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ITEM 2 - Implement and test Add_and_Double for Point multiplication over Doppio. #32

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CPerezz opened this issue Jun 27, 2019 · 2 comments · Fixed by #64
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ITEM 2 - Implement and test Add_and_Double for Point multiplication over Doppio. #32

CPerezz opened this issue Jun 27, 2019 · 2 comments · Fixed by #64
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@CPerezz @LukePearson1
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enhancement New feature or request testing This feature requires to be tested.

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CPerezz commented Jun 27, 2019 •
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This issue lives under the item: https://gitlab.dusk.network/dusk-org/tech/issues/2

The last operation to implement over the Doppio Curve is add and doubling which allows us to:

Given k and G compute P = kG.

In order to do it, we should design a table with pre-computed values [G, 2G, 4G, 8G, 16G .... ] So we can then pick just the ones we need seeing our Scalar in binary form.

I think this can reduce the amount of time we spend computing against adding a point to itself Scalar times.

For a better understanding, take a look at:
enter image description here

Maybe @decentralisedkev can help us discussing about the implementation possibilities.
@CPerezz CPerezz added enhancement New feature or request research Need to research about this. labels Jun 27, 2019
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CPerezz commented Jun 27, 2019

After talking with @decentralisedkev and @Bounce23 , we will go for an implementation of the standard add and double point multiplication algorithm.

Since it will allow us to use fewer constraints on the R1CS and so, be more performant.

@CPerezz CPerezz mentioned this issue Jun 28, 2019
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CPerezz commented Jul 3, 2019

This was done on 4f11878. We will now wait until we get values for testing the implementation of the algorithm.

@CPerezz CPerezz added testing This feature requires to be tested. and removed research Need to research about this. labels Jul 3, 2019
@CPerezz CPerezz changed the title ITEM 2 - Implement Add_and_Double for Point multiplication over Doppio. ITEM 2 - Implement and test Add_and_Double for Point multiplication over Doppio. Jul 3, 2019
@CPerezz CPerezz mentioned this issue Jul 9, 2019
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CPerezz added a commit that referenced this issue Jul 10, 2019
@CPerezz
Implement Mul trait for &ProjectiveEdwards.
d698aaa 
This closes the development part of #32.

Scalar multiplication: compute `Scalar * self`.
This implementation uses the algorithm:
`add_and_doubling` which is the standard one for
this operations and also adds less constraints on
R1CS.

Hankerson, Darrel; Vanstone, Scott; Menezes, Alfred (2004).
Guide to Elliptic Curve Cryptography.
Springer Professional Computing. New York: Springer-Verlag.
@CPerezz CPerezz mentioned this issue Jul 17, 2019
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Point Generation implementation dusk-network/dusk-zerocaf
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