Finite-field discrete logarithms
Compute discrete logarithms in multiplicative groups of finite fields, separating prime fields, characteristic growth and extension structure.
8 variants · 11 entries. Compare bounds only within the same variant.
COMPARISON VARIANTREGIME / INSTANCEENTRIESBEST c
Finite-field DLPPrime fields · classical heuristicClassical · HeuristicNo deliberately supplied special-form modulus; includes full relation generation and logarithm computationgeneral prime fields F_p31.901884 Finite-field DLPSmall characteristic · heuristic expressionsClassical · HeuristicCharacteristic growth and field presentations as specified in each sourcesmall-characteristic finite fields2— Finite-field DLPFixed characteristic · provenClassical randomized · ProvableF_{p^n}, with p fixed; randomized expected timeall extension fields of fixed prime characteristic1— Finite-field DLPFixed extension degree · classical heuristicClassical · HeuristicQ=p^n with n fixed and p growingfinite fields of arbitrary fixed extension degree11.922999 Finite-field DLPPrime fields · quantumQuantum · source dependentLogical circuit and classical post-processing; assumptions stated per paperprime fields1— Finite-field DLPSmall characteristic · heuristic L(1/3)Classical · Heuristicp ≤ n^{o(√n)} in the cited function-field-sieve analysisF_{p^n} with restricted characteristic11.526286 Finite-field DLPSmall characteristic · provenClassical randomized · ProvableF_{p^n} with n > p in the cited theoremall finite fields of small characteristic1— Finite-field DLPSpecial prime fields · classical heuristicClassical · Heuristicp = r^e − s with r and s small; exploitable representation suppliedspecial-form prime fields F_p11.526286