init: v1.0.0

he/elgamal/elgamal.go

@@ -0,0 +1,114 @@
+package elgamal
+
+import (
+	"crypto/rand"
+	"errors"
+	"io"
+	"math/big"
+
+	"xdx.jelly/xgcl/grand"
+)
+
+var Reader = grand.Reader
+
+type Params struct {
+	isMont bool // Is Montgomery represent
+	p      *big.Int
+	q      *big.Int
+	g      *big.Int
+	pMont  *big.Int
+	qMont  *big.Int
+	gMont  *big.Int
+}
+
+func (p *Params) P() *big.Int {
+	return p.p
+}
+func (p *Params) Q() *big.Int {
+	return p.q
+}
+func (p *Params) G() *big.Int {
+	return p.g
+}
+
+type PublicKey struct {
+	y      big.Int
+	Params *Params
+}
+
+type PrivateKey struct {
+	x big.Int
+	PublicKey
+}
+type Cipher struct {
+	u big.Int
+	v big.Int
+}
+
+func GenerateKey(rnd io.Reader, params *Params) (*PrivateKey, *PublicKey, error) {
+	x, err := rand.Int(rnd, params.q)
+	if err != nil {
+		return nil, nil, err
+	}
+	y := new(big.Int).Exp(params.g, x, params.p)
+	sk := &PrivateKey{
+		x: *x,
+		PublicKey: PublicKey{
+			y:      *y,
+			Params: P1024,
+		},
+	}
+	pk := &sk.PublicKey
+	return sk, pk, nil
+}
+
+// m = g^M mod p for some M
+// rnd can be nil, io.Reader or []byte
+func (pk *PublicKey) Encryption(m *big.Int, rnd any) (*Cipher, error) {
+	var r *big.Int
+	var err error
+	p := pk.Params.p
+	q := pk.Params.q
+	g := pk.Params.g
+
+	switch rnd := rnd.(type) {
+	case nil:
+		rnd = Reader
+	case io.Reader:
+		r, err = rand.Int(rnd, q)
+		if err != nil {
+			return nil, err
+		}
+	case []byte:
+		r = new(big.Int).SetBytes(rnd)
+		if r.Cmp(q) >= 0 {
+			return nil, errors.New("random bytes too large")
+		}
+	default:
+		return nil, errors.New("rnd must be io.Reader or []bytes")
+	}
+
+	c := &Cipher{}
+	c.u.Exp(g, r, p)
+	c.v.Exp(&pk.y, r, p)
+	c.v.Mul(&c.v, m)
+	return c, nil
+}
+
+func (sk *PrivateKey) Decryption(c *Cipher) (*big.Int, error) {
+	p := sk.PublicKey.Params.p
+	u := &c.u
+	v := &c.v
+	z := new(big.Int)
+	z.Exp(u, &sk.x, p)
+	z.ModInverse(z, p)
+	z.Mul(z, v)
+	z.Mod(z, p)
+	return z, nil
+}
+
+func (c *Cipher) HomoMap(c1 *Cipher, c2 *Cipher) (*Cipher, error) {
+	c.u.Mul(&c1.u, &c2.u)
+	c.v.Mul(&c1.v, &c2.v)
+	return c, nil
+}

he/elgamal/elgamal_test.go

@@ -0,0 +1,37 @@
+package elgamal
+
+import (
+	"crypto/rand"
+	"encoding/hex"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"xdx.jelly/xgcl/grand"
+)
+
+func TestElGamal(t *testing.T) {
+	x := bigFromBase16("013d5955a5e91b8fed1b56b6bdcd467939de9bfc")
+	y := bigFromBase16("b7866990d044b1bccbbcf84c29f145ee17d4f4608c79a55e249e9e108b91e36381944fa3c0c3f51876f63bce7bb30ffde9ca02265e916dd3fb2e060b0dfeaaa67d5a359159b948c3df1141f0e0a22380a3633c1ffbcb1c228ffe4ef0bab52293bfdff4b64e3f362d63b11a4d2507f6e9e98de71aff09fdb64e3737c046044138")
+	// M := bigFromBase16("4142434445464748494a31323334353637383930")
+	// m := new(big.Int).Exp(P1024.g, M, P1024.p)
+	m, _ := rand.Int(grand.Reader, P1024.p)
+	sk := &PrivateKey{
+		x: *x,
+		PublicKey: PublicKey{
+			y:      *y,
+			Params: P1024,
+		},
+	}
+	pk := &sk.PublicKey
+	b, _ := hex.DecodeString("d8d0f2d6a3e2d745ab4410e2042a740e7a81a280")
+	c1, err := pk.Encryption(m, b)
+	assert.Nil(t, err)
+	c2, err := pk.Encryption(m, grand.Reader)
+	c, _ := new(Cipher).HomoMap(c1, c2)
+	mm0, _ := sk.Decryption(c)
+	mm1 := new(big.Int).Mul(m, m)
+	mm1.Mod(mm1, pk.Params.p)
+
+	assert.Zero(t, mm0.Cmp(mm1))
+}

he/elgamal/params.go

@@ -0,0 +1,20 @@
+package elgamal
+
+import (
+	"encoding/hex"
+	"math/big"
+)
+
+func bigFromBase16(s string) *big.Int {
+	b, err := hex.DecodeString(s)
+	if err != nil {
+		panic(err)
+	}
+	return new(big.Int).SetBytes(b)
+}
+
+var P1024 = &Params{
+	p: bigFromBase16("e5256a788f875183ec56a332d38db31de883cded25ae635a656823b5c801b44a104f4e1d604153adaaa5d6d107feb3a8e721a32f3e6780645c85de2d4f4f85568767efc9b8363193497c052a5b832464b81a209d393eb6d3a464cba0b7607dc79b3611dcd1544e4ed329cc913f68234b1d5f209ae7081c0d44662ee1f86c458f"),
+	q: bigFromBase16("e6fa5be8dfd1a200fd699a9ff4b02761f05fca69"),
+	g: bigFromBase16("5a0c1ebde9c0787f3d426e2036455fcd25bc32b1e666b2ba90dad169af7043c18b266d530d0f607ea46c182dd7c88d919158343441e001b10e36c8ffa03cb80dadcf7e84393561d2f4f2d067222d5a33157b81f4f4a46c9526375920cac73c23e100e8b43eb8a4bc83047ae45b079bca6dbf69b4b0c1e6bffdfd232b99c5d61a"),
+}