Implantation FPGA de l'algorithme de chiffrement à courbes elliptiques : génération de clefs privées représentées directement en format w-NAF

Authors: Dupont, Louis
Advisor: Roy, SébastienChouinard, Jean-Yves
Abstract: The encryption of a communication on a given channel may appear hazardous. An interlocutor must transmit to another one enough information allowing both interlocutors to encrypt or decrypt the communication. Since the communication channel is visible to potentially malicious actors, this preliminary information must be exchanged without worrying about others intercepting it. Several algorithms were developed making that exchange possible. Among the most commonly used algorithms, elliptic curve cryptography provides the highest strength per bit. Elliptic curve cryptography is based on the multiplication of a point on this curve by a scalar. This operation is relatively complex when implemented in software. The use of a specialized co-processor becomes an interesting approach to perform this operation. This thesis describes the development of such a co-processor. It has been developed targeting a FPGA, minimizing the use of logical resources while maximizing the operating frequency. Moreover, the number of operations on the elliptic curve have been minimized by representing the scalar multiplying the point of the elliptic curve in its ω-NAF form. A method randomly generating an integer in its ω-NAF representation is also proposed. This method can be implemented in hardware using a minimum of logical resources.
Document Type: Mémoire de maîtrise
Issue Date: 2006
Open Access Date: 12 April 2018
Grantor: Université Laval
Collection:Thèses et mémoires

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