Abstract
We consider four variants of the RSA cryptosystem with an RSA modulus \(N=pq\) where the public exponent e and the private exponent d satisfy an equation of the form \(ed-k\left( p^2-1\right) \left( q^2-1\right) =1\). We show that, if the prime numbers p and q share most significant bits, that is, if the prime difference \(|p-q|\) is sufficiently small, then one can solve the equation for larger values of d, and factor the RSA modulus, which makes the systems insecure.
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Cherkaoui-Semmouni, M., Nitaj, A., Susilo, W., Tonien, J. (2021). Cryptanalysis of RSA Variants with Primes Sharing Most Significant Bits. In: Liu, J.K., Katsikas, S., Meng, W., Susilo, W., Intan, R. (eds) Information Security. ISC 2021. Lecture Notes in Computer Science(), vol 13118. Springer, Cham. https://doi.org/10.1007/978-3-030-91356-4_3
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