Abstract
Side channel attacks have been attracted by most implementers of cryptographic primitives. And Randomized Exponentiation Algorithm (REA) is believed to be a good countermeasure against them. This paper analyzes the security of the two well-known REAs, the Ha-Moon algorithm and the MIST algorithm. Finding the fact that the intermediate values are variable in two cases, this paper shows that Ha-Moon algorithm is not secure even when it deploys both randomized binary recording technique and branch removing technique for DPA and SPA, respectively. In addition, this paper analyzes the security of the MIST algorithm. Some adaptively chosen ciphertext attacker can lower the security deeply, which can be placed more below than Walter’s analysis.
This research was done during the first author was enrolled in POSTECH. This research was supported by University IT Research Center Project, the Brain Korea 21 Project.
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
Chari, S., Rao, J.R., Rohatgi, P.: Template attacks. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 13–28. Springer, Heidelberg (2003)
Ebeid, N., Hasan, A.: Analysis of DPA countermeasures based on randomizing the binary algorithm. Technical Report, CORR 2003-14, Centre for Applied Cryptographic Research, Univ. of Waterloo (2003)
Ebeid, N., Hasan, A.: On randomizing private keys to counteract DPA attacks. Technical Report, CORR 2003-11, Centre for Applied Cryptographic Research, Univ. of Waterloo (2003)
Fouque, P.-A., Muller, F., Poupard, G., Valette, F.: Defeating countermeasures based on randomized BSD representation. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 312–327. Springer, Heidelberg (2004)
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)
Goubin, L.: A refinded power-analysis attack on elliptic curve cryptosystems. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 199–210. Springer, Heidelberg (2002)
Ha, J.C., Moon, S.J.: Randomized signed-scalar multiplication of ECC to resist power attacks. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 551–563. Springer, Heidelberg (2003)
Han, D.-G., Okeya, K., Kim, T.H., Hwang, Y.S., Park, Y.H., Jung, S.: Cryptanalysis of the countermeasures using randomized binary signed digits. In: Jakobsson, M., Yung, M., Zhou, J. (eds.) ACNS 2004. LNCS, vol. 3089, pp. 398–413. Springer, Heidelberg (2004)
Han, D.-G., Chang, N.S., Jung, S.W., Park, Y.-H., Kim, C.H., Ryu, H.: Cryptanalysis of the full version randomized addition-subtraction chains. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 67–78. Springer, Heidelberg (2003)
Itoh, K., Yajima, J., Takenaka, M., Torii, N.: DPA countermeasures by improving the window method. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 303–317. Springer, Heidelberg (2003)
Kocher, P., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
Liardet, P.-Y., Smart, N.P.: Preventing SPA/DPA in ECC systems using the Jacobi Form. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 391–401. Springer, Heidelberg (2001)
Messerges, T.S., Dabbish, E.A., Sloan, R.H.: Power analysis attacks of modular exponentiation in smartcards. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 144–157. Springer, Heidelberg (1999)
Okeya, K., Han, D.-G.: Side channel attack on Ha-Moon’s countermeasure of randomized signer scalar multiplication. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 334–348. Springer, Heidelberg (2003)
Okeya, K., Sakurai, K.: On insecurity of the side channel attack countermeasure using addition-subtraction chains under distinguishability between addition and doubling. In: Batten, L.M., Seberry, J. (eds.) ACISP 2002. LNCS, vol. 2384, pp. 420–435. Springer, Heidelberg (2002)
Okeya, K., Takagi, T.: A more flexible countermeasure against side channel attacks using window method. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 397–410. Springer, Heidelberg (2003)
Okeya, K., Sakurai, K.: A multiple power analysis breaks the advanced version of the randomized addition-subtraction chains countermeasure against side channel attacks. In: IEEE Information Theory Workshop - ITW 2003, pp. 175–178 (2003)
Oswald, E., Aigner, M.: Randomized addition-subtraction chains as a countermeasure against power attacks. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 39–50. Springer, Heidelberg (2001)
Oswald, E.: A very short note on the security of the MIST exponentiation algorithm (2002) (preprint), Available from http://www.iaik.tugraz.at/aboutus/people/oswald
Walter, C.D.: Exponentiation using division chains. IEEE Transactions on Computers 47(7), 757–765 (1998)
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)
Walter, C.D.: MIST: an efficient, randomized exponentiation algorithm for resisting power analysis. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 53–66. Springer, Heidelberg (2002)
Walter, C.D.: Some security aspects of the MIST randomized exponentiation algorithm. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 276–290. Springer, Heidelberg (2003)
Walter, C.D.: Breaking the Liardet-Smart randomized exponentiation algorithm. In: CARDIS 2002, pp. 59–68, USENIX Assoc. (2002)
Walter, C.D.: Seeing through MIST given a small fraction of an RSA private key. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 391–402. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sim, S.G., Park, D.J., Lee, P.J. (2004). New Power Analysis on the Ha-Moon Algorithm and the MIST Algorithm. In: Lopez, J., Qing, S., Okamoto, E. (eds) Information and Communications Security. ICICS 2004. Lecture Notes in Computer Science, vol 3269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30191-2_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-30191-2_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23563-7
Online ISBN: 978-3-540-30191-2
eBook Packages: Springer Book Archive