New vulnerability on system of Ni = p²iqi using good approximation of Φ(N)
This paper proposes new vulnerability in m moduli of the form Ni = p2iqi for m ≥ 2 and i = 1, ...,m. The attack works when m public keys (Ni, ei) there exist m relations of the form eid − kΦ (Ni) = 1 or eidi − kiΦ (Ni) = 1 with the parameters d, di, k and ki are suitably small. By using the term N −...
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| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
Institute for Mathematical Research, Universiti Putra Malaysia
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/66552/1/Cryptology2018-7.pdf http://psasir.upm.edu.my/id/eprint/66552/ |
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| Institution: | Universiti Putra Malaysia |
| Language: | English |
| Summary: | This paper proposes new vulnerability in m moduli of the form Ni = p2iqi for m ≥ 2 and i = 1, ...,m. The attack works when m public keys (Ni, ei) there exist m relations of the form eid − kΦ (Ni) = 1 or eidi − kiΦ (Ni) = 1 with the parameters d, di, k and ki are suitably small. By using the term N − 2N2/3 − N1/3 as a good approximation of Φ(N) applying the LLL algorithm enables one to factor m moduli of the form Ni = p2iqi simultaneously. |
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