From 5996bcbe25af46fafceed7d2a4659d9c8b6bf3ac Mon Sep 17 00:00:00 2001
From: arnaucode <arnaucode@gmail.com>
Date: Sat, 21 Jul 2018 12:39:43 +0200
Subject: [PATCH] rsa encrypt & decrypt, blind signatures, homomorphic
 multiplication

---
 README.md       | 18 +++++++++
 prime/prime.go  | 49 +++++++++++++++++++++++++
 rsa/rsa.go      | 98 +++++++++++++++++++++++++++++++++++++++++++++++++
 rsa/rsa_test.go | 54 +++++++++++++++++++++++++++
 4 files changed, 219 insertions(+)
 create mode 100644 README.md
 create mode 100644 prime/prime.go
 create mode 100644 rsa/rsa.go
 create mode 100644 rsa/rsa_test.go

diff --git a/README.md b/README.md
new file mode 100644
index 0000000..71c2f46
--- /dev/null
+++ b/README.md
@@ -0,0 +1,18 @@
+# cryptofun
+
+Crypto algorithms from scratch. Academic purposes only.
+
+
+## RSA
+- [x] GenerateKeyPair
+- [x] Encrypt
+- [x] Decrypt
+- [x] Blind
+- [x] Blind Signature
+- [x] Unblind Signature
+- [x] Verify Signature
+- [x] Homomorphic Multiplication
+
+## Paillier
+## ECC
+## Shamir Secret Sharing
diff --git a/prime/prime.go b/prime/prime.go
new file mode 100644
index 0000000..a412287
--- /dev/null
+++ b/prime/prime.go
@@ -0,0 +1,49 @@
+package prime
+
+import "math/rand"
+
+func RandInt(min int, max int) int {
+	r := rand.Intn(max-min) + min
+	return r
+}
+func RandPrime(min int, max int) int {
+	primes := SieveOfEratosthenes(max)
+	randN := rand.Intn(len(primes)-0) + 0
+	return primes[randN]
+}
+
+// return list of primes less than N
+func SieveOfEratosthenes(N int) (primes []int) {
+	b := make([]bool, N)
+	for i := 2; i < N; i++ {
+		if b[i] == true {
+			continue
+		}
+		primes = append(primes, i)
+		for k := i * i; k < N; k += i {
+			b[k] = true
+		}
+	}
+	return
+}
+
+func Gcd(a, b int) int {
+	var bgcd func(a, b, res int) int
+	bgcd = func(a, b, res int) int {
+		switch {
+		case a == b:
+			return res * a
+		case a%2 == 0 && b%2 == 0:
+			return bgcd(a/2, b/2, 2*res)
+		case a%2 == 0:
+			return bgcd(a/2, b, res)
+		case b%2 == 0:
+			return bgcd(a, b/2, res)
+		case a > b:
+			return bgcd(a-b, b, res)
+		default:
+			return bgcd(a, b-a, res)
+		}
+	}
+	return bgcd(a, b, 1)
+}
diff --git a/rsa/rsa.go b/rsa/rsa.go
new file mode 100644
index 0000000..7d02224
--- /dev/null
+++ b/rsa/rsa.go
@@ -0,0 +1,98 @@
+package rsa
+
+import (
+	"bytes"
+	"math/big"
+	"math/rand"
+	"time"
+
+	prime "../prime"
+)
+
+const (
+	MaxPrime = 2000
+	MinPrime = 500
+)
+
+type PublicKey struct {
+	E *big.Int `json:"e"`
+	N *big.Int `json:"n"`
+}
+type PublicKeyString struct {
+	E string `json:"e"`
+	N string `json:"n"`
+}
+type PrivateKey struct {
+	D *big.Int `json:"d"`
+	N *big.Int `json:"n"`
+}
+
+type Key struct {
+	PubK  PublicKey
+	PrivK PrivateKey
+}
+
+func GenerateKeyPair() (key Key) {
+	rand.Seed(time.Now().Unix())
+	p := prime.RandPrime(MinPrime, MaxPrime)
+	q := prime.RandPrime(MinPrime, MaxPrime)
+
+	n := p * q
+	phi := (p - 1) * (q - 1)
+	e := 65537
+	var pubK PublicKey
+	pubK.E = big.NewInt(int64(e))
+	pubK.N = big.NewInt(int64(n))
+
+	d := new(big.Int).ModInverse(big.NewInt(int64(e)), big.NewInt(int64(phi)))
+
+	var privK PrivateKey
+	privK.D = d
+	privK.N = big.NewInt(int64(n))
+
+	key.PubK = pubK
+	key.PrivK = privK
+	return key
+}
+
+func Encrypt(m *big.Int, pubK PublicKey) *big.Int {
+	Me := new(big.Int).Exp(m, pubK.E, nil)
+	c := new(big.Int).Mod(Me, pubK.N)
+	return c
+}
+func Decrypt(c *big.Int, privK PrivateKey) *big.Int {
+	Cd := new(big.Int).Exp(c, privK.D, nil)
+	m := new(big.Int).Mod(Cd, privK.N)
+	return m
+}
+
+func Blind(m *big.Int, r *big.Int, pubK PublicKey) *big.Int {
+	rE := new(big.Int).Exp(r, pubK.E, nil)
+	mrE := new(big.Int).Mul(m, rE)
+	mBlinded := new(big.Int).Mod(mrE, pubK.N)
+	return mBlinded
+}
+
+func BlindSign(m *big.Int, privK PrivateKey) *big.Int {
+	sigma := new(big.Int).Exp(m, privK.D, privK.N)
+	return sigma
+}
+func Unblind(sigma *big.Int, r *big.Int, pubK PublicKey) *big.Int {
+	r1 := new(big.Int).ModInverse(r, pubK.N)
+	bsr := new(big.Int).Mul(sigma, r1)
+	sig := new(big.Int).Mod(bsr, pubK.N)
+	return sig
+}
+func Verify(msg *big.Int, mSigned *big.Int, pubK PublicKey) bool {
+	//decrypt the mSigned with pubK
+	Cd := new(big.Int).Exp(mSigned, pubK.E, nil)
+	m := new(big.Int).Mod(Cd, pubK.N)
+	return bytes.Equal(msg.Bytes(), m.Bytes())
+}
+
+func HomomorphicMul(c1 *big.Int, c2 *big.Int, pubK PublicKey) *big.Int {
+	c1c2 := new(big.Int).Mul(c1, c2)
+	n2 := new(big.Int).Mul(pubK.N, pubK.N)
+	d := new(big.Int).Mod(c1c2, n2)
+	return d
+}
diff --git a/rsa/rsa_test.go b/rsa/rsa_test.go
new file mode 100644
index 0000000..30a234f
--- /dev/null
+++ b/rsa/rsa_test.go
@@ -0,0 +1,54 @@
+package rsa
+
+import (
+	"bytes"
+	"math/big"
+	"testing"
+)
+
+func TestEncryptDecrypt(t *testing.T) {
+	key := GenerateKeyPair()
+
+	mBytes := []byte("Hi")
+	m := new(big.Int).SetBytes(mBytes)
+	c := Encrypt(m, key.PubK)
+
+	d := Decrypt(c, key.PrivK)
+	if m == d {
+		t.Errorf("m not equal to decrypted")
+	}
+}
+func TestBlindSignature(t *testing.T) {
+	key := GenerateKeyPair()
+
+	mBytes := []byte("Hi")
+	m := new(big.Int).SetBytes(mBytes)
+	c := Encrypt(m, key.PubK)
+
+	d := Decrypt(c, key.PrivK)
+	if m == d {
+		t.Errorf("decrypted d not equal to original m")
+	}
+	rVal := big.NewInt(int64(101))
+	mBlinded := Blind(m, rVal, key.PubK)
+	sigma := BlindSign(mBlinded, key.PrivK)
+	mSigned := Unblind(sigma, rVal, key.PubK)
+	verified := Verify(m, mSigned, key.PubK)
+	if !verified {
+		t.Errorf("false, signature not verified")
+	}
+}
+
+func TestHomomorphiMultiplication(t *testing.T) {
+	key := GenerateKeyPair()
+
+	n1 := big.NewInt(int64(11))
+	n2 := big.NewInt(int64(15))
+	c1 := Encrypt(n1, key.PubK)
+	c2 := Encrypt(n2, key.PubK)
+	c3c4 := HomomorphicMul(c1, c2, key.PubK)
+	d := Decrypt(c3c4, key.PrivK)
+	if !bytes.Equal(new(big.Int).Mul(n1, n2).Bytes(), d.Bytes()) {
+		t.Errorf("decrypted result not equal to original result")
+	}
+}