Welcome to the resource topic for 2024/1329
Title:
Small Public Exponent Brings More: Improved Partial Key Exposure Attacks against RSA
Authors: Yansong Feng, Abderrahmane Nitaj, Yanbin Pan
Abstract:Let (N,e) be a public key of the RSA cryptosystem, and d be the corresponding private key. In practice, we usually choose a small e for quick encryption. In this paper, we improve partial private key exposure attacks against RSA with MSBs of d and small e. The key idea is that under such a setting we can usually obtain more information about the prime factors of N and then, by solving a univariate modular polynomial equation using Coppersmith’s method, N can be factored in polynomial time. Compared to previous results, we reduce the number of the leaked bits in d that are needed to mount the attack by \log_2 (e) bits. For e=65537, previous work required an additional enumeration of 17 bits to achieve our new bound, resulting in a 2^{10} (or 1,024x) increase in time consumption. Furthermore, our experiments show that for a 1024-bit modulus N, our attack can achieve the theoretical bound on a simple personal computer, which verifies the new method.
ePrint: https://eprint.iacr.org/2024/1329
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