#11539. Increment of insecure RSA private exponent bound through perfect square RSA diophantine parameters cryptanalysis

August 2026publication date
Proposal available till 31-05-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Law;
Computer Science (all);
Computer Science Applications;
Software;
Hardware and Architecture;
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Abstract:
The public parameters of the RSA cryptosystem are represented by the pair of integers N and e. In this work, first we show that if e satisfies the Diophantine equation for appropriate values of x,y and z under certain specified conditions, then one is able to factor N. That is, the unknown [Formula] can be found amongst the convergents of [Formula] via continued fractions algorithm. Consequently, Coppersmiths theorem is applied to solve for prime factors p and q in polynomial time. We also report a second weakness that enabled us to factor k instances of RSA moduli. This weakness was identified by solving the simultaneous Diophantine approximations using the lattice basis reduction technique. We note that this work extends the bound of insecure RSA decryption exponents.
Keywords:
Algebraic cryptanalysis; Diophantine approximations; Integer factorization problem; Kleptography; Lattice basis reduction; RSA cryptosystem

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