fix(math): reduce Bézout coefficient modulo irreducible polynomial in gfExtendedEuclideanWithTrace (#1715) - #1811
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… gfExtendedEuclideanWithTrace (csxark#1715) - Apply polynomial modulo reduction (gfDivide(s0, modulus).r) after Extended Euclidean algorithm loop in lib/math/galoisField.ts - Format inverseHex as 2 uppercase hex digits, guaranteeing canonical 8-bit element representation in GF(2^8) - Add unit test coverage in tests/math/galoisField.test.ts asserting EEA inverseHex matches gfInverse for all non-zero elements [1..255] across field polynomials (0x11b, 0x11d, 0x12d)
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Pull Request
Description
Fixes issue #1715 by applying polynomial modulo reduction ($s_0$ in $\text{GF}(2^8)$ matching
gfDivide(s0, modulus).r) to the Bézout coefficientgfExtendedEuclideanWithTrace. This guarantees thatinverseHexoutputs a canonical 2-digit uppercase 8-bit hex string ingfInverse(a)across all non-zero field elements.Related Issue
Closes #1715
Scope
lib/cipher/**,lib/math/**)app/**,components/**)lib/workers/**,hooks/use*Worker.ts)docs/**,*.md, MDX content)tests/**)Changes Made
const finalS = gfDivide(s0, modulus).ringfExtendedEuclideanWithTraceinsidelib/math/galoisField.tsafter the Euclidean loop completes.finalSas a 2-character uppercase hex string (padStart(2, '0').toUpperCase()).tests/math/galoisField.test.tsverifyinggfExtendedEuclideanWithTracematchesgfInversefor all non-zero elements0x11b,0x11d, and0x12dfield polynomials.Testing
npm testpasses locally.npm run typecheckpasses locally.npm run lintpasses locally.lib/math/**file stays at or above 80%.Simulation vs. Live Data
Screenshots
N/A (Galois Field Polynomial Modulo Reduction & Trace Formatting)
Checklist
Applicable Checklist
Architecture Review Checklist
lib/math/galoisField.tstests/math/galoisField.test.tsAdditional Notes
All Galois Field math unit tests (
npx vitest run tests/math/galoisField.test.ts) passed cleanly.