Computing Logarithms in Finite Fields of Characteristic Two

DOI10.1137/0605029zbMath0536.12010OpenAlexW1984753839WikidataQ56340552 ScholiaQ56340552MaRDI QIDQ3320493

Scott A. Vanstone, Ryoh Fuji-Hara, Ronald C. Mullin, Ian F. Blake

Publication date: 1984

Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0605029

zbMATH Keywords

algorithmEuclidean algorithmcharacteristic twocomputation of logarithmprimitive element of finite field

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Number-theoretic algorithms; complexity (11Y16) Polynomials over finite fields (11T06)

Related Items (16)

Computing discrete logarithms in cryptographically-interesting characteristic-three finite fields ⋮ Complexity of a determinate algorithm for the discrete logarithm ⋮ The generalized Weil pairing and the discrete logarithm problem on elliptic curves ⋮ Guest editorial: Special issue in honor of Scott A. Vanstone ⋮ Finding shortest lattice vectors faster using quantum search ⋮ Individual discrete logarithm with sublattice reduction ⋮ Computation of low-weight parity checks for correlation attacks on stream ciphers ⋮ Faster individual discrete logarithms in finite fields of composite extension degree ⋮ The index calculus method using non-smooth polynomials ⋮ Computation of discrete logarithms in prime fields ⋮ Computational problems in the theory of finite fields ⋮ Analysis of Rabin's irreducibility test for polynomials over finite fields ⋮ Weakness of \(\mathbb{F}_{3^{6 \cdot 1429}}\) and \(\mathbb{F}_{2^{4 \cdot 3041}}\) for discrete logarithm cryptography ⋮ A serial version of the Pohlig-Hellman algorithm for computing discrete logarithms ⋮ Faster initial splitting for small characteristic composite extension degree fields ⋮ Koblitz curves over quadratic fields

Cites Work

• New directions in cryptography
• A method for obtaining digital signatures and public-key cryptosystems
• An improved algorithm for computing logarithms over<tex>GF(p)</tex>and its cryptographic significance (Corresp.)
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