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73 lines
1.5 KiB
Go
73 lines
1.5 KiB
Go
package bn256
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import (
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"github.com/consensys/gnark-crypto/ecc/bn254/fp"
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)
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// This is just the addition formula
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// but given we know that we do not need Jacobian
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// coordinates, we use the naive implementation.
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//
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// Ideally, we push this into gnark
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func (g *G1) addAffine(a_, b_ *G1) {
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// Get the gnark specific points
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var a = a_.inner
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var b = b_.inner
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// If a is 0, then return b
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if a.IsInfinity() {
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g.inner.Set(&b)
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return
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}
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// If b is 0, then return a
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if b.IsInfinity() {
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g.inner.Set(&a)
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return
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}
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// If a == -b, then return 0
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g.inner.Neg(&b)
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if a.Equal(&g.inner) {
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g.inner.X.SetZero()
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g.inner.Y.SetZero()
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return
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}
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// Compute lambda based on whether we
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// are doing a point addition or a point doubling
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//
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// Check if points are equal
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var pointsAreEqual = a.Equal(&b)
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var denominator fp.Element
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var lambda fp.Element
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// If a == b, then we need to compute lambda for double
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// else we need to compute lambda for addition
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if pointsAreEqual {
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// Compute numerator
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lambda.Square(&a.X)
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fp.MulBy3(&lambda)
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denominator.Add(&a.Y, &a.Y)
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} else {
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// Compute numerator
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lambda.Sub(&b.Y, &a.Y)
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denominator.Sub(&b.X, &a.X)
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}
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denominator.Inverse(&denominator)
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lambda.Mul(&lambda, &denominator)
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// Compute x_3 as lambda^2 - a_x - b_x
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g.inner.X.Square(&lambda)
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g.inner.X.Sub(&g.inner.X, &a.X)
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g.inner.X.Sub(&g.inner.X, &b.X)
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// Compute y as lambda * (a_x - x_3) - a_y
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g.inner.Y.Sub(&a.X, &g.inner.X)
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g.inner.Y.Mul(&g.inner.Y, &lambda)
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g.inner.Y.Sub(&g.inner.Y, &a.Y)
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}
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