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2016-04-05 15:21:12 +0200 asked a question Represent field element in normal basis

Hi there

I'm having a normal basis, which is a basis of Fpn over Fp where (n=2) NB = [zeta, zeta*p] and a point P = E2.change_ring(Fpn).random_element() I would like to find a,b in Fp such that P = aNB[0] + b*NB[1]

Naive solutions result is memory overflow, and the Solve() function can't give me solutions with a,b in Fp. Any ideas?

2016-04-04 19:12:18 +0200 commented answer Finite field q power computations

I think what i'm searching for is a = GF(q^m).element.primitive() V = VectorSpace(GF(q),1) S = V.subspace([V([a]),V([a^q])]) now I just need to represent x,y in GF(q^m) in form the vector space S? and then transforme (x,y,1) into a point on an elliptic curve defined over GF(q^m), any ideas?

2016-04-04 18:56:36 +0200 answered a question Finite field q power computations

Thanks, but I need it representet in its normal basis? Not its polynomial basis such that I can make shift operations. That is: x in GF(q^m) Represent GF(q^m) over GF(q) in its normal basis like {a, a^q, ..., a^q^(m-1)} Represent x in form of the basis {a, a^q, ..., a^q^(m-1)}, say (v_1, v_2, ... v_m) make shift (v_m, v_1, ... v_m-1) use it to compute further stuff.. Also i might as if Sage has such an operation?

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2016-03-29 14:19:40 +0200 asked a question Finite field q power computations

Hey there, i'm trying to make a fast computation algorithm using shift operations. I'm having a field GF(q) and a field GF(q^m) for some integer m and i have an element x \in GF(q^m). I want to represent x in a normal basis of the vectorspace GF(q^m) over GF(q), so that I can use shift operations for computing x^q^k fast. Are there any way of doing this ?

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2016-03-25 14:52:26 +0200 asked a question Elliptic curve scalar multiplication algorithm

I'm doing a prespective on supersinguar elliptic curves. I was wondering how saga calculates scalar multiplications? Does it just calculate it naively or does it use succesive doubling as default? Til is most interesting since there are well known ways of making "shortcuts" when oberating with supersingular curves, but does sage use these?

2016-03-25 14:52:26 +0200 asked a question Elliptic curve scalar multiplication algorithm

I'm doing a prespective on supersinguar elliptic curves. I was wondering how saga calculates scalar multiplications? Does it just calculate it naively or does it use succesive doubling as default? Til is most interesting since there are well known ways of making "shortcuts" when oberating with supersingular curves, but does sage use these?