diff --git a/LICENSE b/LICENSE index 0eae6e7..c3f5b52 100644 --- a/LICENSE +++ b/LICENSE @@ -1,21 +1,674 @@ -MIT License - -Copyright (c) 2018 arnau - -Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 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If not, see . + +Also add information on how to contact you by electronic and paper mail. + +If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) +This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. +This is free software, and you are welcome to redistribute it +under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + +You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + +The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/README.md b/README.md index b49be32..a85ce63 100644 --- a/README.md +++ b/README.md @@ -186,15 +186,15 @@ if err!=nil { fmt.Println(err) } -// define how many secrets are needed to recover the secret -nNeededSecrets := big.NewInt(int64(3)) - // define how many shares want to generate nShares := big.NewInt(int64(6)) +// define how many shares are needed to recover the secret +nNeededShares := big.NewInt(int64(3)) + // create the shares shares, err := Create( - nNeededSecrets, + nNeededShares, nShares, p, big.NewInt(int64(k))) diff --git a/bn128/README.md b/bn128/README.md new file mode 100644 index 0000000..ff43b3e --- /dev/null +++ b/bn128/README.md @@ -0,0 +1,145 @@ +## Bn128 +**[not finished]** + +This is implemented followng the implementations and info from: +- https://github.com/zcash/zcash/tree/master/src/snark +- https://github.com/iden3/snarkjs +- https://github.com/ethereum/py_ecc/tree/master/py_ecc/bn128 +- `Multiplication and Squaring on Pairing-Friendly +Fields`, Augusto Jun Devegili, Colm Ó hÉigeartaigh, Michael Scott, and Ricardo Dahab https://pdfs.semanticscholar.org/3e01/de88d7428076b2547b60072088507d881bf1.pdf +- `Optimal Pairings`, Frederik Vercauteren https://www.cosic.esat.kuleuven.be/bcrypt/optimal.pdf +- `Double-and-Add with Relative Jacobian +Coordinates`, Björn Fay https://eprint.iacr.org/2014/1014.pdf +- `Fast and Regular Algorithms for Scalar Multiplication +over Elliptic Curves`, Matthieu Rivain https://eprint.iacr.org/2011/338.pdf + +- [x] Fq, Fq2, Fq6, Fq12 operations +- [x] G1, G2 operations + + +#### Usage +First let's define three basic functions to convert integer compositions to big integer compositions: +```go +func iToBig(a int) *big.Int { + return big.NewInt(int64(a)) +} + +func iiToBig(a, b int) [2]*big.Int { + return [2]*big.Int{iToBig(a), iToBig(b)} +} + +func iiiToBig(a, b int) [2]*big.Int { + return [2]*big.Int{iToBig(a), iToBig(b)} +} +``` + +- Finite Fields (1, 2, 6, 12) operations +```go +// new finite field of order 1 +fq1 := NewFq(iToBig(7)) + +// basic operations of finite field 1 +res := fq1.Add(iToBig(4), iToBig(4)) +res = fq1.Double(iToBig(5)) +res = fq1.Sub(iToBig(5), iToBig(7)) +res = fq1.Neg(iToBig(5)) +res = fq1.Mul(iToBig(5), iToBig(11)) +res = fq1.Inverse(iToBig(4)) +res = fq1.Square(iToBig(5)) + +// new finite field of order 2 +nonResidueFq2str := "-1" // i / Beta +nonResidueFq2, ok := new(big.Int).SetString(nonResidueFq2str, 10) +fq2 := Fq2{fq1, nonResidueFq2} +nonResidueFq6 := iiToBig(9, 1) + +// basic operations of finite field of order 2 +res := fq2.Add(iiToBig(4, 4), iiToBig(3, 4)) +res = fq2.Double(iiToBig(5, 3)) +res = fq2.Sub(iiToBig(5, 3), iiToBig(7, 2)) +res = fq2.Neg(iiToBig(4, 4)) +res = fq2.Mul(iiToBig(4, 4), iiToBig(3, 4)) +res = fq2.Inverse(iiToBig(4, 4)) +res = fq2.Div(iiToBig(4, 4), iiToBig(3, 4)) +res = fq2.Square(iiToBig(4, 4)) + + +// new finite field of order 6 +nonResidueFq6 := iiToBig(9, 1) // TODO +fq6 := Fq6{fq2, nonResidueFq6} + +// define two new values of Finite Field 6, in order to be able to perform the operations +a := [3][2]*big.Int{ + iiToBig(1, 2), + iiToBig(3, 4), + iiToBig(5, 6)} +b := [3][2]*big.Int{ + iiToBig(12, 11), + iiToBig(10, 9), + iiToBig(8, 7)} + +// basic operations of finite field order 6 +res := fq6.Add(a, b) +res = fq6.Sub(a, b) +res = fq6.Mul(a, b) +divRes := fq6.Div(mulRes, b) + + +// new finite field of order 12 +q, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10) // i +if !ok { + fmt.Println("error parsing string to big integer") +} + +fq1 := NewFq(q) +nonResidueFq2, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208582", 10) // i +assert.True(t, ok) +nonResidueFq6 := iiToBig(9, 1) + +fq2 := Fq2{fq1, nonResidueFq2} +fq6 := Fq6{fq2, nonResidueFq6} +fq12 := Fq12{fq6, fq2, nonResidueFq6} + +``` + +- G1 operations +```go +bn128, err := NewBn128() +assert.Nil(t, err) + +r1 := big.NewInt(int64(33)) +r2 := big.NewInt(int64(44)) + +gr1 := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(r1)) +gr2 := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(r2)) + +grsum1 := bn128.G1.Add(gr1, gr2) +r1r2 := bn128.Fq1.Add(r1, r2) +grsum2 := bn128.G1.MulScalar(bn128.G1.G, r1r2) + +a := bn128.G1.Affine(grsum1) +b := bn128.G1.Affine(grsum2) +assert.Equal(t, a, b) +assert.Equal(t, "0x2f978c0ab89ebaa576866706b14787f360c4d6c3869efe5a72f7c3651a72ff00", utils.BytesToHex(a[0].Bytes())) +assert.Equal(t, "0x12e4ba7f0edca8b4fa668fe153aebd908d322dc26ad964d4cd314795844b62b2", utils.BytesToHex(a[1].Bytes())) +``` + +- G2 operations +```go +bn128, err := NewBn128() +assert.Nil(t, err) + +r1 := big.NewInt(int64(33)) +r2 := big.NewInt(int64(44)) + +gr1 := bn128.G2.MulScalar(bn128.G2.G, bn128.Fq1.Copy(r1)) +gr2 := bn128.G2.MulScalar(bn128.G2.G, bn128.Fq1.Copy(r2)) + +grsum1 := bn128.G2.Add(gr1, gr2) +r1r2 := bn128.Fq1.Add(r1, r2) +grsum2 := bn128.G2.MulScalar(bn128.G2.G, r1r2) + +a := bn128.G2.Affine(grsum1) +b := bn128.G2.Affine(grsum2) +assert.Equal(t, a, b) +``` diff --git a/bn128/fq.go b/bn128/fq.go index 615122e..9021802 100644 --- a/bn128/fq.go +++ b/bn128/fq.go @@ -89,3 +89,6 @@ func (fq Fq) Copy(a *big.Int) *big.Int { func (fq Fq) Affine(a *big.Int) *big.Int { return a } +func (fq Fq) Equal(a, b *big.Int) bool { + return bytes.Equal(a.Bytes(), b.Bytes()) +} diff --git a/bn128/fq2.go b/bn128/fq2.go index 401bab5..db1fe82 100644 --- a/bn128/fq2.go +++ b/bn128/fq2.go @@ -135,3 +135,6 @@ func (fq2 Fq2) Affine(a [2]*big.Int) [2]*big.Int { fq2.F.Affine(a[1]), } } +func (fq2 Fq2) Equal(a, b [2]*big.Int) bool { + return fq2.F.Equal(a[0], b[0]) && fq2.F.Equal(a[1], b[1]) +} diff --git a/bn128/g2.go b/bn128/g2.go index 614fe72..ebb33b8 100644 --- a/bn128/g2.go +++ b/bn128/g2.go @@ -21,8 +21,8 @@ func NewG2(f Fq2, g [2][2]*big.Int) G2 { return g2 } -func (g2 G2) Zero() [2][2]*big.Int { - return [2][2]*big.Int{g2.F.Zero(), g2.F.Zero()} +func (g2 G2) Zero() [3][2]*big.Int { + return [3][2]*big.Int{g2.F.Zero(), g2.F.One(), g2.F.Zero()} } func (g2 G2) IsZero(p [3][2]*big.Int) bool { return g2.F.IsZero(p[2]) @@ -155,7 +155,7 @@ func (g2 G2) MulScalar(base [3][2]*big.Int, e *big.Int) [3][2]*big.Int { return res } -func (g2 G2) Affine(p [3][2]*big.Int) [2][2]*big.Int { +func (g2 G2) Affine(p [3][2]*big.Int) [3][2]*big.Int { if g2.IsZero(p) { return g2.Zero() } @@ -167,8 +167,12 @@ func (g2 G2) Affine(p [3][2]*big.Int) [2][2]*big.Int { zinv3 := g2.F.Mul(zinv2, zinv) y := g2.F.Mul(p[1], zinv3) - return [2][2]*big.Int{ + return [3][2]*big.Int{ x, y, + [2]*big.Int{ + big.NewInt(int64(0)), + big.NewInt(int64(0)), + }, } } diff --git a/ecdsa/README.md b/ecdsa/README.md new file mode 100644 index 0000000..70c8014 --- /dev/null +++ b/ecdsa/README.md @@ -0,0 +1,49 @@ +## ECC ECDSA +- https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm + +- [x] define ECDSA data structure +- [x] ECDSA Sign +- [x] ECDSA Verify signature + + +#### Usage +```go +// define new elliptic curve +ec := ecc.NewEC(big.NewInt(int64(1)), big.NewInt(int64(18)), big.NewInt(int64(19))) +// define new point +g := ecc.Point{big.NewInt(int64(7)), big.NewInt(int64(11))} + +// define new ECDSA system +dsa, err := NewDSA(ec, g) +if err!=nil { + fmt.Println(err) +} + +// define privK&pubK over the elliptic curve +privK := big.NewInt(int64(5)) +pubK, err := dsa.PubK(privK) +if err!=nil { + fmt.Println(err) +} + +// hash value to sign +hashval := big.NewInt(int64(40)) + +// define r +r := big.NewInt(int64(11)) + +// sign hashed value +sig, err := dsa.Sign(hashval, privK, r) +if err!=nil { + fmt.Println(err) +} + +// verify signature +verified, err := dsa.Verify(hashval, sig, pubK) +if err!=nil { + fmt.Println(err) +} +if verified { + fmt.Println("signature correctly verified") +} +``` diff --git a/elgamal/README.md b/elgamal/README.md new file mode 100644 index 0000000..e164f36 --- /dev/null +++ b/elgamal/README.md @@ -0,0 +1,50 @@ +## ECC ElGamal +- https://en.wikipedia.org/wiki/ElGamal_encryption + +- [x] ECC ElGamal key generation +- [x] ECC ElGamal Encrypton +- [x] ECC ElGamal Decryption + + +#### Usage +- NewEG, Encryption, Decryption +```go +// define new elliptic curve +ec := ecc.NewEC(big.NewInt(int64(1)), big.NewInt(int64(18)), big.NewInt(int64(19))) + +// define new point +g := ecc.Point{big.NewInt(int64(7)), big.NewInt(int64(11))} + +// define new ElGamal crypto system with the elliptic curve and the point +eg, err := NewEG(ec, g) +if err!=nil { + fmt.Println(err) +} + +// define privK&pubK over the elliptic curve +privK := big.NewInt(int64(5)) +pubK, err := eg.PubK(privK) +if err!=nil { + fmt.Println(err) +} + +// define point to encrypt +m := ecc.Point{big.NewInt(int64(11)), big.NewInt(int64(12))} + +// encrypt +c, err := eg.Encrypt(m, pubK, big.NewInt(int64(15))) +if err!=nil { + fmt.Println(err) +} + +// decrypt +d, err := eg.Decrypt(c, privK) +if err!=nil { + fmt.Println(err) +} + +// check that decryption is correct +if !m.Equal(d) { + fmt.Println("decrypted not equal to original") +} +``` diff --git a/paillier/README.md b/paillier/README.md new file mode 100644 index 0000000..0b206f7 --- /dev/null +++ b/paillier/README.md @@ -0,0 +1,56 @@ +## Paillier cryptosystem & Homomorphic Addition +- https://en.wikipedia.org/wiki/Paillier_cryptosystem +- https://en.wikipedia.org/wiki/Homomorphic_encryption + +- [x] GenerateKeyPair +- [x] Encrypt +- [x] Decrypt +- [x] Homomorphic Addition + +#### Usage +- Encrypt, Decrypt +```go +// key generation +key, err := GenerateKeyPair() +if err!=nil { + fmt.Println(err) +} + +mBytes := []byte("Hi") +m := new(big.Int).SetBytes(mBytes) + +// encryption +c := Encrypt(m, key.PubK) + +// decryption +d := Decrypt(c, key.PubK, key.PrivK) +if m == d { + fmt.Println("ciphertext decrypted correctly") +} +``` + +- Homomorphic Addition +```go +// key generation [Alice] +key, err := GenerateKeyPair() +if err!=nil { + fmt.Println(err) +} + +// define values [Alice] +n1 := big.NewInt(int64(110)) +n2 := big.NewInt(int64(150)) + +// encrypt values [Alice] +c1 := Encrypt(n1, key.PubK) +c2 := Encrypt(n2, key.PubK) + +// compute homomorphic addition [Bob] +c3c4 := HomomorphicAddition(c1, c2, key.PubK) + +// decrypt the result [Alice] +d := Decrypt(c3c4, key.PubK, key.PrivK) +if !bytes.Equal(new(big.Int).Add(n1, n2).Bytes(), d.Bytes()) { + fmt.Println("decrypted result not equal to expected result") +} +``` diff --git a/rsa/README.md b/rsa/README.md new file mode 100644 index 0000000..a5ba489 --- /dev/null +++ b/rsa/README.md @@ -0,0 +1,94 @@ +## RSA cryptosystem & Blind signature & Homomorphic Multiplication +- https://en.wikipedia.org/wiki/RSA_(cryptosystem)# +- https://en.wikipedia.org/wiki/Blind_signature +- https://en.wikipedia.org/wiki/Homomorphic_encryption + +- [x] GenerateKeyPair +- [x] Encrypt +- [x] Decrypt +- [x] Blind +- [x] Blind Signature +- [x] Unblind Signature +- [x] Verify Signature +- [x] Homomorphic Multiplication + + +#### Usage +- Key generation, Encryption, Decryption +```go +// generate key pair +key, err := GenerateKeyPair() +if err!=nil { + fmt.Println(err) +} +mBytes := []byte("Hi") +m := new(big.Int).SetBytes(mBytes) + +// encrypt message +c := Encrypt(m, key.PubK) + +// decrypt ciphertext +d := Decrypt(c, key.PrivK) +if m == d { + fmt.Println("correctly decrypted") +} +``` + +- Blind signatures +```go +// key generation [Alice] +key, err := GenerateKeyPair() +if err!=nil { + fmt.Println(err) +} + +// create new message [Alice] +mBytes := []byte("Hi") +m := new(big.Int).SetBytes(mBytes) + +// define r value [Alice] +rVal := big.NewInt(int64(101)) + +// blind message [Alice] +mBlinded := Blind(m, rVal, key.PubK) + +// Blind Sign the blinded message [Bob] +sigma := BlindSign(mBlinded, key.PrivK) + +// unblind the blinded signed message, and get the signature of the message [Alice] +mSigned := Unblind(sigma, rVal, key.PubK) + +// verify the signature [Alice/Bob/Trudy] +verified := Verify(m, mSigned, key.PubK) +if !verified { + fmt.Println("signature could not be verified") +} +``` + +- Homomorphic Multiplication +```go +// key generation [Alice] +key, err := GenerateKeyPair() +if err!=nil { + fmt.Println(err) +} + +// define values [Alice] +n1 := big.NewInt(int64(11)) +n2 := big.NewInt(int64(15)) + +// encrypt the values [Alice] +c1 := Encrypt(n1, key.PubK) +c2 := Encrypt(n2, key.PubK) + +// compute homomorphic multiplication with the encrypted values [Bob] +c3c4 := HomomorphicMul(c1, c2, key.PubK) + +// decrypt the result [Alice] +d := Decrypt(c3c4, key.PrivK) + +// check that the result is the expected +if !bytes.Equal(new(big.Int).Mul(n1, n2).Bytes(), d.Bytes()) { + fmt.Println("decrypted result not equal to expected result") +} +``` diff --git a/schnorr/README.md b/schnorr/README.md new file mode 100644 index 0000000..5f57e38 --- /dev/null +++ b/schnorr/README.md @@ -0,0 +1,47 @@ +## Schnorr signature +- https://en.wikipedia.org/wiki/Schnorr_signature + +- [x] Hash[M || R] (where M is the msg bytes and R is a Point on the ECC, using sha256 hash function) +- [x] Generate Schnorr scheme +- [x] Sign +- [x] Verify signature + + +#### Usage +```go +// define new elliptic curve +ec := ecc.NewEC(big.NewInt(int64(0)), big.NewInt(int64(7)), big.NewInt(int64(11))) +// define new point +g := ecc.Point{big.NewInt(int64(11)), big.NewInt(int64(27))} // Generator +// define new random r +r := big.NewInt(int64(23)) // random r + +// define new Schnorr crypto system using the values +schnorr, sk, err := Gen(ec, g, r) +if err!=nil { + fmt.println(err) +} + +// define message to sign +m := []byte("hola") + +// also we can hash the message, but it's not mandatory, as it will be done inside the schnorr.Sign, but we can perform it now, just to check the function +h := Hash([]byte("hola"), c) +if h.String() != "34719153732582497359642109898768696927847420320548121616059449972754491425079") { + fmt.Println("not correctly hashed") +} + +s, rPoint, err := schnorr.Sign(sk, m) +if err!=nil { + fmt.println(err) +} + +// verify Schnorr signature +verified, err := Verify(schnorr.EC, sk.PubK, m, s, rPoint) +if err!=nil { + fmt.println(err) +} +if verified { + fmt.Println("Schnorr signature correctly verified") +} +``` diff --git a/schnorr/schnorr.go b/schnorr/schnorr.go index 184f528..75f261e 100644 --- a/schnorr/schnorr.go +++ b/schnorr/schnorr.go @@ -130,6 +130,9 @@ func Verify(ec ecc.EC, pk PubK, m []byte, s *big.Int, rPoint ecc.Point) (bool, e // s x P sp, err := ec.Mul(pk.P, s) + if err != nil { + return false, err + } // return reQ.Equal(sp), nil return eQ.Equal(sp), nil diff --git a/shamirsecretsharing/README.md b/shamirsecretsharing/README.md new file mode 100644 index 0000000..ff411d8 --- /dev/null +++ b/shamirsecretsharing/README.md @@ -0,0 +1,48 @@ +## Shamir Secret Sharing +- https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing + +- [x] create secret sharing from number of secrets needed, number of shares, random point p, secret to share +- [x] Lagrange Interpolation to restore the secret from the shares + +#### Usage +```go +// define secret to share +k := 123456789 + +// define random prime +p, err := rand.Prime(rand.Reader, bits/2) +if err!=nil { + fmt.Println(err) +} + +// define how many shares want to generate +nShares := big.NewInt(int64(6)) + +// define how many shares are needed to recover the secret +nNeededShares := big.NewInt(int64(3)) + +// create the shares +shares, err := Create( + nNeededShares, + nShares, + p, + big.NewInt(int64(k))) +assert.Nil(t, err) +if err!=nil { + fmt.Println(err) +} + +// select shares to use +var sharesToUse [][]*big.Int +sharesToUse = append(sharesToUse, shares[2]) +sharesToUse = append(sharesToUse, shares[1]) +sharesToUse = append(sharesToUse, shares[0]) + +// recover the secret using Lagrange Interpolation +secr := LagrangeInterpolation(sharesToUse, p) + +// check that the restored secret matches the original secret +if !bytes.Equal(k.Bytes(), secr.Bytes()) { + fmt.Println("reconstructed secret not correspond to original secret") +} +``` diff --git a/shamirsecretsharing/shamirsecretsharing_test.go b/shamirsecretsharing/shamirsecretsharing_test.go index b1048c5..f326ecc 100644 --- a/shamirsecretsharing/shamirsecretsharing_test.go +++ b/shamirsecretsharing/shamirsecretsharing_test.go @@ -15,10 +15,10 @@ func TestCreate(t *testing.T) { p, err := rand.Prime(rand.Reader, bits/2) assert.Nil(t, err) - nNeededSecrets := big.NewInt(int64(3)) nShares := big.NewInt(int64(6)) + nNeededShares := big.NewInt(int64(3)) shares, err := Create( - nNeededSecrets, + nNeededShares, nShares, p, k)