Question: 9.6. In practice, a and k are both in the range p ? 2150 2250, and computing T = a P and y0 = k

9.6. In practice, a and k are both in the range p ? 2150 2250, and computing T = a P and y0 = k P is done using the Double-and-Add algorithm as shown in the corresponding slide on ECC. 1. Illustrate how the algorithm works for a = 19 and for a = 160. Do not perform elliptic curve operations, but keep P a variable. 2. How many (i) point additions and (ii) point doublings are required on average for one "multiplication"? Assume that all integers have [n=log2p] bit . 3. Assume that all integers have n = 160 bit, i.e. p is a 160-bit prime. Assume one group operation (addition or doubling) requires 20 ?sec. What is the time for one double-and-add operation?

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