Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)
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- Candidate signal: MethodsConsensus signal: none
- Teacher disagreement score
- 0.702
- Threshold uncertainty score
- 0.942
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
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- Teacher spread
- 0.231 · how far apart the two teachers sit on this one work
- Validation status
score_only:v0-immature-baseline· verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it
Abstract
Representing the field elements with respect to the polynomial (or standard) basis, we consider bit parallel architectures for multiplication over the finite field GF(2m). In this effect, first we derive a new formulation for polynomial basis multiplication in terms of the reduction matrix Q. The main advantage of this new formulation is that it can be used with any field defining irreducible polynomial. Using this formulation, we then develop a generalized architecture for the multiplier and analyze the time and gate complexities of the proposed multiplier as a function of degree m and the reduction matrix Q. To the best of our knowledge, this is the first time that these complexities are given in terms of Q. Unlike most other articles on bit parallel finite field multipliers, here we also consider the number of signals to be routed in hardware implementation and we show that, compared to the well-known Mastrovito's multiplier, the proposed architecture has fewer routed signals. The proposed generalized architecture is further optimized for three special types of polynomials, namely, equally spaced polynomials, trinomials, and pentanomials. We have obtained explicit formulas and complexities of the multipliers for these three special irreducible polynomials. This makes it very easy for a designer to implement the proposed multipliers using hardware description languages like VHDL and Verilog with minimum knowledge of finite field arithmetic.
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The record
- Venue
- IEEE Transactions on Computers
- Topic
- Cryptography and Residue Arithmetic
- Field
- Computer Science
- Canadian institutions
- University of Waterloo
- Funders
- Natural Sciences and Engineering Research Council of Canada
- Keywords
- Finite fieldTrinomialPolynomial basisMultiplier (economics)Multiplication (music)Irreducible polynomialGF(2)MathematicsFinite field arithmeticPrimitive polynomialArithmeticPolynomialMatrix multiplicationDiscrete mathematicsComputer scienceMatrix polynomialCombinatorics
- Has abstract in OpenAlex
- yes