New attacks on RSA with modulus N = p2q using continued fractions
In this paper, we propose two new attacks on RSA with modulus N = p2q using continued fractions. Our first attack is based on the RSA key equation ed - φ(N)k = 1 where φ(N) = p(p - 1)(q - 1). Assuming that and , we show that can be recovered among the convergents of the continued fraction expansion...
| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
IOP Publishing
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/43055/1/jpconf15_622_012019.pdf |
| Summary: | In this paper, we propose two new attacks on RSA with modulus N = p2q using continued fractions. Our first attack is based on the RSA key equation ed - φ(N)k = 1 where φ(N) = p(p - 1)(q - 1). Assuming that and , we show that can be recovered among the convergents of the continued fraction expansion of . Our second attack is based on the equation eX - (N - (ap2 + bq2)) Y = Z where a,b are positive integers satisfying gcd(a,b) = 1, |ap2 - bq2| < N1/2 and ap2 + bq2 = N2/3+α with 0 < α < 1/3. Given the conditions , we show that one can factor N = p2q in polynomial time. |
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