scientific article

zbMath0780.11064MaRDI QIDQ3137899

Igor E. Shparlinski

Publication date: 11 October 1993

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

computational complexityelliptic curveslinear recurring sequencesautomatafast algorithmsfinite fieldscryptographyrational pointspolynomial factorizationalgebraic curves over finite fieldsdiscrete logarithm problemcomputer sciencecoding theoryalgebraic geometryirreducible polynomialsalgebraic complexity theoryprimitive polynomialsinteger factorizationfast exponentiationalgebraic number theorypolynomial multiplicationpolynomials with integer coefficientsconstruction of basescomputational algebraic number theorydistribution of primitive pointsdistribution of primitive polynomialsfactorization of bivariate polynomialsstrengthening of the Weil-Serre bound

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Rational points (14G05) Number-theoretic algorithms; complexity (11Y16) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Curves over finite and local fields (11G20) Polynomials over finite fields (11T06) Algebraic number theory computations (11Y40) Arithmetic theory of polynomial rings over finite fields (11T55) Finite fields and commutative rings (number-theoretic aspects) (11Txx)

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Uses Software

• FAST16

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