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I have implemented the Serial Pollard Rho Algorithm for solving Elliptic curve discrete log problem . Now I am try to parallelize it using the Parallel Pollard Rho Algorithm.

so I just need some help to understand what kind property I can use for selecting distinguished points for collision detection. It would be a great help if some examples can be suggested also.

Shivam Sharma
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1 Answers1

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You could use any property. The thing to get right is the probability for some point to be a distinguished point. For example if we want one distinguished* point per 2^32 points, we could define a distinguished point as a point which has all last x 32 bits 0.

For example in Sage with point P:

>>> P.xy()[0].lift() & 0xffffffff == 0
True/False

In the normal case, this will do, but I admit that this is not really ideal when you are calculating elliptic curve arithmetic in a projective or Jacobian coordinate system, because you will have to do an inversion for every distinguished-point-test.

dusk
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