ANOTHER PROOF OF WIENER'S SHORT SECRET EXPONENT
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Published:
Feb 28, 2019
Keywords:
RSA cryptosystem continued fractions secret exponent cryptanalysis Wiener’s theorem
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Abstract
Wiener’s short secret exponent attack is a well-known crypt-analytical result upon the RSA cryptosystem using a Diophantine’s method called continued fractions. We recall that Wiener’s attack works efficiently on RSA with the condition that the secret exponent . Later, the upper bound was improved satisfying
. In this work, we present another proof to Wiener’s short secret exponent satisfying
. We remark that our result is slightly better than the previously mentioned attacks.
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How to Cite
Asbullah, M. A., & Kamel Ariffin, M. R. (2019). ANOTHER PROOF OF WIENER’S SHORT SECRET EXPONENT. Malaysian Journal of Science, 38(Sp 1), 67–73. https://doi.org/10.22452/mjs.sp2019no1.6
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ICMSS2018 (Published)
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References
Asbullah, M. A. and Ariffin, M. R. K. (2014). Comparative Analysis of Three Asymmetric Encryption Schemes Based Upon the Intractability of Square Roots Modulo N=p^2 q. 4th International Cryptology and Information Security Conference 2014 (CRYPTOLOGY2014) 24-26 June 2014, Putrajaya, 86-99.
Asbullah, M. A. and Ariffin, M. R. K. (2015). New Attack on RSA with Modulus N=〖 p〗^2 q Using Continued Fractions, Journal of Physics 622 191-199.
Asbullah, M. A. and Ariffin, M. R. K. (2016a) Analysis on the AA _β Cryptosystem. 5th International Cryptology and Information Security Conference 2016 (Cryptology2016), 31 May-2 June 2016, Sabah, Malaysia, 41-48.
Asbullah, M. A. and Ariffin, M. R. K. (2016b). Analysis on the Rabin-p cryptosystem. 4th International Conference on Fundamental and Applied Sciences (ICFAS2016). AIP Conf. Proc. 1787 080012-1 - 080012-8
Asbullah, M. A. and Ariffin, M. R. K. (2016c). Design of Rabin-like cryptosystem without decryption failure. Malaysian Journal of Mathematical Sciences 10 (S) 1 - 18.
de Weger, B. (2002). Cryptanalysis of RSA with Small Prime Difference Applicable Algebra in Enginering, Commnication and Computing AAECC 13 17-28.
Maitra, S. and Sarkar, S. (2008). Revisiting Wiener’s Attack- New Weak Keys in RSA. 11th International Conference on Information Security ISC Taipei.
Nitaj, A. (2013). Diophantine and lattice cryptanalysis of the RSA cryptosystem In Artificial Intelligence, Evolutionary Computing and Metaheuristics Springer Berlin Heidelberg 139-168.
Rivest, R., Shamir, A. and Adleman, L. (1978). A Method for Obtaining digital signatures and public-key cryptosystems Communications of the ACM 21 (2) 120-126.
Wiener M. (1990). Cryptanalysis of Short RSA Secret Exponents IEEE Trans. Inform. Theory 36 3 553-558.
Asbullah, M. A. and Ariffin, M. R. K. (2015). New Attack on RSA with Modulus N=〖 p〗^2 q Using Continued Fractions, Journal of Physics 622 191-199.
Asbullah, M. A. and Ariffin, M. R. K. (2016a) Analysis on the AA _β Cryptosystem. 5th International Cryptology and Information Security Conference 2016 (Cryptology2016), 31 May-2 June 2016, Sabah, Malaysia, 41-48.
Asbullah, M. A. and Ariffin, M. R. K. (2016b). Analysis on the Rabin-p cryptosystem. 4th International Conference on Fundamental and Applied Sciences (ICFAS2016). AIP Conf. Proc. 1787 080012-1 - 080012-8
Asbullah, M. A. and Ariffin, M. R. K. (2016c). Design of Rabin-like cryptosystem without decryption failure. Malaysian Journal of Mathematical Sciences 10 (S) 1 - 18.
de Weger, B. (2002). Cryptanalysis of RSA with Small Prime Difference Applicable Algebra in Enginering, Commnication and Computing AAECC 13 17-28.
Maitra, S. and Sarkar, S. (2008). Revisiting Wiener’s Attack- New Weak Keys in RSA. 11th International Conference on Information Security ISC Taipei.
Nitaj, A. (2013). Diophantine and lattice cryptanalysis of the RSA cryptosystem In Artificial Intelligence, Evolutionary Computing and Metaheuristics Springer Berlin Heidelberg 139-168.
Rivest, R., Shamir, A. and Adleman, L. (1978). A Method for Obtaining digital signatures and public-key cryptosystems Communications of the ACM 21 (2) 120-126.
Wiener M. (1990). Cryptanalysis of Short RSA Secret Exponents IEEE Trans. Inform. Theory 36 3 553-558.