Abstract
Side-channel attacks (SCA) may exploit leakage information to break cryptosystems. In this paper we present a new SCA resistant Elliptic Curve scalar multiplication algorithm. The proposed algorithm, builds a sequence of bit-strings representing the scalar k, characterized by the fact that all bit-strings are different from zero; this property will ensure a uniform computation behavior for the algorithm, and thus will make it secure against simple power analysis attacks (SPA). With other randomization techniques, the proposed countermeasures do not penalize the computation time. The proposed scheme is more efficient than MÖller's one, its cost being about 5% to 10% smaller than MÖller's one.
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References
Okeya K, Han D G. Side Channel Attack on Ha-Moon's Countermeasure of Randomized Signed Scale Multiplication [C]//Indocrypt 2003 (LNCS 2904), Berlin: Springer-Verlag, 2003:334–348.
Coron J S. Resistance Against Differential Power Analysis for Elliptic Curve Cryptosystems[C]//Cryptography Hardware and Embedded Systems-CHES'99 (LNCS 1717) Berlin: Springer-Verlag, 1999:292–302.
Liardet P V, Smart N. Preventing SPA/DPA in ECC Systems Using the Jacobi Form[C]//Cryptography Hardware and Embedded Systems-CHES'01 (LNCS 2106) Berlin Heidelberg: Springer-Verlag, 2001:401–411.
Joye M, Quisquater J J. Hessian Elliptic Curves and Side-Channel Attacks[C]//Cryptography Hardware and Embedded Systems-CHES'01 (LNCS 2162), Berlin Heidelberg: Springer-Verlag, 2001:412–420.
Joye M, Tymen C. Protections Against Differential Analysis for Elliptic Curve Cryptography: An Algebraic Approach [C]//Cryptography Hardware and Embedded Systems- CHES'01(LNCS 2162), Berlin: Springer-Verlag, 2001:386–400.
Lopez J, Dahab R. Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation[C]//Cryptography Hardware and Embedded Systems-CHES'99(LNCS 1717), Berlin: Springer-Verlag, 1999:316–327.
Okeya K, Sakurai K. A Second-Order DPA Attacks Breaks a Window-Method Based Countermeasure Against Side Channel Attacks[C]//Information Security Conference2002(LNCS 2433), Berlin: Springer-Verlag, 2002:389–401.
MÖller B. Securing Elliptic Curve Point Multiplication Against Side-Channel Attacks [C]//Information Security Conference2001 (LNCS 2200), Berlin: Springer-Verlag, 2001:324–334.
Montgomery P L. Speeding up the Pollard and Elliptic Curve Methods of Factorization[J].Mathematics of Computation, 198748(177):243–264.
National Institute of Standard and Technology(NIST). Digital Signature Standard(DSS)[S].FIPS PUB, 186-2 2000.
Certicom Research. Standard for Efficient Cryptography[S]. Version 1.0, 2000, Available at url http:/www.secg.org/.
Brown M, Hankerson D, Lopez J,et al., Software Implementation of the NIST Elliptic Curves over Prime Fields [C]//Progress in Cryptology CT-RSA 2001 (LNCS 2020), Berlin: Springer-Verlag, 2001:250–265.
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Foundation item: Supported by the National Natural Science Foundation of China (60473029)
Biography: LIU Shuanggen (1979-) male, Ph. D. candidate, working in Jiangxi Normal University, research direction: cryptology and information Security.
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Shuanggen, L., Yupu, H. & Wensheng, X. An efficient method against side-channel attacks on ECC. Wuhan Univ. J. Nat. Sci. 11, 1573–1576 (2006). https://doi.org/10.1007/BF02831823
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DOI: https://doi.org/10.1007/BF02831823