Coppersmith's lattices and ``focus groups: an attack on small-exponent RSA

DOI10.1016/j.jnt.2021.01.002zbMath1469.11476arXiv1708.09445OpenAlexW2949397001MaRDI QIDQ1998906

Stephen D. Miller, Ramarathnam Venkatesan, Bhargav P. Narayanan

Publication date: 9 March 2021

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.09445

zbMATH Keywords

factoringCoppersmith's methodlattice basis reductionlattice attackssmall exponent RSA

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Lattices and convex bodies (number-theoretic aspects) (11H06)

Related Items (2)

Practical attacks on small private exponent RSA: new records and new insights ⋮ Forty years of attacks on the RSA cryptosystem: A brief survey

Uses Software

• NTL
• fpLLL

Cites Work

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• Factoring polynomials with rational coefficients
• A variant of Wiener's attack on RSA
• Factoring RSA Keys from Certified Smart Cards: Coppersmith in the Wild
• Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known
• Mathematics of Public Key Cryptography
• A Unified Framework for Small Secret Exponent Attack on RSA
• Approximate common divisors via lattices
• Cryptanalysis of short RSA secret exponents
• Maximizing Small Root Bounds by Linearization and Applications to Small Secret Exponent RSA
• An LLL Algorithm with Quadratic Complexity
• A method for obtaining digital signatures and public-key cryptosystems
• Cryptanalysis of RSA with private key d less than N/sup 0.292/
• Toward a Rigorous Variation of Coppersmith’s Algorithm on Three Variables
• A Strategy for Finding Roots of Multivariate Polynomials with New Applications in Attacking RSA Variants

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