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Public: y^2 = x^3 + 11x + 19 (mod 167) and the point (2,7). ---------(I)

Alice and Bob each must randomly select their own secret multipliers. Suppose Alice selects A = 15 and Bob selects B = 22. Then Alice computes

A(2,7) = 15(2,7) = (102,88),

where all arithmetic is done on the curve in equation (i). Alice sends her computed result to Bob. Bob computes

B(2,7) = 22(2,7) = (9,43),

which he sends to Alice. Now Alice multiplies the value she received from Bob by her secret multiplier A, that is, A(9,43) = 15(9,43) = (131,140).

Similarly, Bob computes B(102,88) = 22(102,88) = (131,140)

Here how to get A for (102,88) and B for (9,43)??

Tumeng
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  • Are you asking mathematically or programmatically? Mathematically it is scalar multiplication requires ECC addition and doubling rules, and the double-and-add algorithm. Programatically easiest is SageMath. – kelalaka Dec 05 '21 at 12:22
  • [Scalar multuplication](https://crypto.stackexchange.com/a/68595/18298) – kelalaka Dec 05 '21 at 12:24
  • i want to know just mathematically. how do get those values? Thanks in advance – Tumeng Dec 05 '21 at 13:04
  • Well, then you are in the wrong SE, Here [the formulas](https://crypto.stackexchange.com/a/66296/18298) – kelalaka Dec 05 '21 at 13:06
  • okay thanks. but can you just show me how to get this line? A(2,7) = 15(2,7) = (102,88), – Tumeng Dec 05 '21 at 13:29
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    Nope. Once or Twice doubling and adding formulas can be done by hand, the rest is error-prone and time-consuming. Use Sagemath. – kelalaka Dec 05 '21 at 13:31

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