Implementation of Elliptic Curve25519 in Cryptography

Intan Muchtadi-Alamsyah and Yanuar Bhakti Wira Tama

### Abstract

Bernstein's design implementation of elliptic Curve25519 in key exchange is claimed to be highly secure and efficient. This curve is, for example, used in the key exchange scheme of TextSecure for Instant Messaging. In this paper, we present an implementation of elliptic Curve25519 in the simplified Elliptic Curve Integrated Encryption Scheme, thus showing that elliptic Curve25519 can also serve other purposes than key exchange. The curve is in Montgomery form, which makes it possible to use Montgomery ladder. Point compression, point decompression, encryption, and decryption algorithms are presented for the simplified Elliptic Curve Integrated Encryption Scheme.

Keywords: elliptic curve, cryptography, Montgomery ladder, integrated encryption scheme
