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06:09 < kanzure> d4de: https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2017-November/015283.html
06:09 < kanzure> https://github.com/ElementsProject/secp256k1-zkp/tree/secp256k1-zkp/src/modules/rangeproof
06:09 < d4de> reading through that
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08:33 < jl2012> jnewbery: so the bug is in IsWitnessSeasoned() ?
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11:23 < d4de> I was reding this https://people.xiph.org/~greg/confidential_values.txt, and in there's the expression `H = to_point(SHA256(ENCODE(G)))` to obtain a new generator for use in the Pedersen commitment scheme
11:23 < d4de> How do we know if `H` is an irreducible polynomial?
11:24 < waxwing> d4de, H is a point on the elliptic curve (secp256k1)
11:24 < sipa> H is a point, not a polynomial
11:24 < sipa> and we know it is a generator because every point in secp256k1 is a generator
11:24 < sipa> (its cofactor is 1)
11:26 < d4de> I'm confused, but G is the generating polynomial of the finite field of which addition is carried on
11:26 < d4de> right?
11:26 < sipa> no
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11:28 < sipa> there is a finite field, which is just Z modulo a big prime
11:28 < sipa> which is used for the _coordinates_ of points
11:28 < sipa> then there is an elliptic curve with equation y^2 = x^3 + 7 over that field
11:28 < sipa> that elliptic curve defines a mathematical cyclic group
11:29 < sipa> every point in that group happens to be a generator of the group
11:29 < d4de> addition/multiplications are defined modulo p?
11:29 <@andytoshi> d4de: there is a group whose elements are elliptic curve points (and whose addition is some weird rational function of the coordinates) which is conceptually totally independent of the underlying field that the curve is defined over
11:30 <@andytoshi> so for the purpose of CT/CA you can think of the curvepoints as just abstract group elements
11:30 <@andytoshi> and forget about the field and the curve equation entirely
11:30 < d4de> ah
11:30 < sipa> d4de: addition/multiplication on _coordinates_ is indeed done modulo p
11:30 < sipa> d4de: addition of elliptic curve points is weird
11:31 <@andytoshi> importantly the addition formula is _not_ coordinate-wise addition, it's some rational function (which is indeed computed mod p). you can find the exact formula on wikipedia if you're more comfortable knowing it
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11:35 < arubi> if we're on the subject..  what causes this weird thing where the three cube roots of 1 mod p added to each other are equal to n, and same with the three cube roots of 1 mod n, added to each other are equal to p.  I can't explain this to myself
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11:37 <@andytoshi> well, you can just run through the addition formula and see that when a = 0, multiplying x by a cube root of 1 in the field is an automorphism (if A + B = C and you multiply each x-coord by lambda the equation's truth value will be preserved). you can see this in a non-enlightening way by just working out the formula
11:38 <@andytoshi> oops, beta, not lambda. here beta is a cube root of 1 in the field
11:38 <@andytoshi> then observe that in a prime-order group, _every_ automorphism needs to be "multiplication by lambda" for some lambda..
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11:38 <@andytoshi> and this automorphism is the identity if you do it thrice (since multiplying x by beta three times is just multiplying x by 1), so this lambda needs to be a cube root of 1 in the _group_ order as well
11:39 <@andytoshi> which creates this spooky effect where whenever you have a field with a nontrivial cube root of 1, and an elliptic curve of j-invariant 0 defined over that field, the integers mod the curve's order must also have a cube root of 1
11:43 < arubi> okay, suddenly the way endomorphism works is a bit clearer now :),  I'll try out some walking through the addition
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11:46 <@andytoshi> IIRC you need to use the fact that beta^2 = 1/beta and beta = 1/beta^2 to see that the addition works (this is why being a cube root of 1 is special and other numbers don't work)
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11:50 < arubi> oh!  I guess I was close, previously I tried walking through three equations :
11:50 < arubi> k1*lambda + k1 = tweak1
11:50 < arubi> k1/lambda + k1 = tweak2
11:50 < arubi> tweak1/tweak2 = lambda
11:51 < arubi> and tried to figure out how to use beta with the x coordinate for k1G
11:52 < kanzure> d4de: still alive?
11:52 < d4de> yes
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--- Log closed Sat Nov 18 00:00:18 2017