Document Type dissertation Author Name Karakoyunlu, Deniz URN etd-080810-024142 Title Efficient Side-Channel Aware Elliptic Curve Cryptosystems over Prime Fields Degree PhD Department Electrical & Computer Engineering Advisors Berk Sunar, Advisor Xinming Huang, Committee Member Wenjing Lou, Committee Member Erkay Savas, Committee Member Keywords elliptic curve cryptography Edwards elliptic curves side-channel attacks ASIC implementation prime fields Date of Presentation/Defense 2010-08-08 Availability unrestricted
Elliptic Curve Cryptosystems (ECCs) are utilized as an alternative to traditional public-key cryptosystems, and are more suitable for resource limited environments due to smaller parameter size. In this dissertation we carry out a thorough investigation of side-channel attack aware ECC implementations over finite fields of prime characteristic including the recently introduced Edwards formulation of elliptic curves, which have built-in resiliency against simple side-channel attacks. We implement Joye's highly regular add-always scalar multiplication algorithm both with the Weierstrass and Edwards formulation of elliptic curves. We also propose a technique to apply non-adjacent form (NAF) scalar multiplication algorithm with side-channel security using the Edwards formulation. Our results show that the Edwards formulation allows increased area-time performance with projective coordinates. However, the Weierstrass formulation with affine coordinates results in the simplest architecture, and therefore has the best area-time performance as long as an efficient modular divider is available.
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