Cryptanalysis of a cubic Pell variant of RSA with primes sharing least significant bits
In this paper, we push further the cryptanalysis of a cryptosystem of the RSA’s variant which utilized a cubic Pell equation with the key equation ed − k(p2 + p + 1)(q2 + q + 1) = 1 where N = pq is an RSA modulus, e, N are publicized, while d, p, q are kept private. We consider the case where the pr...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | en |
| Published: |
Taru Publications
2024
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| Online Access: | http://eprints.utem.edu.my/id/eprint/29228/2/01197180820241529161021.pdf http://eprints.utem.edu.my/id/eprint/29228/ https://tarupublications.com/doi/10.47974/JIOS-1333 |
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| Summary: | In this paper, we push further the cryptanalysis of a cryptosystem of the RSA’s variant which utilized a cubic Pell equation with the key equation ed − k(p2 + p + 1)(q2 + q + 1) = 1 where N = pq is an RSA modulus, e, N are publicized, while d, p, q are kept private. We consider the case where the prime factors share an amount of their least significant bits (LSBs), that is p and q satisfy p – q = 2m u where m is known, and u is unknown. Through this work, we show that via Coppermith’s method and lattice basis reduction, it is feasible to retrieve the secret key d and factor N for larger values of d. |
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