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Randomizing scalar multiplication using exact covering systems of congruences

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Fig. 1. The set {1 (mod 2); 2, 3 (mod 4); 0, 2, 4 (mod 6); 0, 1, 4, 5 (mod 8)} is an exact 2-cover
Table 1. Scalar multiplication algorithms and their corresponding covering system of congruences Algorithm Covering System of Congruences
Table 2. The array representation of the covering system {1 (mod 2); 2, 3 (mod 4); 0, 2, 4 (mod 6);
Table 3. Average operation counts per bit and number of precomputed points for short Weierstrass curves.
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