Elliptic curve cryptosystems offer security comparable to that of traditional asymmetric cryptosystems, such as those based on the RSA encryption and digital signature algorithms, with smaller keys and computationally more efficient algorithms. The ability to use smaller keys and computationally more efficient algorithms than traditional asymmetric cryptographic algorithms are two of the main reasons why elliptic curve cryptography has become popular. As the popularity of elliptic curve cryptography increases, the need for efficient hardware solutions that accelerate the computation of elliptic curve point multiplications also increases. This dissertation introduces elliptic curve processor architectures suitable for the computation of point multiplications for curves defined over fields GF(2^m) and curves defined over fields GF(p). Each of the processor architectures presented here allows designers to tailor the performance and hardware requirements according to their performance and cost goals. Moreover, these architectures are well suited for implementation in modern field programmable gate arrays (FPGAs). This point was proved with prototyped implementations. The fastest prototyped GF(2^m) processor can compute an arbitrary point multiplication for curves defined over fields GF(2^167) in 0.21 milliseconds and the prototyped processor for the field GF(2^192-2^64-1) is capable of computing a point multiplication in about 3.6 milliseconds. The most critical component of an elliptic curve processor is its arithmetic unit. A typical arithmetic unit includes an adder/subtractor, a multiplier, and possibly a squarer. Some of the architectures presented in this work are based on multiplier and squarer architectures developed as part of the work presented in this dissertation. The GF(2^m) least significant bit super-serial multiplier architecture, the GF(2^m) most significant bit super-serial multiplier architecture, and a new GF(p) Montgomery multiplier architecture were developed as part of this work together with a new squaring architecture for GF(2^m).
Worcester Polytechnic Institute
Electrical & Computer Engineering
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Orlando, G. (2002). Efficient Elliptic Curve Processor Architectures for Field Programmable Logic. Retrieved from https://digitalcommons.wpi.edu/etd-dissertations/77
computer arithmetic, elliptic curves, cryptography, Data encryption (Computer science), Curves, Elliptic, Field programmable gate arrays