New vulnerabilities of RSA modulus type N = p²q
This paper proposes new attacks on RSA modulus of type N = p²q. Given k RSA moduli Nі = p²iqi for k ≥ 2 and i = 1, ..., k, the attack works when k RSA public keys (Ni, ei) are such that there exist k relations of the shape eix - Niyi = zi – (ap²i + bq²i)yi or of the shape eixi −Niy = zi −(ap²i + bq²...
| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
Institute for Mathematical Research, Universiti Putra Malaysia
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/66511/1/Cryptology2016-4.pdf |
| Summary: | This paper proposes new attacks on RSA modulus of type N = p²q. Given k RSA moduli Nі = p²iqi for k ≥ 2 and i = 1, ..., k, the attack works when k RSA public keys (Ni, ei) are such that there exist k relations of the shape eix - Niyi = zi – (ap²i + bq²i)yi or of the shape eixi −Niy = zi −(ap²i + bq²i)y where the parameters x, xi, y, yi and zi are suitably small in terms of the prime factors of the moduli. The proposed attacks utilizing the LLL algorithm enables one to factor the k RSA moduli Ni simultaneously. |
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