# A Random M-ary Method Based Countermeasure against Side Channel Attacks

## Abstract

The randomization of scalar multiplication in ECC is one of the fundamental concepts in defense methods against side channel attacks. This paper proposes a countermeasure against simple and differential power analyses attacks through randomizing the transformed m-ary method based on a random m-ary recoding algorithm. Therefore, the power consumption is independent of the secret key. We show that the proposed algorithm has fewer computational cost than the previous countermeasures against power attacks in ECC. Accordingly, since the variable window width arrays and random computational tracks can resist against the SPA and DPA, the proposed countermeasure can provide a higher security for smartcards.

## Keywords

Elliptic Curve Cryptosystems Side Channel Attacks Power Analysis Attacks SPA DPA Random m-ary Recoding Algorithm## Preview

Unable to display preview. Download preview PDF.

## References

- 1.R. Anderson and M. Kuhn, “Tamper resistance-a cautionary note”,
*In Proceedings of the 2nd USENIX Workshop on Electronic Commerce*, pp. 1–11, 1996.Google Scholar - 2.P. Kocher, J. Jaffe, and B. Jun, “Differential Power Analysis”,
*In Proceedings of Advances in Cryptology-CRYTO’99*, pp. 388–397, Springer-Verlag, 1999.Google Scholar - 3.J.R. Rao and P. Rohatgi., “The EM Side-Channel(s)”,
*In Pre-Proceedings of Workshop on Cryptographic hardware and Embedded Systems-CHES’02*, pp. 29–45, Springer-Verlag, 2002.Google Scholar - 4.V. S. Miller, “Use of elliptic curve in cryptography”,
*In Advances in Cryptology-CRYPTO’85*, LNCS 218, pp. 417–426, Springer-Verlag, 1986.Google Scholar - 5.N. Koblitz, “Elliptic curve cryptosystems”,
*In Mathematics of Computation*, Vol. 48, pp. 203–209, 1987.zbMATHCrossRefMathSciNetGoogle Scholar - 6.J. S. Coron, “Resistance against differential power analysis for elliptic curve cryptosystems”,
*In Proceeding of Workshop on Cryptographic hardware and Embedded Systems-CHES’99*, LNCS 1717, pp. 292–302, Springer-Verlag, 1999.Google Scholar - 7.Yvonne Hitchcock and Paul Montague, “A New Elliptic curve scalar multiplication algorithm to resistant simple power analysis”,
*In Proceedings of Information Security and Privacy-ACISP’02*, 7th Australian Conference, LNCS 2384, pp. 214–225, Springer-Verlag, 2002.Google Scholar - 8.J. C. Ha and S. J. Moon, “Randomized signed-scalar multiplication of ECC to resist Power Attacks”,
*In Pre-Proceedings of Workshop on Cryptographic Hardware and Embedded Systems-CHES’02*, pp. 553–565, Springer-Verlag, 2002.Google Scholar - 9.B. Möller, “Securing elliptic curve point multiplication against side-channel attacks”,
*In Proceedings of Information Security Conference-ISC’01*, LNCS 2200, pp. 324–334, Springer-Verlag, 2001.Google Scholar - 10.P. Y. Liardet and N. P. Smart, “Preventing SPA/DPA in ECC systems using the Jacobi form”,
*In Proceedings of Workshop on Cryptographic hardware and Embedded Systems-CHES’01*, LNCS 2162, pp. 391–401, Springer-Verlag, 2001.Google Scholar - 11.I. F. Blake, G. Seroussi and N. P. Smart, Elliptic Curves in Cryptography,
*London Mathematical Society Lecture Note Series*.*265*, pp. 66–72, 1999.Google Scholar - 12.Oswald E. and Aigner M., “Randomized Addition-Subtraction Chains as a Countermeasure against Power Attacks”,
*In Proceedings of Workshop on Cryptographic Hardware and Embedded Systems-CHES’01*, LNCS 2162, pp. 39–50, Springer-Verlag, 2001.Google Scholar - 13.C. D. Walter, “Some Security Aspects of the MIST Randomized Exponentiation Algorithm”,
*In Pre-Proceedings of Workshop on Cryptographic Hardware and Embedded Systems-CHES’02*, pp. 277–291, Springer-Verlag, 2002.Google Scholar - 14.K. ITOH, J. YAJIMA, M. TAKENAKA and N. TORII, “DPA Countermeasure by Improving the Window Method”,
*In Pre-Proceedings of Workshop on Cryptographic Hardware and Embedded Systems-CHES’02*, pp. 304–319, Springer-Verlag, 2002.Google Scholar - 15.Kris T., Moonmoon A. and Ingrid V., “A Dynamic and Differential CMOS Logic with Signal Independent Power Comsumption to Withstand Differential Power Analysis on Smart Cards”,
*In 28th European Solid-State Circuits Conference*, 2002.Google Scholar - 16.Okeya K. and Sakurai K., “Power analysis breaks elliptic curve cryptosystems even secure against the timing attack”,
*In Proceedings of INDOCRYPT’00*, LNCS 1977, pp. 475–486, Springer-Verlag, 2000.Google Scholar - 17.Okeya K. and Sakurai K., “A Second-Order DPA Attack Breaks aWindow-method based Countermeasure against Side Channel Attacks”,
*In Proceedings of Information Security Conference-ISC’02*, LNCS2433, pp. 389–401, Springer-Verlag, 2002.Google Scholar - 18.Okeya K. and Sakurai K., “On Insecurity of the Side Channel Attack Countermeasure using Addition-Subtraction Chains under Distinguishability between Addition and Doubling”,
*In Proceedings of Information Security and Privacy-ACISP’02*, 7th Australian Conference, LNCS 2384, pp. 420–435, Springer-Verlag, 2002.Google Scholar - 19.T. Izu, B. Moller and T. Takagi, “Improved Elliptic Curve Multiplication Methods Resistant against Side Channel Attacks”,
*In the proceedings of INDOCRYPT’02*, LNCS 2551, pp. 296–313, Springer-Verlag, 2002.Google Scholar - 20.C.D Walter, “Breaking the Liardet-Smart Randomized Exponentiation Algorithm”,
*In the proceedings of Cardis’02, USENIX*, pp. 59–68, 2002.Google Scholar - 21.T. S. Messerges, E. A. Dabbish, and R. H. Sloan, “Power Analysis Attacks on Modular Exponentiation in Smartcards”,
*In Proceeding of Workshop on Cryptographic hardware and Embedded Systems-CHES’99*, LNCS 1717, pp. 144–157, Springer-Verlag, 1999.Google Scholar