Factoring with Cyclotomic Polynomials

DOI10.2307/2008664zbMath0661.10008OpenAlexW4254415077MaRDI QIDQ3809851

Eric Bach, Jeffrey O. Shallit

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2008664

zbMATH Keywords

cyclotomic fieldfactorizationcomputational number theoryMACSYMA

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Software, source code, etc. for problems pertaining to number theory (11-04) Cyclotomic extensions (11R18) Primes (11A41)

Related Items (21)

Sieve algorithms for perfect power testing ⋮ Optimal strong primes ⋮ Diffie-Hellman Oracles ⋮ Fast generation of prime numbers and secure public-key cryptographic parameters. ⋮ Mathematical problems in cryptology ⋮ On the oracle complexity of factoring integers ⋮ Fast norm computation in smooth-degree abelian number fields ⋮ Factoring integers and oracles for elliptic and hyperelliptic curves ⋮ Factorization, malleability and equivalent problems ⋮ Newman cyclotomic polynomials, refinable splines and the Euler binary partition function ⋮ Constructing nonresidues in finite fields and the extended Riemann hypothesis ⋮ A Subexponential Algorithm for Discrete Logarithms Over all Finite Fields ⋮ Factoring polynomials over special finite fields ⋮ Abelian groups, Gauss periods, and normal bases ⋮ A deterministic version of Pollard’s $p-1$ algorithm ⋮ Explicit Bounds for Primality Testing and Related Problems ⋮ Using number fields to compute logarithms in finite fields ⋮ Prime-number algorithm for public-key systems ⋮ Explicit bounds for primes in residue classes ⋮ Sequences of numbers generated by addition in formal groups and new primality and factorization tests ⋮ Algorithms for exponentiation in finite fields

Uses Software

• MACSYMA

Cites Work

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• Factoring integers with elliptic curves
• Riemann's hypothesis and tests for primality
• A bound for the least prime ideal in the Chebotarev density theorem
• Some effective cases of the Brauer-Siegel theorem
• Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers
• Factorization and Primality Tests
• A Monte Carlo Factoring Algorithm With Linear Storage
• Sums of Divisors, Perfect Numbers and Factoring
• A p + 1 Method of Factoring
• Determination of the Primality of N by Using Factors of N 2 ± 1
• Some Algorithms for Prime Testing Using Generalized Lehmer Function
• A generalization of Lehmer's functions
• What is a Reciprocity Law?
• Number fields

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