Elliptic Curve Cryptosystems on Reconfigurable Hardware

by Martin Christopher Rosner
Security issues will play an important role in the majority of communication and computer networks of the future. As the Internet becomes more and more accessible to the public, security measures will have to be strengthened. Elliptic curve cryptosystems allow for shorter operand lengths than other public-key schemes based on the discrete logarithm in nite elds and the integer factorization problem and are thus attractive for many applications.
This thesis describes an implementation of a crypto engine based on elliptic curves. The underlying algebraic structures are composite Galois fields GF((2n)m) in a standard base representation. As a major new feature, the system is developed for a recon gurable platform based on Field Programmable Gate Arrays (FPGAs). FPGAs combine the flexibility of software solutions with the security of traditional hardware implementations. In particular, it is possible to easily change all algorithm parameters such as curve coefficients, field order, or field representation.
The thesis deals with the design and implementation of elliptic curve point multiplication architectures. The architectures are described in VHDL and mapped to Xilinx FPGA devices. Architectures over Galois fields of dierent order and representation were implemented and compared. Area and timing measurements are provided for all architectures. It is shown that a full point multiplication on elliptic curves of real-world size can be implemented on commercially available FPGAs.

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