Encryption Scheme (ECIES), included in standards from ANSI, IEEE, and also ISO/IEC. In the present work, we provid...

Elliptic curve cryptography (ECC) is an alternative to traditional techniques for public key cryptography. It offers smaller key size without sacrificing security level. In a typical elliptic curve cryptosystem, elliptic curve point multiplication is the most computationally expensive component. So it would be more attractive to implement this unit using hardware than using software. In this pa...

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...