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/**
* @title Library to validate AZTEC zero-knowledge proofs
* @author Zachary Williamson, AZTEC
* @dev Don't include this as an internal library. This contract uses a static memory table to cache elliptic curve primitives and hashes.
* Calling this internally from another function will lead to memory mutation and undefined behaviour.
* The intended use case is to call this externally via `staticcall`. External calls to OptimizedAZTEC can be treated as pure functions as this contract contains no storage and makes no external calls (other than to precompiles)
* Copyright Spilbury Holdings Ltd 2018. All rights reserved.
* We will be releasing AZTEC as an open-source protocol that provides efficient transaction privacy for Ethereum.
* This will include our bespoke AZTEC decentralized exchange, allowing for cross-asset transfers with full transaction privacy
* and interopability with public decentralized exchanges.
* Stay tuned for updates!
*
* Permission to use as test case in the Solidity compiler granted by the author:
* https://github.com/ethereum/solidity/pull/5713#issuecomment-449042830
**/
{
validateJoinSplit()
// should not get here
mstore(0x00, 404)
revert(0x00, 0x20)
function validateJoinSplit() {
mstore(0x80, 7673901602397024137095011250362199966051872585513276903826533215767972925880) // h_x
mstore(0xa0, 8489654445897228341090914135473290831551238522473825886865492707826370766375) // h_y
let notes := add(0x04, calldataload(0x04))
let m := calldataload(0x24)
let n := calldataload(notes)
let gen_order := 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
let challenge := mod(calldataload(0x44), gen_order)
// validate m <= n
if gt(m, n) { mstore(0x00, 404) revert(0x00, 0x20) }
// recover k_{public} and calculate k_{public}
let kn := calldataload(sub(calldatasize(), 0xc0))
// add kn and m to final hash table
mstore(0x2a0, caller())
mstore(0x2c0, kn)
mstore(0x2e0, m)
kn := mulmod(sub(gen_order, kn), challenge, gen_order) // we actually want c*k_{public}
hashCommitments(notes, n)
let b := add(0x300, mul(n, 0x80))
// Iterate over every note and calculate the blinding factor B_i = \gamma_i^{kBar}h^{aBar}\sigma_i^{-c}.
// We use the AZTEC protocol pairing optimization to reduce the number of pairing comparisons to 1, which adds some minor alterations
for { let i := 0 } lt(i, n) { i := add(i, 0x01) } {
// Get the calldata index of this note
let noteIndex := add(add(notes, 0x20), mul(i, 0xc0))
let k
let a := calldataload(add(noteIndex, 0x20))
let c := challenge
switch eq(add(i, 0x01), n)
case 1 {
k := kn
// if all notes are input notes, invert k
if eq(m, n) {
k := sub(gen_order, k)
}
}
case 0 { k := calldataload(noteIndex) }
// Check this commitment is well formed...
validateCommitment(noteIndex, k, a)
// If i > m then this is an output note.
// Set k = kx_j, a = ax_j, c = cx_j, where j = i - (m+1)
switch gt(add(i, 0x01), m)
case 1 {
// before we update k, update kn = \sum_{i=0}^{m-1}k_i - \sum_{i=m}^{n-1}k_i
kn := addmod(kn, sub(gen_order, k), gen_order)
let x := mod(mload(0x00), gen_order)
k := mulmod(k, x, gen_order)
a := mulmod(a, x, gen_order)
c := mulmod(challenge, x, gen_order)
// calculate x_{j+1}
mstore(0x00, keccak256(0x00, 0x20))
}
case 0 {
// nothing to do here except update kn = \sum_{i=0}^{m-1}k_i - \sum_{i=m}^{n-1}k_i
kn := addmod(kn, k, gen_order)
}
calldatacopy(0xe0, add(noteIndex, 0x80), 0x40)
calldatacopy(0x20, add(noteIndex, 0x40), 0x40)
mstore(0x120, sub(gen_order, c))
mstore(0x60, k)
mstore(0xc0, a)
// Using call instead of staticcall here to make it work on all targets.
let result := call(gas(), 7, 0, 0xe0, 0x60, 0x1a0, 0x40)
result := and(result, call(gas(), 7, 0, 0x20, 0x60, 0x120, 0x40))
result := and(result, call(gas(), 7, 0, 0x80, 0x60, 0x160, 0x40))
result := and(result, call(gas(), 6, 0, 0x120, 0x80, 0x160, 0x40))
result := and(result, call(gas(), 6, 0, 0x160, 0x80, b, 0x40))
if eq(i, m) {
mstore(0x260, mload(0x20))
mstore(0x280, mload(0x40))
mstore(0x1e0, mload(0xe0))
mstore(0x200, sub(0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47, mload(0x100)))
}
if gt(i, m) {
mstore(0x60, c)
result := and(result, call(gas(), 7, 0, 0x20, 0x60, 0x220, 0x40))
result := and(result, call(gas(), 6, 0, 0x220, 0x80, 0x260, 0x40))
result := and(result, call(gas(), 6, 0, 0x1a0, 0x80, 0x1e0, 0x40))
}
if iszero(result) { mstore(0x00, 400) revert(0x00, 0x20) }
b := add(b, 0x40) // increase B pointer by 2 words
}
if lt(m, n) {
validatePairing(0x64)
}
let expected := mod(keccak256(0x2a0, sub(b, 0x2a0)), gen_order)
if iszero(eq(expected, challenge)) {
// No! Bad! No soup for you!
mstore(0x00, 404)
revert(0x00, 0x20)
}
// Great! All done. This is a valid proof so return ```true```
mstore(0x00, 0x01)
return(0x00, 0x20)
}
function validatePairing(t2) {
let field_order := 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47
let t2_x_1 := calldataload(t2)
let t2_x_2 := calldataload(add(t2, 0x20))
let t2_y_1 := calldataload(add(t2, 0x40))
let t2_y_2 := calldataload(add(t2, 0x60))
// check provided setup pubkey is not zero or g2
if or(or(or(or(or(or(or(
iszero(t2_x_1),
iszero(t2_x_2)),
iszero(t2_y_1)),
iszero(t2_y_2)),
eq(t2_x_1, 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed)),
eq(t2_x_2, 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2)),
eq(t2_y_1, 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa)),
eq(t2_y_2, 0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b))
{
mstore(0x00, 400)
revert(0x00, 0x20)
}
mstore(0x20, mload(0x1e0)) // sigma accumulator x
mstore(0x40, mload(0x200)) // sigma accumulator y
mstore(0x80, 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed)
mstore(0x60, 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2)
mstore(0xc0, 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa)
mstore(0xa0, 0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b)
mstore(0xe0, mload(0x260)) // gamma accumulator x
mstore(0x100, mload(0x280)) // gamma accumulator y
mstore(0x140, t2_x_1)
mstore(0x120, t2_x_2)
mstore(0x180, t2_y_1)
mstore(0x160, t2_y_2)
let success := call(gas(), 8, 0, 0x20, 0x180, 0x20, 0x20)
if or(iszero(success), iszero(mload(0x20))) {
mstore(0x00, 400)
revert(0x00, 0x20)
}
}
function validateCommitment(note, k, a) {
let gen_order := 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
let field_order := 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47
let gammaX := calldataload(add(note, 0x40))
let gammaY := calldataload(add(note, 0x60))
let sigmaX := calldataload(add(note, 0x80))
let sigmaY := calldataload(add(note, 0xa0))
if iszero(
and(
and(
and(
eq(mod(a, gen_order), a), // a is modulo generator order?
gt(a, 1) // can't be 0 or 1 either!
),
and(
eq(mod(k, gen_order), k), // k is modulo generator order?
gt(k, 1) // and not 0 or 1
)
),
and(
eq( // y^2 ?= x^3 + 3
addmod(mulmod(mulmod(sigmaX, sigmaX, field_order), sigmaX, field_order), 3, field_order),
mulmod(sigmaY, sigmaY, field_order)
),
eq( // y^2 ?= x^3 + 3
addmod(mulmod(mulmod(gammaX, gammaX, field_order), gammaX, field_order), 3, field_order),
mulmod(gammaY, gammaY, field_order)
)
)
)
) {
mstore(0x00, 400)
revert(0x00, 0x20)
}
}
function hashCommitments(notes, n) {
for { let i := 0 } lt(i, n) { i := add(i, 0x01) } {
let index := add(add(notes, mul(i, 0xc0)), 0x60)
calldatacopy(add(0x300, mul(i, 0x80)), index, 0x80)
}
mstore(0x00, keccak256(0x300, mul(n, 0x80)))
}
}
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// ====
// step: fullSuite
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// ----
// {
// {
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// mstore(0x80, 7673901602397024137095011250362199966051872585513276903826533215767972925880)
// mstore(0xa0, 8489654445897228341090914135473290831551238522473825886865492707826370766375)
// let notes := add(0x04, calldataload(0x04))
// let m := calldataload(0x24)
// let n := calldataload(notes)
// let gen_order := 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
// let challenge := mod(calldataload(0x44), gen_order)
// if gt(m, n)
// {
// mstore(0x00, 404)
// revert(0x00, 0x20)
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// }
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// let kn := calldataload(add(calldatasize(), not(191)))
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// mstore(0x2a0, caller())
// mstore(0x2c0, kn)
// mstore(0x2e0, m)
// kn := mulmod(sub(gen_order, kn), challenge, gen_order)
// hashCommitments(notes, n)
// let b := add(0x300, mul(n, 0x80))
// let i := 0
// let i_1 := i
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// for { } lt(i, n) { i := add(i, 0x01) }
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// {
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// let _1 := add(calldataload(0x04), mul(i, 0xc0))
// let noteIndex := add(_1, 0x24)
// let k := i_1
// let a := calldataload(add(_1, 0x44))
// let c := challenge
// let _2 := add(i, 0x01)
// switch eq(_2, n)
// case 1 {
// k := kn
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// if eq(m, n) { k := sub(gen_order, kn) }
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// }
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// case 0 { k := calldataload(noteIndex) }
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// validateCommitment(noteIndex, k, a)
// switch gt(_2, m)
// case 1 {
// kn := addmod(kn, sub(gen_order, k), gen_order)
// let x := mod(mload(i_1), gen_order)
// k := mulmod(k, x, gen_order)
// a := mulmod(a, x, gen_order)
// c := mulmod(challenge, x, gen_order)
// mstore(i_1, keccak256(i_1, 0x20))
// }
// case 0 {
// kn := addmod(kn, k, gen_order)
// }
// let _3 := 0x40
// calldatacopy(0xe0, add(_1, 164), _3)
// calldatacopy(0x20, add(_1, 100), _3)
// mstore(0x120, sub(gen_order, c))
// mstore(0x60, k)
// mstore(0xc0, a)
// let result := call(gas(), 7, i_1, 0xe0, 0x60, 0x1a0, _3)
// let result_1 := and(result, call(gas(), 7, i_1, 0x20, 0x60, 0x120, _3))
// let result_2 := and(result_1, call(gas(), 7, i_1, 0x80, 0x60, 0x160, _3))
// let result_3 := and(result_2, call(gas(), 6, i_1, 0x120, 0x80, 0x160, _3))
// result := and(result_3, call(gas(), 6, i_1, 0x160, 0x80, b, _3))
// if eq(i, m)
// {
// mstore(0x260, mload(0x20))
// mstore(0x280, mload(_3))
// mstore(0x1e0, mload(0xe0))
// mstore(0x200, sub(0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47, mload(0x100)))
// }
// if gt(i, m)
// {
// mstore(0x60, c)
// let result_4 := and(result, call(gas(), 7, i_1, 0x20, 0x60, 0x220, _3))
// let result_5 := and(result_4, call(gas(), 6, i_1, 0x220, 0x80, 0x260, _3))
// result := and(result_5, call(gas(), 6, i_1, 0x1a0, 0x80, 0x1e0, _3))
// }
// if iszero(result)
// {
// mstore(i_1, 400)
// revert(i_1, 0x20)
// }
// b := add(b, _3)
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// }
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// if lt(m, n) { validatePairing(0x64) }
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// if iszero(eq(mod(keccak256(0x2a0, add(b, not(671))), gen_order), challenge))
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// {
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// mstore(i_1, 404)
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// revert(i_1, 0x20)
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// }
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// mstore(i_1, 0x01)
// return(i_1, 0x20)
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// }
// function validatePairing(t2)
// {
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// let t2_x := calldataload(t2)
// let _1 := 0x20
// let t2_x_1 := calldataload(add(t2, _1))
// let t2_y := calldataload(add(t2, 0x40))
// let t2_y_1 := calldataload(add(t2, 0x60))
// let _2 := 0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b
// let _3 := 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa
// let _4 := 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2
// let _5 := 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed
// if or(or(or(or(or(or(or(iszero(t2_x), iszero(t2_x_1)), iszero(t2_y)), iszero(t2_y_1)), eq(t2_x, _5)), eq(t2_x_1, _4)), eq(t2_y, _3)), eq(t2_y_1, _2))
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// {
// mstore(0x00, 400)
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// revert(0x00, _1)
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// }
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// mstore(_1, mload(0x1e0))
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// mstore(0x40, mload(0x200))
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// mstore(0x80, _5)
// mstore(0x60, _4)
// mstore(0xc0, _3)
// mstore(0xa0, _2)
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// mstore(0xe0, mload(0x260))
// mstore(0x100, mload(0x280))
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// mstore(0x140, t2_x)
// mstore(0x120, t2_x_1)
// let _6 := 0x180
// mstore(_6, t2_y)
// mstore(0x160, t2_y_1)
// let success := call(gas(), 8, 0, _1, _6, _1, _1)
// if or(iszero(success), iszero(mload(_1)))
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// {
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// mstore(0, 400)
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// revert(0, _1)
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// }
// }
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// function validateCommitment(note, k, a)
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// {
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// let gen_order := 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
// let field_order := 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47
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// let gammaX := calldataload(add(note, 0x40))
// let gammaY := calldataload(add(note, 0x60))
// let sigmaX := calldataload(add(note, 0x80))
// let sigmaY := calldataload(add(note, 0xa0))
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// if iszero(and(and(and(eq(mod(a, gen_order), a), gt(a, 1)), and(eq(mod(k, gen_order), k), gt(k, 1))), and(eq(addmod(mulmod(mulmod(sigmaX, sigmaX, field_order), sigmaX, field_order), 3, field_order), mulmod(sigmaY, sigmaY, field_order)), eq(addmod(mulmod(mulmod(gammaX, gammaX, field_order), gammaX, field_order), 3, field_order), mulmod(gammaY, gammaY, field_order)))))
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// {
// mstore(0x00, 400)
// revert(0x00, 0x20)
// }
// }
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// function hashCommitments(notes, n)
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// {
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// let i := 0
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// for { } lt(i, n) { i := add(i, 0x01) }
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// {
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// calldatacopy(add(0x300, mul(i, 0x80)), add(add(notes, mul(i, 0xc0)), 0x60), 0x80)
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// }
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// mstore(0, keccak256(0x300, mul(n, 0x80)))
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// }
// }
