Abstract
Consider the RSA public key cryptosystem with the parameters N = pq, q < p < 2q, public encryption exponent e and private decryption exponent d. In this paper, cryptanalysis of RSA is studied given that some amount of the Most Significant Bits (MSBs) of d is exposed. In Eurocrypt 2005, a lattice based attack on this problem was proposed by Ernst, Jochemsz, May and de Weger. In this paper, we present a variant of their method which provides better experimental results depending on practical lattice parameters and the values of d. We also propose a sublattice structure that improves the experimental results significantly for smaller decryption exponents.
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References
Aono, Y.: A New Lattice Construction for Partial Key Exposure Attack for RSA. In: Jarecki, S., Tsudik, G. (eds.) Public Key Cryptography – PKC 2009. LNCS, vol. 5443, pp. 34–53. Springer, Heidelberg (2009)
Blömer, J., May, A.: New Partial Key Exposure Attacks on RSA. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 27–43. Springer, Heidelberg (2003)
Boneh, D., Durfee, G., Frankel, Y.: Exposing an RSA Private Key Given a Small Fraction of its Bits. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 25–34. Springer, Heidelberg (1998)
Cohen, H.: A Course in Computational Algebraic Number Theory. Springer, Heidelberg (1996)
Coppersmith, D.: Small Solutions to Polynomial Equations and Low Exponent Vulnerabilities. Journal of Cryptology 10(4), 223–260 (1997)
Coron, J.-S.: Finding Small Roots of Bivariate Integer Equations Revisited. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 492–505. Springer, Heidelberg (2004)
Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd edn. Springer, New York (2007)
Ernst, M., Jochemsz, E., May, A., de Weger, B.: Partial Key Exposure Attacks on RSA up to Full Size Exponents. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 371–386. Springer, Heidelberg (2005)
Herrmann, M., May, A.: Maximizing Small Root Bounds by Linearization and Applications to Small Secret Exponent RSA. In: Nguyen, P.Q., Pointcheval, D. (eds.) Public Key Cryptography – PKC 2010. LNCS, vol. 6056, pp. 53–69. Springer, Heidelberg (2010)
Jochemsz, E., May, A.: A Strategy for Finding Roots of Multivariate Polynomials with new Applications in Attacking RSA Variants. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 267–282. Springer, Heidelberg (2006)
Jochemsz, E., May, A.: A Polynomial Time Attack on RSA with Private CRT-Exponents Smaller Than N 0.073. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 395–411. Springer, Heidelberg (2007)
Kocher, P.: Timing attacks on implementations of Diffie-Hellman, RSA, DSS and other systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996)
Kocher, P., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring Polynomials with Rational Coefficients. Mathematische Annalen 261, 513–534 (1982)
Rivest, R.L., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of ACM 21(2), 158–164 (1978)
Sarkar, S., Maitra, S.: Improved Partial Key Exposure Attacks on RSA by Guessing a Few Bits of One of the Prime Factors. In: Lee, P.J., Cheon, J.H. (eds.) ICISC 2008. LNCS, vol. 5461, pp. 37–51. Springer, Heidelberg (2009)
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Sarkar, S., Sen Gupta, S., Maitra, S. (2010). Partial Key Exposure Attack on RSA – Improvements for Limited Lattice Dimensions. In: Gong, G., Gupta, K.C. (eds) Progress in Cryptology - INDOCRYPT 2010. INDOCRYPT 2010. Lecture Notes in Computer Science, vol 6498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17401-8_2
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DOI: https://doi.org/10.1007/978-3-642-17401-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17400-1
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