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Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 52-402
Full Name: Abdelhakim Chillali
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Age: ON
Sex: Male
Address: Fés
Country: MOROCCO
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E-mail address: chil2007@voila.fr
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Title of the Paper: Elliptic Curve And Cryptography
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Number of paper pages: 10
Abstract: 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[e], with Fq a finite field of order q and with the relation en = 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 s!
tudy their cryptographic properties, an attack of the elliptic discrete logarithm problem, a new cryptosystem over these curves.
Keywords: Elliptic Curve, Rings, Cryptography, DLP, the elliptic discrete logarithm problem
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