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The study aims to investigate the efficacy of the generalized Wiener attack on the RSA cryptosystem, focusing on secret exponents.

January 24, 2026

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Wiener attack and weak keys of the RSA cryptosystem

ATAndrey E. Trishin

Key Points

The study aims to investigate the efficacy of the generalized Wiener attack on the RSA cryptosystem, focusing on secret exponents.
Analyzed the generalized Wiener attack on RSA
Estimated the fraction of weak secret exponents
Assessed both small and large secret exponents.
Proved the ability to find large secret exponents.
Heuristically estimated that the fraction of weak exponents is O(N−1/2).

Abstract

Abstract It is proved that the generalized Wiener attack on the RSA cryptosystem allows one to find not only small, but also some large secret exponents d , and the fraction of exponents d which are weak against this attack is heuristically estimated as O ( N −1/2 ).

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Andrey E. Trishin (Wed,) studied this question.

synapsesocial.com/papers/69746050bb9d90c67120a265 https://doi.org/https://doi.org/10.1515/dma-2025-0027

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Wiener attack and weak keys of the RSA cryptosystem

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Abstract

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