Encryption Of Data Using Elliptic Curve Over Finite Fields

Encryption of Data using Elliptic Curve over Finite fields

Cryptography is the study of techniques for ensuring the secrecy and authentication of the information. Public –key encryption schemes are secure only if the authenticity of the public-key is assured. Elliptic curve arithmetic can be used to develop a variety of elliptic curve cryptographic (ECC) schemes including key exchange, encryption and digital signature. The principal attraction of ellip...

Multi-sources Randomness Extraction over Finite Fields and Elliptic Curve

This work is based on the proposal of a deterministic randomness extractor of a random Diffie-Hellman element defined over two prime order multiplicative subgroups of a finite fields Fpn , G1 and G2. We show that the least significant bits of a random element in G1 ∗G2, are indistinguishable from a uniform bit-string of the same length. One of the main application of this extractor is to replac...

Java Card Implementation of the Elliptic Curve Integrated Encryption Scheme Using Prime and Binary Finite Fields

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 Curves over Finite Fields

In this chapter, we study elliptic curves defined over finite fields. Our discussion will include the Weil conjectures for elliptic curves, criteria for supersingularity and a description of the possible groups arising as E(Fq). We shall use basic algebraic geometry of elliptic curves. Specifically, we shall need the notion and properties of isogenies of elliptic curves and of the Weil pairing....

Elliptic Curves over Finite Fields