A new RSA vulnerability using continued fractions

Authors:
Dieaa I. Nassr;Hatem M. Bahig;Ashraf Bhery;Sameh S. Daoud
Affiliations:
Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt;Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt;Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt;Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt
Venue:
AICCSA '08 Proceedings of the 2008 IEEE/ACS International Conference on Computer Systems and Applications
Year:
2008

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Abstract

Let (n = pq, e) be an RSA public key with private exponent d = nδ where p and q are large primes of the same bit size. Suppose that p0 ≥ be √n approximation of p with |p − p0| ≤ 1/8nα, α ≤ 1/2. Using continued fractions, we show that the system is insecure if δ