ristretto255: add test for feSqrtRatio

ristretto255_test.go

@@ -2,8 +2,66 @@ package ristretto255
 
 import (
 	"testing"
+
+	"github.com/gtank/ristretto255/internal/radix51"
 )
 
+func assertFeEqual(value, expect *radix51.FieldElement) {
+	if value.Equal(expect) == 1 {
+		return
+	} else {
+		panic("failed equality assertion")
+	}
+}
+
+type sqrtRatioTest struct {
+	u, v     *radix51.FieldElement
+	sqrt     *radix51.FieldElement
+	choice   int
+	negative int
+}
+
+// These tests can be found in curve25519-dalek's 'field.rs'
+func TestSqrtRatioM1(t *testing.T) {
+	var (
+		zero, one = radix51.Zero, radix51.One
+
+		// Two is nonsquare in our field, 4 is square
+		two  = new(radix51.FieldElement).Add(one, one)
+		four = new(radix51.FieldElement).Add(two, two)
+
+		// 2*i
+		twoTimesSqrtM1 = new(radix51.FieldElement).Mul(two, sqrtM1)
+
+		sqrt2i = fieldElementFromDecimal(
+			"38214883241950591754978413199355411911188925816896391856984770930832735035196")
+
+		invSqrt4 = fieldElementFromDecimal(
+			"28948022309329048855892746252171976963317496166410141009864396001978282409974")
+	)
+
+	// Check the construction of those magic numbers.
+	assertFeEqual(new(radix51.FieldElement).Mul(sqrt2i, sqrt2i), twoTimesSqrtM1)
+	assertFeEqual(new(radix51.FieldElement).Mul(new(radix51.FieldElement).Square(invSqrt4), four), one)
+
+	var tests = []sqrtRatioTest{
+		{u: zero, v: zero, sqrt: zero, choice: 1, negative: 0},    // 0
+		{u: one, v: zero, sqrt: zero, choice: 0, negative: 0},     // 1
+		{u: two, v: one, sqrt: sqrt2i, choice: 0, negative: 0},    // 2
+		{u: four, v: one, sqrt: two, choice: 1, negative: 0},      // 3
+		{u: one, v: four, sqrt: invSqrt4, choice: 1, negative: 0}, // 4
+	}
+
+	for idx, tt := range tests {
+		sqrt := new(radix51.FieldElement)
+		choice := feSqrtRatio(sqrt, tt.u, tt.v)
+		if choice != tt.choice || sqrt.Equal(tt.sqrt) != 1 || sqrt.IsNegative() != tt.negative {
+			t.Errorf("Failed test %d", idx)
+			t.Logf("Got {u: %v, v: %v, sqrt: %v, choice: %d, neg: %d}", tt.u, tt.v, sqrt, choice, sqrt.IsNegative())
+		}
+	}
+}
+
 func TestRistrettoBasepointDecode(t *testing.T) {
 	extendedBasepoint := &Element{}
 	err := extendedBasepoint.Decode(encodedBasepoint)