TY - JFULL
AU - Chillali Abdelhakim
PY - 2011/7/
TI - Cryptography Over Elliptic Curve Of The Ring Fq[e], e4 = 0
T2 - International Journal of Mathematical and Computational Sciences
SP - 916
EP - 919
VL - 5
SN - 1307-6892
UR - https://publications.waset.org/pdf/125
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 54, 2011
N2 - Groups where the discrete logarithm problem (DLP) is believed to be intractable have proved to be inestimable building blocks for cryptographic applications. They are at the heart of numerous protocols such as key agreements, public-key cryptosystems, digital signatures, identification schemes, publicly verifiable secret sharings, hash functions and bit commitments. The search for new groups with intractable DLP is therefore of great importance.The goal of this article is to study elliptic curves over the ring Fq[], with Fq a finite field of order q and with the relation n = 0, n ≥ 3. The motivation for this work came from the observation that several practical discrete logarithm-based cryptosystems, such as ElGamal, the Elliptic Curve Cryptosystems . In a first time, we describe these curves defined over a ring. Then, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. In anther article we study their cryptographic properties, an attack of the elliptic discrete logarithm problem, a new cryptosystem over these curves.
ER -