1 files changed, 132 insertions, 0 deletions
diff --git a/src/crypto/internal/nistec/p224_sqrt.go b/src/crypto/internal/nistec/p224_sqrt.go
new file mode 100644
index 0000000..0c77579
--- /dev/null
+++ b/src/crypto/internal/nistec/p224_sqrt.go
@@ -0,0 +1,132 @@
+// Copyright 2022 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package nistec
+
+import (
+	"crypto/internal/nistec/fiat"
+	"sync"
+)
+
+var p224GG *[96]fiat.P224Element
+var p224GGOnce sync.Once
+
+// p224SqrtCandidate sets r to a square root candidate for x. r and x must not overlap.
+func p224SqrtCandidate(r, x *fiat.P224Element) {
+	// Since p = 1 mod 4, we can't use the exponentiation by (p + 1) / 4 like
+	// for the other primes. Instead, implement a variation of Tonelli–Shanks.
+	// The constant-time implementation is adapted from Thomas Pornin's ecGFp5.
+	//
+	// https://github.com/pornin/ecgfp5/blob/82325b965/rust/src/field.rs#L337-L385
+
+	// p = q*2^n + 1 with q odd -> q = 2^128 - 1 and n = 96
+	// g^(2^n) = 1 -> g = 11 ^ q (where 11 is the smallest non-square)
+	// GG[j] = g^(2^j) for j = 0 to n-1
+
+	p224GGOnce.Do(func() {
+		p224GG = new([96]fiat.P224Element)
+		for i := range p224GG {
+			if i == 0 {
+				p224GG[i].SetBytes([]byte{0x6a, 0x0f, 0xec, 0x67,
+					0x85, 0x98, 0xa7, 0x92, 0x0c, 0x55, 0xb2, 0xd4,
+					0x0b, 0x2d, 0x6f, 0xfb, 0xbe, 0xa3, 0xd8, 0xce,
+					0xf3, 0xfb, 0x36, 0x32, 0xdc, 0x69, 0x1b, 0x74})
+			} else {
+				p224GG[i].Square(&p224GG[i-1])
+			}
+		}
+	})
+
+	// r <- x^((q+1)/2) = x^(2^127)
+	// v <- x^q = x^(2^128-1)
+
+	// Compute x^(2^127-1) first.
+	//
+	// The sequence of 10 multiplications and 126 squarings is derived from the
+	// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
+	//
+	//	_10      = 2*1
+	//	_11      = 1 + _10
+	//	_110     = 2*_11
+	//	_111     = 1 + _110
+	//	_111000  = _111 << 3
+	//	_111111  = _111 + _111000
+	//	_1111110 = 2*_111111
+	//	_1111111 = 1 + _1111110
+	//	x12      = _1111110 << 5 + _111111
+	//	x24      = x12 << 12 + x12
+	//	i36      = x24 << 7
+	//	x31      = _1111111 + i36
+	//	x48      = i36 << 17 + x24
+	//	x96      = x48 << 48 + x48
+	//	return     x96 << 31 + x31
+	//
+	var t0 = new(fiat.P224Element)
+	var t1 = new(fiat.P224Element)
+
+	r.Square(x)
+	r.Mul(x, r)
+	r.Square(r)
+	r.Mul(x, r)
+	t0.Square(r)
+	for s := 1; s < 3; s++ {
+		t0.Square(t0)
+	}
+	t0.Mul(r, t0)
+	t1.Square(t0)
+	r.Mul(x, t1)
+	for s := 0; s < 5; s++ {
+		t1.Square(t1)
+	}
+	t0.Mul(t0, t1)
+	t1.Square(t0)
+	for s := 1; s < 12; s++ {
+		t1.Square(t1)
+	}
+	t0.Mul(t0, t1)
+	t1.Square(t0)
+	for s := 1; s < 7; s++ {
+		t1.Square(t1)
+	}
+	r.Mul(r, t1)
+	for s := 0; s < 17; s++ {
+		t1.Square(t1)
+	}
+	t0.Mul(t0, t1)
+	t1.Square(t0)
+	for s := 1; s < 48; s++ {
+		t1.Square(t1)
+	}
+	t0.Mul(t0, t1)
+	for s := 0; s < 31; s++ {
+		t0.Square(t0)
+	}
+	r.Mul(r, t0)
+
+	// v = x^(2^127-1)^2 * x
+	v := new(fiat.P224Element).Square(r)
+	v.Mul(v, x)
+
+	// r = x^(2^127-1) * x
+	r.Mul(r, x)
+
+	// for i = n-1 down to 1:
+	//     w = v^(2^(i-1))
+	//     if w == -1 then:
+	//         v <- v*GG[n-i]
+	//         r <- r*GG[n-i-1]
+
+	var p224MinusOne = new(fiat.P224Element).Sub(
+		new(fiat.P224Element), new(fiat.P224Element).One())
+
+	for i := 96 - 1; i >= 1; i-- {
+		w := new(fiat.P224Element).Set(v)
+		for j := 0; j < i-1; j++ {
+			w.Square(w)
+		}
+		cond := w.Equal(p224MinusOne)
+		v.Select(t0.Mul(v, &p224GG[96-i]), v, cond)
+		r.Select(t0.Mul(r, &p224GG[96-i-1]), r, cond)
+	}
+}