TY - GEN

T1 - A fast parallel elliptic curve multiplication resistant against side channel attacks

AU - Izu, Tetsuya

AU - Takagi, Tsuyoshi

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

PY - 2002

Y1 - 2002

N2 - This paper proposes a fast elliptic curve multiplication algorithm applicable for any types of curves over finite fields Fp (p a prime), based on [Mon87], together with criteria which make our algorithm resistant against the side channel attacks (SCA). The algorithm improves both on an addition chain and an addition formula in the scalar multiplication. Our addition chain requires no table look-up (or a very small number of pre-computed points) and a prominent property is that it can be implemented in parallel. The computing time for n-bit scalar multiplication is one ECDBL + (n −1) ECADDs in the parallel case and (n −1) ECDBLs + (n −1) ECADDs in the single case. We also propose faster addition formulas which only use the x-coordinates of the points. By combination of our addition chain and addition formulas, we establish a faster scalar multiplication resistant against the SCA in both single and parallel computation. The improvement of our scalar multiplications over the previous method is about 37% for two processors and 5.7% for a single processor. Our scalar multiplication is suitable for the implementation on smart cards.

AB - This paper proposes a fast elliptic curve multiplication algorithm applicable for any types of curves over finite fields Fp (p a prime), based on [Mon87], together with criteria which make our algorithm resistant against the side channel attacks (SCA). The algorithm improves both on an addition chain and an addition formula in the scalar multiplication. Our addition chain requires no table look-up (or a very small number of pre-computed points) and a prominent property is that it can be implemented in parallel. The computing time for n-bit scalar multiplication is one ECDBL + (n −1) ECADDs in the parallel case and (n −1) ECDBLs + (n −1) ECADDs in the single case. We also propose faster addition formulas which only use the x-coordinates of the points. By combination of our addition chain and addition formulas, we establish a faster scalar multiplication resistant against the SCA in both single and parallel computation. The improvement of our scalar multiplications over the previous method is about 37% for two processors and 5.7% for a single processor. Our scalar multiplication is suitable for the implementation on smart cards.

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U2 - 10.1007/3-540-45664-3_20

DO - 10.1007/3-540-45664-3_20

M3 - Conference contribution

AN - SCOPUS:84958955271

SN - 3540431683

SN - 9783540431688

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 280

EP - 296

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Naccache, David

A2 - Paillier, Pascal

PB - Springer Verlag

T2 - 5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002

Y2 - 12 February 2002 through 14 February 2002

ER -