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.

Creator

• Karakoyunlu, Deniz

Contributors

• Huang, Xinming
• Sunar, Berk
• Lou, Wenjing
• Savas, Erkay

Degree

• PhD

Unit

• Electrical & Computer Engineering

Publisher

• Worcester Polytechnic Institute

Language

• English

Identifier

• etd-080810-024142

Keyword

• elliptic curve cryptography
• prime fields
• Edwards elliptic curves
• side-channel attacks
• ASIC implementation

Advisor

• Sunar, Berk

Committee

• Huang, Xinming
• Lou, Wenjing
• Savas, Erkay

Defense date

• 2010-08-08

Year

• 2010

Date created

• 2010-08-08

Resource type

• Dissertation

Rights statement

• In Copyright