Works, thanks!
I am using now "secp256k1_fe_equal_var" and results are indeed like expected.
Good to know there is no one single way to do something.
Topic: Comparing Jacobian/Affine points (Read 145 times)
You could use the method for comparing two jacobian points directly.
(xa, ya, za=1) and (xj, yj, zj)
No inversion, so this is considerably faster.
It depends on how many affine points you want to compare to. In the above case each check costs two multiplications (since we compute zj^2 and zj^3 once). It might be cheaper to convert the point to affine, and just compare. Additionally the known public keys might be organized in a radix tree for even faster comparison, which is not possible in jacobian coordinates.
(xa, ya, za=1) and (xj, yj, zj)
Code:
xa / za^2 = xj / zj^2
ya / za^3 = yj / zj^3
xa * zj^2 = xj * za^2
ya * zj^3 = yj * za^2
which becomes
xa * zj^2 = xj
ya * zj^3 = yj
ya / za^3 = yj / zj^3
xa * zj^2 = xj * za^2
ya * zj^3 = yj * za^2
which becomes
xa * zj^2 = xj
ya * zj^3 = yj
No inversion, so this is considerably faster.
It depends on how many affine points you want to compare to. In the above case each check costs two multiplications (since we compute zj^2 and zj^3 once). It might be cheaper to convert the point to affine, and just compare. Additionally the known public keys might be organized in a radix tree for even faster comparison, which is not possible in jacobian coordinates.
Hello,
Please correct me if I am fundamentally wrong, but recently I was wondering about one thing - is it possible to somehow compare points from two different representations? We know that theoretically Affine point (xa,ya) could come from operations on Jacobian point (xj/zj^2, yj/zj^3). On the other hand, Jacobian (x,z,y) from Affine would be just (xa, ya, 1).
I would like to compare Affine point (AP) with a given Jacobian point (JP) - or at least exclude possibility that JP would be converted into given AP.
In other words: https://github.com/bitcoin-core/secp256k1/blob/master/src/secp256k1.c
We have JP (secp256k1_gej) and to receive "well-known" public key (through secp256k1_ge), we must launch launch:
Now, the question is:
Is there any step where I may stay (or operations I may skip) in that path (Jp->AP pubkey), if for a given generated Jacobian Point (secp256k1_gej) I want to exclude/ (or confirm) possibility that JP will == known public key? If I convert my pubkey into secp256k1_ge, which is basically (x, y, 1), may I compare it with unprocessed secp256k1_gej ?
Please correct me if I am fundamentally wrong, but recently I was wondering about one thing - is it possible to somehow compare points from two different representations? We know that theoretically Affine point (xa,ya) could come from operations on Jacobian point (xj/zj^2, yj/zj^3). On the other hand, Jacobian (x,z,y) from Affine would be just (xa, ya, 1).
I would like to compare Affine point (AP) with a given Jacobian point (JP) - or at least exclude possibility that JP would be converted into given AP.
In other words: https://github.com/bitcoin-core/secp256k1/blob/master/src/secp256k1.c
We have JP (secp256k1_gej) and to receive "well-known" public key (through secp256k1_ge), we must launch launch:
Code:
secp256k1_ec_pubkey_create_helper + secp256k1_pubkey_save
which basically is (forget variables names, operations are important):Code:
secp256k1_fe_sqr(&zi2, zi);
secp256k1_fe_mul(&zi3, &zi2, zi);
secp256k1_fe_mul(&r->x, &a->x, &zi2);
secp256k1_fe_mul(&r->y, &a->y, &zi3);
secp256k1_fe_normalize_var(&ge->x);
secp256k1_fe_normalize_var(&ge->y);
secp256k1_fe_get_b32(pubkey->data, &ge->x);
secp256k1_fe_get_b32(pubkey->data + 32, &ge->y);
secp256k1_fe_mul(&zi3, &zi2, zi);
secp256k1_fe_mul(&r->x, &a->x, &zi2);
secp256k1_fe_mul(&r->y, &a->y, &zi3);
secp256k1_fe_normalize_var(&ge->x);
secp256k1_fe_normalize_var(&ge->y);
secp256k1_fe_get_b32(pubkey->data, &ge->x);
secp256k1_fe_get_b32(pubkey->data + 32, &ge->y);
Now, the question is:
Is there any step where I may stay (or operations I may skip) in that path (Jp->AP pubkey), if for a given generated Jacobian Point (secp256k1_gej) I want to exclude/ (or confirm) possibility that JP will == known public key? If I convert my pubkey into secp256k1_ge, which is basically (x, y, 1), may I compare it with unprocessed secp256k1_gej ?
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