Cryptography over Sextic Extension with Cubic Subfield

UPLICkey cryptographic is the fundamental technology in secure communications. It was devised by Diffie and Hellman [8], in 1976, to secret key distribution. In 1985, Coblitz [5] and Miller [7] independently proposed the implementation of a public key cryptosystem [3] using elliptic curve. The elliptic curve discrete logarithm problem appeared to be much more difficult than above discussed algorithms [6]. In this paper we present the cryptographic protocols based on a sextic extension with a cubic subfield of typeL α, β ,whose difficulty is based on discrete logarithm problem inOL α, β . Problem: Let X, Y OL and X non-invertible. Then there is a unique integer n such that X Y, we call this unique integer n, the discrete logarithm of Y with base X.