Abstract
The RSA and Rabin encryption function are respectively defined as E N(x) = x e mod N and E N(x) = x 2 mod N, where N is a product of two large random primes p, q and e is relatively prime to φ(N). We present a much simpler and stronger proof of the result of Alexi, Chor, Goldreich and Schnorr [ACGS88] that the following problems are equivalent by probabilistic polynomial time reductions: (1) given E N(x) find x; (2) given E N(x) predict the least-significant bit of x with success probability \( \frac{1} {2} + \frac{1} {{poly(n)}} \), where N has n bits. The new proof consists of a more efficient algorithm for inverting the RSA/Rabin-function with the help of an oracle that predicts the least-significant bit of x. It yields provable security guarantees for RSA-message bits and for the RSA-random number generator for moduli N of practical size.
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Fischlin, R., Schnorr, C.P. (1997). Stronger Security Proofs for RSA and Rabin Bits. In: Fumy, W. (eds) Advances in Cryptology — EUROCRYPT ’97. EUROCRYPT 1997. Lecture Notes in Computer Science, vol 1233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69053-0_19
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DOI: https://doi.org/10.1007/3-540-69053-0_19
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