Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A practical algorithm for exact array dependence analysis
Communications of the ACM
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
Reed-Solomon Codes and Their Applications
Reed-Solomon Codes and Their Applications
TPCD '94 Proceedings of the Second International Conference on Theorem Provers in Circuit Design - Theory, Practice and Experience
Verification of Floating-Point Adders
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Design Methodology for a One-Shot Reed-Solomon Encoder and Decoder
ICCD '99 Proceedings of the 1999 IEEE International Conference on Computer Design
Circuit Design from Kronecker Galois Field Decision Diagrams for Multiple-Valued Functions
ISMVL '97 Proceedings of the 27th International Symposium on Multiple-Valued Logic
An Optimized S-Box Circuit Architecture for Low Power AES Design
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Efficient gröbner basis reductions for formal verification of galois field multipliers
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
| Hi-index | 0.00 |
The Galois field GF(2m) is an important number system that is widely used in applications such as error correction codes (ECC), and complicated combinations of arithmetic operations are performed in those applications. However, few practical formal methods for algorithm verification at the word-level have ever been developed. We have defined a logic system, GF2m -arithmetic, that can treat non-linear and nonconvex constraints, for describing specifications and implementations of arithmetic algorithms over GF(2m). We have investigated various decision techniques for the GF2m -arithmetic and its subclasses, and have performed an automatic correctness proof of a (n, n 4) Reed-Solomon ECC decoding algorithm. Because the correctness criterion is in an efficient subclass of the GF2m -arithmetic (k -field-size independent), the proof is completed in significantly reduced time, less than one second for any m ≥ 3 and n ≥ 5, by using a combination of polynomial division and variable elimination over GF(2m), without using any costly techniques such as factoring or a decision over GF(2) that can easily increase the verification time to more than a day.