SWhat changed
Lenstra, Lenstra and Lovász gave a polynomial-time lattice-basis reduction algorithm with short-vector approximation guarantees and used it to factor univariate polynomials over the rational numbers in polynomial time.
Scientific scope
Lenstra, Lenstra and Lovász gave a polynomial-time lattice-basis reduction algorithm with short-vector approximation guarantees and used it to factor univariate polynomials over the rational numbers in polynomial time. The algorithm reduces a lattice basis under specified rational/integer input and size-reduction/Lovász conditions; it does not generally find an exact shortest vector. Its polynomial bit bound includes input size. Polynomial factorization uses its own coefficient and precision assumptions. Later stronger reductions, floating-point variants and practical cryptographic successes are separate.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- A. K. Lenstra · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- H. W. Lenstra Jr. · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- L. Lovász · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Lenstra, Lenstra and Lovasz, Factoring Polynomials with Rational Coefficients, Math Ann 261(4)515-534(1982), author-hosted journal original
- Publisher Crossref deposit for 10.1007/BF 01457454
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