Hardware Implementation of Finite-Field Arithmetic

by Deschamps

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Implement Finite-Field Arithmetic in Specific Hardware (FPGA and ASIC) Master cutting-edge electronic circuit synthesis and design with help from this detailed guide. Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation, and division. This comprehensive resource begins with an overview of mathematics, covering algebra, number theory, finite fields, and cryptography. The book then presents algorithms which can be executed and verified with actual input data. Logic schemes and VHDL models are described in such a way that the corresponding circuits can be easily simulated and synthesized. The book concludes with a real-world example of a finite-field application--elliptic-curve cryptography. This is an essential guide for hardware engineers involved in the development of embedded systems. Get detailed coverage of:

368 pages, Hardcover

First published January 12, 2009

Reviews

[Kevin Neilson · Rating 3 out of 5]

Overall, this is a decent book on a complex subject. Admittedly, Galois arithmetic is a hard subject to make clear, but I thought a lot of the book could have been clearer. It skews more toward cryptography than error correction, so there are no sections, on, say, the Chien Search, or finding roots of polynomials. The choice of Ada to show algorithms is odd: the code is understandable, but Matlab/Octave code would have been much more useful. The hardware implementations could have been more practical. I saw no mention of using lookup tables, for example, for inversions with small m. The section on Itoh-Tsujii was very brief, even though it's probably more practical than the other inversion algorithms detailed. There was a lot of emphasis on bit-serial algorithms, which are no longer very useful. If you have enough time to do something bit-serially, you'd do it in software. Everything I build these days must operate on hundreds of symbols per cycle; doing one symbol in m cycles is a glacial pace. Again, though, it's a tough subject to cover, and this is one of the better volumes on the subject.

[Rex · Rating 5 out of 5]

Great book for hardware people who have zero knowledge in number theory! It gives the most fundamental number theory introduction. Then, it uses the language that electrical engineer can understand to explain what finite field circuit should look like.

Lots of codes are also provided to facilitate fast learning.

[Chenglu Jin · Rating 5 out of 5]

Good for hardware implementation, but it is hard for beginner to learn the math background for finite field.