Abstract
Embedded exponentiation techniques have become a key concern for security and efficiency in hardware devices using public key cryptography. An exponentiation is basically a sequence of multiplications and squarings, but this sequence may reveal exponent bits to an attacker on an unprotected implementation. Although this subject has been covered for years, we present in this paper new exponentiation algorithms based on trading multiplications for squarings. Our method circumvents attacks aimed at distinguishing squarings from multiplications at a lower cost than previous techniques. Last but not least, we present new algorithms using two parallel squaring blocks which provide the fastest exponentiation to our knowledge.
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
Preview
Unable to display preview. Download preview PDF.
References
Amiel, F., Feix, B., Marcel, L., Villegas, K.: Passive and Active Combined Attacks. In: Workshop on Fault Detection and Tolerance in Cryptography - FDTC 2007, IEEE Computer Society Press, Los Alamitos (2007)
Amiel, F., Feix, B., Tunstall, M., Whelan, C., Marnane, W.P.: Distinguishing Multiplications from Squaring Operations. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 346–360. Springer, Heidelberg (2009)
Barrett, P.: Implementing the Rivest Shamir and Adleman Public Key Encryption Algorithm on a Standard Digital Signal Processor. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 311–323. Springer, Heidelberg (1987)
Chevallier-Mames, B., Ciet, M., Joye, M.: Low-Cost Solutions for Preventing Simple Side-Channel Analysis: Side-Channel Atomicity. IEEE Transactions on Computers 53(6), 760–768 (2004)
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)
Diffie, W., Hellman, M.E.: New Directions in Cryptography. IEEE Transactions on Information Theory 22(6), 644–654 (1976)
FIPS PUB 186-3. Digital Signature Standard. National Institute of Standards and Technology (October 2009)
Fouque, P.-A., Valette, F.: The Doubling Attack – Why Upwards is Better Than Downwards. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 269–280. Springer, Heidelberg (2003)
Hankerson, D., Menezes, A.J., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer Professional Computing Series (January 2003)
Joye, M., Yen, S.-M.: The Montgomery Powering Ladder. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 291–302. Springer, Heidelberg (2003)
Kocher, P., Jaffe, J., Jun, B.: Introduction to Differential Power Analysis and Related Attacks (1998)
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)
Kocher, P.C., Jaffe, J., Jun, B.: Differential Power Analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
Menezes, A., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press (1996)
Montgomery, P.L.: Speeding the Pollard and Elliptic Curve Methods of Factorization. MC 48, 243–264 (1987)
Rivest, R.L., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public-Key Cryptosystems. Communications of the ACM 21, 120–126 (1978)
Schmidt, J.-M., Tunstall, M., Avanzi, R., Kizhvatov, I., Kasper, T., Oswald, D.: Combined Implementation Attack Resistant Exponentiation. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol. 6212, pp. 305–322. Springer, Heidelberg (2010)
Yen, S.-M., Joye, M.: Checking Before Output Not Be Enough Against Fault-Based Cryptanalysis. IEEE Trans. Computers 49(9), 967–970 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clavier, C., Feix, B., Gagnerot, G., Roussellet, M., Verneuil, V. (2011). Square Always Exponentiation. In: Bernstein, D.J., Chatterjee, S. (eds) Progress in Cryptology – INDOCRYPT 2011. INDOCRYPT 2011. Lecture Notes in Computer Science, vol 7107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25578-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-25578-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25577-9
Online ISBN: 978-3-642-25578-6
eBook Packages: Computer ScienceComputer Science (R0)