Abstract
Partial key exposure attacks, introduced by Boneh, Durfee and Frankel in 1998, aim at retrieving an RSA private key when a fraction of its bits is known. These attacks are of particular interest in the context of side-channel attacks, where the attacker can retrieve bits of the key exploiting leakages in the implementation. In this work we analyze the effectiveness of partial key exposure when a countermeasure for side-channel attacks is adopted. In particular, we consider the exponent blinding technique, which consists in randomizing the private exponent at each execution. We address our analysis to both RSA and CRT-RSA, providing theoretical proofs and experimental results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sage Mathematics Software (Version 6.2). http://www.sagemath.org
Wiener, M.J.: Cryptanalysis of short RSA secret exponents. IEEE Trans. Inf. Theory 36, 553–558 (1990)
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)
Coppersmith, D.: Finding a small root of a univariate modular equation. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 155–165. Springer, Heidelberg (1996)
Howgrave-Graham, N.: Finding small roots of univariate modular equations revisited. In: Darnell, Michael J. (ed.) Cryptography and Coding 1997. LNCS, vol. 1355, pp. 131–142. Springer, Heidelberg (1997)
Joye, M., Lepoint, T.: Partial key exposure on RSA with private exponents larger than N. In: Ryan, M.D., Smyth, B., Wang, G. (eds.) ISPEC 2012. LNCS, vol. 7232, pp. 369–380. Springer, Heidelberg (2012)
Boneh, D., Durfee, G., Frankel, Y.: An attack on RSA given a small fraction of the private key bits. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 25–34. Springer, Heidelberg (1998)
Lu, Y., Zhang, R., Lin, D.: New partial key exposure attacks on CRT-RSA with large public exponents. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 151–162. Springer, Heidelberg (2014)
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)
Herrmann, M., May, A.: Solving linear equations modulo divisors: on factoring given any bits. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 406–424. Springer, Heidelberg (2008)
Coppersmith, D.: Finding a small root of a bivariate integer equation; factoring with high bits known. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 178–189. Springer, Heidelberg (1996)
NIST: FIPS PUB 186–4 Federal Information Processing Standards Publication, Digital Signature Standard (DSS) (2013)
May, A.: New RSA vulnerabilities using lattice reduction methods. Ph.D. thesis (2003)
Kocher, P.C.: 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)
Coron, J.-S.: Resistance against differential power analysis for elliptic curve cryptosystems. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 292–302. Springer, Heidelberg (1999)
Kocher, P.C., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, p. 388. Springer, Heidelberg (1999)
Walter, C.D.: Sliding windows succumbs to big mac attack. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 286–299. Springer, Heidelberg (2001)
Clavier, C., Feix, B., Gagnerot, G., Roussellet, M., Verneuil, V.: Horizontal correlation analysis on exponentiation. In: Soriano, M., Qing, S., López, J. (eds.) ICICS 2010. LNCS, vol. 6476, pp. 46–61. Springer, Heidelberg (2010)
Fouque, P.-A., Kunz-Jacques, S., Martinet, G., Muller, F., Valette, F.: Power attack on small RSA public exponent. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 339–353. Springer, Heidelberg (2006)
Lenstra, A.K., Lenstra, H.W.J., Lovász, L.: Factoring polynomials with rational coefficients. Math. Ann. 261, 515–534 (1982)
Quisquater, J.-J., Couvreur, C.: Fast decipherment algorithm for RSA public-key cryptosystem. Electron. Lett. 18, 905–907 (1982)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Cimato, S., Mella, S., Susella, R. (2016). Partial Key Exposure Attacks on RSA with Exponent Blinding. In: Obaidat, M., Lorenz, P. (eds) E-Business and Telecommunications. ICETE 2015. Communications in Computer and Information Science, vol 585. Springer, Cham. https://doi.org/10.1007/978-3-319-30222-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-30222-5_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30221-8
Online ISBN: 978-3-319-30222-5
eBook Packages: Computer ScienceComputer Science (R0)