Optimizing Galois Field Arithmetic forDiverse Processor Architectures and Applications

encrypt blocks ofdatainthecurrent NISTadvanced encryption standard [14]. Current memory, CPUcache sizes Galoisfield implementations arecentral tothedesign of andpreferred approaches limit mostapplications topermanyreliable andsecure systems, withmanysystems im- forming computation ineither GF(28) orGF(216). The plementing theminsoftware. ThetwomostcommonGalois goalofourresearch istostudy themultiplication perforfield operations areaddition andmultiplication; typically, manceofthese commonfields, propose analternate repmultiplication isfarmoreexpensive thanaddition. Insoft- resentation forarbitrary-sized fields andcompare perforware, multiplication isgenerally donewithalook-up toa manceacross allrepresentations ondifferent CPUarchipre-computed table, limiting thesize ofthefield andresult- tectures andfordifferent workloads. inginuneven performance across architectures andappli- Multiplication inGF(2.) isusually done precations. Mutplaln1 F2)1 sal oeusingpe Iathions pp,wfraay extntl-sdm computed look-up tables, whileaddition oftwoelements