Re: What's the code for doing the reverse of this code over the altbn128 curve

Hi, sorry yes : I initially wanted to have pairings happenning on the same finite field used by the cryptosystems using the altbn254.
But since my aim is diffie Hellman like, I thought after writing the message that I can perform the pairing on the code you wrote. This is in a similar way I intend to use the Weil pairing instead of the optimal ate pairing.

I’ve 4 distinct points creating finite field A and B. My aim is to compute a pair of point for finite field C such as A×B×C=(identity element) with a way to do it being C=(A×B)^order−1 

The next problem is the current one of this question withhttps://pari.math.u-bordeaux.fr/archives/pari-users-2507/msg00068.html

*Algorithm 4.1 <cid:[email protected]>.*
*Input:*

  * d∈Nd∈N satisfying l∣dl∣d and d∣(s+1)d∣(s+1) ,
  * v∈Frv∈Fr ,
  * point A∈G0−{O}A∈G0−{O} . // Note that AA may not be a generator (if
    ll is composite).

*Output:*

  * Q∈G1−{O}Q∈G1−{O} satisfying hd,A(Q)=vhd,A(Q)=v if such QQ exists.
    Otherwise, *nil*.

*Procedure:*

 1. u:=(v(s+1)/d)(s+1)/2u:=(v(s+1)/d)(s+1)/2 ;
 2. if u∉Fsu∉Fs then return *nil* ;
 3. x1:=ξ(A)+ux1:=ξ(A)+u ; x2:=ξ(A)−ux2:=ξ(A)−u ;
 4. Build a set Li:={Q∈E(Fq):ξ(Q)=xi}Li:={Q∈E(Fq):ξ(Q)=xi} for
    i=1,2i=1,2 . // Note 0≤#Li≤20≤#Li≤2 .
 5. for each Q∈L1∪L2Q∈L1∪L2
 6.   if lQ=OlQ=O and hd,A(Q)=vhd,A(Q)=v then return QQ ;
 7. return *nil* ;

*Theorem 4.2.* /Algorithm 4.1 returns a correct result with 
O((klogq)3)O((klog⁡q)3) bit operations./

On Fri, Jul 18, 2025 at 02:12:22PM +0200, Laël Cellier wrote:
> The altbn254 curve is defined here : https://github.com/ethereum/EIPs/blob/master/EIPS/eip-197.md#definition-of-the-groups
> 
> This is the code responsible for mapping points from F_p² to F_p¹² :
> 
>  p=21888242871839275222246405745257275088696311157297823662689037894645226208583;
>  i=ffgen((i^2+1)*Mod(1,p));
>  X=11559732032986387107991004021392285783925812861821192530917403151452391805634*i+10857046999023057135944570762232829481370756359578518086990519993285655852781;
>  Y=4082367875863433681332203403145435568316851327593401208105741076214120093531*i+8495653923123431417604973247489272438418190587263600148770280649306958101930;
>  pt = [X,Y];
>  \\ then define the target field, the target curve and the map from Fp[i] to Fp[w]:
>  w=ffgen((w^12 - 18 * w^6 + 82)*Mod(1,p));
>  E2 = ellinit([0,3],w);
>  map = ffembed(i,w);
>  \\ define the isomorphism:
>  twist(pt)= [ffmap(map,pt[1])*w^2, ffmap(map,pt[2])*w^3];
>  \\ apply to pt
>  pt2=twist(pt);
>  \\ check
>  ellisoncurve(E2,pt2)
>  %11 = 1
>  \\ success!

This code is identical to code I sent to this list and that you rejected.
Puzzled,
Bill.