On the statistical properties of Diffie-Hellman distributions

DOI10.1007/s11856-000-1270-1zbMath0997.11066OpenAlexW191763761WikidataQ101263547 ScholiaQ101263547MaRDI QIDQ5932009

John B. Friedlander, Igor E. Shparlinski, Michael J. Larsen, Ran Canetti, Sergei V. Konyagin, Daniel B. Lieman

Publication date: 12 November 2002

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-000-1270-1

zbMATH Keywords

exponential sumsbounds for double exponential sumsDiffie-Hellman distributionDiffie-Hellman triplesdistribution of the most significant bitsleast significant bits

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Estimates on exponential sums (11L07) Cryptography (94A60) Exponential sums (11T23)

Related Items (25)

New bounds on exponential sums related to the Diffie-Hellman distributions ⋮ Character sums with exponential functions ⋮ Sparse univariate polynomials with many roots over finite fields ⋮ Estimating the number of roots of trinomials over finite fields ⋮ Bounds of Gauss sums in finite fields ⋮ Root repulsion and faster solving for very sparse polynomials over \(p\)-adic fields ⋮ Distribution of integral values for the ratio of two linear recurrences ⋮ On the number of distinct roots of a lacunary polynomial over finite fields ⋮ Roots of sparse polynomials over a finite field ⋮ On the uniformity of distribution of the RSA pairs ⋮ Security of polynomial transformations of the Diffie-Hellman key. ⋮ Double exponential sums over thin sets ⋮ On the distribution of the power generator ⋮ Common composites of triangular polynomial systems and hash functions ⋮ Threshold circuit lower bounds on cryptographic functions ⋮ Exponential function analogue of Kloosterman sums ⋮ On the singularity of generalised Vandermonde matrices over finite fields ⋮ Optimal Randomness Extraction from a Diffie-Hellman Element ⋮ Value Sets of Sparse Polynomials ⋮ Sublinear Root Detection and New Hardness Results for Sparse Polynomials over Finite Fields ⋮ On the complexity of the discrete logarithm and Diffie-Hellman problems ⋮ Exponential Sums with Sparse Polynomials over Finite Fields ⋮ Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition ⋮ Quasirandom arithmetic permutations ⋮ On the distribution of the Diffie-Hellman pairs

Cites Work

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• Algorithms for Black-Box Fields and their Application to Cryptography
• ON THE CONSTRUCTION OF A PRIMITIVE NORMAL BASIS IN A FINITE FIELD
• ARTIN'S CONJECTURE FOR PRIMITIVE ROOTS
• New directions in cryptography
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