Abstract
In the perspective of RSA, given small encryption exponent e (e.g., eā=ā216ā+ā1), the top half of the decryption exponent d can be narrowed down within a small search space. This fact has been previously exploited in RSA cryptanalysis. On the contrary, here we propose certain schemes to exploit this fact towards efficient RSA decryption.
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References
Boneh, D., Durfee, G.: Cryptanalysis of RSA with Private Key d Less Than N 0.292. IEEE Transactions on Information TheoryĀ 46(4), 1339ā1349 (2000)
Boneh, D., Durfee, G., Frankel, Y.: Exposing an RSA Private Key given a Small Fraction of its Bits, http://crypto.stanford.edu/~dabo/abstracts/bits_of_d.html
Coppersmith, D.: Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities. Journal of CryptologyĀ 10(4), 233ā260 (1997)
Galbraith, S., Heneghan, C., McKee, J.: Tunable Balancing RSA, http://www.isg.rhul.ac.uk/~sdg/full-tunable-rsa.pdf
Lenstra, A.: Generating RSA moduli with a predetermined portion. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol.Ā 1514, pp. 1ā10. Springer, Heidelberg (1998)
Lenstra, A.K., Lenstra Jr., H.W.: The Development of the Number Field Sieve. Springer, Heidelberg (1993)
Maitra, S., Sarkar, S.: Efficient CRT-RSA Decryption for Small Encryption Exponents. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol.Ā 5985, pp. 26ā40. Springer, Heidelberg (2010)
Matsumoto, T., Kato, K., Imai, H.: Speeding up secret computations with insecure auxiliary devices. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol.Ā 403, pp. 497ā506. Springer, Heidelberg (1990)
Nguyen, P.Q., Shparlinski, I.: On the Insecurity of a Server-Aided RSA Protocol. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol.Ā 2248, pp. 21ā25. Springer, Heidelberg (2001)
Quisquater, J.-J., Couvreur, C.: Fast decipherment algorithm for RSA public-key cryptosystem. Electronic LettersĀ 18, 905ā907 (1982)
Rivest, R.L., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of ACMĀ 21(2), 158ā164 (1978)
Sakai, R., Morii, M., Kasahara, M.: New Key Generation Algorithm for RSA Cryptosystem. IEICE Transactions on Fundamentals of Electronics, Communications and Computer SciencesĀ 77(1), 89ā97 (1994)
Stinson, D.R.: Cryptography - Theory and Practice. 2nd Edition, Chapman & Hall/CRC (2002)
Sun, H.-M., Hinek, M.J., Wu, M.-E.: On the Design of Rebalanced RSA-CRT, http://www.cacr.math.uwaterloo.ca/techreports/2005/cacr2005-35.pdf
Vanstone, S.A., Zuccherato, R.J.: Short RSA Keys and Their Generation. Journal of CryptologyĀ 8(2), 101ā114 (1995)
Verheul, E., van Tilborg, H.: Cryptanalysis of less short RSA secret exponents. Applicable Algebra in Engineering, Communication and ComputingĀ 18, 425ā435 (1997)
de Weger, B.: Cryptanalysis of RSA with small prime difference. Applicable Algebra in Engineering, Communication and ComputingĀ 13, 17ā28 (2002)
Wiener, M.: Cryptanalysis of Short RSA Secret Exponents. IEEE Transactions on Information TheoryĀ 36(3), 553ā558 (1990)
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Maitra, S., Sarkar, S., Sen Gupta, S. (2010). Publishing Upper Half of RSA Decryption Exponent. In: Echizen, I., Kunihiro, N., Sasaki, R. (eds) Advances in Information and Computer Security. IWSEC 2010. Lecture Notes in Computer Science, vol 6434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16825-3_3
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DOI: https://doi.org/10.1007/978-3-642-16825-3_3
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