Fixed-Hamming-Weight Representation for Indistinguishable Addition Formulae

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In the execution of signature on a smart card, side channel attacks such as simple power analysis (SPA) have become serious threat12). There are the fixed procedure method and the indistinguishable method for SPA resistant methods. The indistinguishable method conceals all branch instructions by using indistinguishable addition formulae but may reveal the hamming-weight when an addition chain with the un-fixed-hamming-weight is used. In the case of hyper-elliptic curve, the indistinguishable method has not been proposed yet. In this paper, we give an indistinguishable addition formulae of hyper-elliptic curve. We also give algorithms which output the fixed-hamming-weight representation for indistinguishable addition formulae and works with or without computation table, which can dissolve the above mentioned problem on the indistinguishable method and are also applied to an elliptic curve scalar multiplication.
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