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crypto/bn256: better comments for u, P and Order #21836

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Nov 13, 2020
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crypto/bn256: better comments for u, P and Order #21836

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5 changes: 3 additions & 2 deletions crypto/bn256/google/constants.go
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Original file line number Diff line number Diff line change
Expand Up @@ -13,13 +13,14 @@ func bigFromBase10(s string) *big.Int {
return n
}

// u is the BN parameter that determines the prime: 1868033³.
// u is the BN parameter that determines the prime.
var u = bigFromBase10("4965661367192848881")

// p is a prime over which we form a basic field: 36u⁴+36u³+24u²+6u+1.
// P is a prime over which we form a basic field: 36u⁴+36u³+24u²+6u+1.
var P = bigFromBase10("21888242871839275222246405745257275088696311157297823662689037894645226208583")

// Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u²+6u+1.
// Order - 1 = 2^28 * 3^2 * 13 * 29 * 983 * 11003 * 237073 * 405928799 * 1670836401704629 * 13818364434197438864469338081.
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This doesn't match..?

>>> 2^28 * 3^2 * 13 * 29 * 983 * 11003 * 237073 * 405928799 * 1670836401704629 * 13818364434197438864469338081 
18120013071297999241489839011809292012244764632993302696031169913432

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https://www.wolframalpha.com/input/?i=2%5E28+*+3%5E2+*+13+*+29+*+983+*+11003+*+237073+*+405928799+*+1670836401704629+*+13818364434197438864469338081

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Or right. Python uses ** not ^.

>>> 2**28 * 3**2 * 13 * 29 * 983 * 11003 * 237073 * 405928799 * 1670836401704629 * 13818364434197438864469338081 
21888242871839275222246405745257275088548364400416034343698204186575808495616

var Order = bigFromBase10("21888242871839275222246405745257275088548364400416034343698204186575808495617")

// xiToPMinus1Over6 is ξ^((p-1)/6) where ξ = i+9.
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