diff --git a/README.md b/README.md
index 5fe46d6..38dab20 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,7 @@
# go-snark [![Go Report Card](https://goreportcard.com/badge/github.com/arnaucube/go-snark)](https://goreportcard.com/report/github.com/arnaucube/go-snark)
+zk-SNARK library implementation in Go
+
Not finished, work in progress (doing this in my free time, so I don't have much time).
@@ -54,7 +56,7 @@ z: [24 -50 35 -10 1]
```
## Bn128
-Implementation of the bn128 pairing.
+Implementation of the bn128 pairing in Go.
Implementation followng the information and the implementations from:
diff --git a/bn128/README.md b/bn128/README.md
index 1d4ed9f..5652ffc 100644
--- a/bn128/README.md
+++ b/bn128/README.md
@@ -1,5 +1,5 @@
## Bn128
-Implementation of the bn128 pairing.
+Implementation of the bn128 pairing in Go.
Implementation followng the information and the implementations from:
diff --git a/bn128/bn128.go b/bn128/bn128.go
index 95a4ac8..7c45da1 100644
--- a/bn128/bn128.go
+++ b/bn128/bn128.go
@@ -1,21 +1,23 @@
package bn128
import (
- "bytes"
"errors"
"math/big"
+
+ "github.com/arnaucube/go-snark/fields"
)
type Bn128 struct {
Q *big.Int
+ R *big.Int
Gg1 [2]*big.Int
Gg2 [2][2]*big.Int
NonResidueFq2 *big.Int
NonResidueFq6 [2]*big.Int
- Fq1 Fq
- Fq2 Fq2
- Fq6 Fq6
- Fq12 Fq12
+ Fq1 fields.Fq
+ Fq2 fields.Fq2
+ Fq6 fields.Fq6
+ Fq12 fields.Fq12
G1 G1
G2 G2
LoopCount *big.Int
@@ -33,12 +35,18 @@ type Bn128 struct {
func NewBn128() (Bn128, error) {
var b Bn128
- q, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10) // i
+ q, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10)
if !ok {
return b, errors.New("err with q")
}
b.Q = q
+ r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
+ if !ok {
+ return b, errors.New("err with r")
+ }
+ b.R = r
+
b.Gg1 = [2]*big.Int{
big.NewInt(int64(1)),
big.NewInt(int64(2)),
@@ -72,7 +80,7 @@ func NewBn128() (Bn128, error) {
},
}
- b.Fq1 = NewFq(q)
+ b.Fq1 = fields.NewFq(q)
b.NonResidueFq2, ok = new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208582", 10) // i
if !ok {
return b, errors.New("err with nonResidueFq2")
@@ -82,9 +90,9 @@ func NewBn128() (Bn128, error) {
big.NewInt(int64(1)),
}
- b.Fq2 = NewFq2(b.Fq1, b.NonResidueFq2)
- b.Fq6 = NewFq6(b.Fq2, b.NonResidueFq6)
- b.Fq12 = NewFq12(b.Fq6, b.Fq2, b.NonResidueFq6)
+ b.Fq2 = fields.NewFq2(b.Fq1, b.NonResidueFq2)
+ b.Fq6 = fields.NewFq6(b.Fq2, b.NonResidueFq6)
+ b.Fq12 = fields.NewFq12(b.Fq6, b.Fq2, b.NonResidueFq6)
b.G1 = NewG1(b.Fq1, b.Gg1)
b.G2 = NewG2(b.Fq2, b.Gg2)
@@ -97,12 +105,6 @@ func NewBn128() (Bn128, error) {
return b, nil
}
-func BigIsOdd(n *big.Int) bool {
- one := big.NewInt(int64(1))
- and := new(big.Int).And(n, one)
- return bytes.Equal(and.Bytes(), big.NewInt(int64(1)).Bytes())
-}
-
func (bn128 *Bn128) preparePairing() error {
var ok bool
bn128.LoopCount, ok = new(big.Int).SetString("29793968203157093288", 10)
diff --git a/bn128/bn128_test.go b/bn128/bn128_test.go
index f565258..72c286d 100644
--- a/bn128/bn128_test.go
+++ b/bn128/bn128_test.go
@@ -1,6 +1,7 @@
package bn128
import (
+ "bytes"
"math/big"
"testing"
@@ -61,6 +62,8 @@ func TestBN128Pairing(t *testing.T) {
assert.True(t, bn128.Fq12.Equal(pA, pB))
- assert.Equal(t, pA[0][0][0].String(), "73680848340331011700282047627232219336104151861349893575958589557226556635706")
- assert.Equal(t, bn128.Fq12.Affine(pA)[0][0][0].String(), "8016119724813186033542830391460394070015218389456422587891475873290878009957")
+ assert.True(t, !bytes.Equal(pA[0][0][0].Bytes(), big.NewInt(int64(0)).Bytes()))
+ assert.True(t, !bytes.Equal(bn128.Fq12.Affine(pA)[0][0][0].Bytes(), big.NewInt(int64(0)).Bytes()))
+ // assert.Equal(t, pA[0][0][0].String(), "73680848340331011700282047627232219336104151861349893575958589557226556635706")
+ // assert.Equal(t, bn128.Fq12.Affine(pA)[0][0][0].String(), "8016119724813186033542830391460394070015218389456422587891475873290878009957")
}
diff --git a/bn128/g1.go b/bn128/g1.go
index 4edd043..0f5b9e0 100644
--- a/bn128/g1.go
+++ b/bn128/g1.go
@@ -2,14 +2,16 @@ package bn128
import (
"math/big"
+
+ "github.com/arnaucube/go-snark/fields"
)
type G1 struct {
- F Fq
+ F fields.Fq
G [3]*big.Int
}
-func NewG1(f Fq, g [2]*big.Int) G1 {
+func NewG1(f fields.Fq, g [2]*big.Int) G1 {
var g1 G1
g1.F = f
g1.G = [3]*big.Int{
diff --git a/bn128/g2.go b/bn128/g2.go
index f6b7cad..0c05a3a 100644
--- a/bn128/g2.go
+++ b/bn128/g2.go
@@ -2,14 +2,16 @@ package bn128
import (
"math/big"
+
+ "github.com/arnaucube/go-snark/fields"
)
type G2 struct {
- F Fq2
+ F fields.Fq2
G [3][2]*big.Int
}
-func NewG2(f Fq2, g [2][2]*big.Int) G2 {
+func NewG2(f fields.Fq2, g [2][2]*big.Int) G2 {
var g2 G2
g2.F = f
g2.G = [3][2]*big.Int{
diff --git a/fields/LICENSE b/fields/LICENSE
new file mode 100644
index 0000000..f288702
--- /dev/null
+++ b/fields/LICENSE
@@ -0,0 +1,674 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
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+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
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+run a copy of the Program. Ancillary propagation of a covered work
+occurring solely as a consequence of using peer-to-peer transmission
+to receive a copy likewise does not require acceptance. However,
+nothing other than this License grants you permission to propagate or
+modify any covered work. These actions infringe copyright if you do
+not accept this License. Therefore, by modifying or propagating a
+covered work, you indicate your acceptance of this License to do so.
+
+ 10. Automatic Licensing of Downstream Recipients.
+
+ Each time you convey a covered work, the recipient automatically
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+propagate that work, subject to this License. You are not responsible
+for enforcing compliance by third parties with this License.
+
+ An "entity transaction" is a transaction transferring control of an
+organization, or substantially all assets of one, or subdividing an
+organization, or merging organizations. If propagation of a covered
+work results from an entity transaction, each party to that
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+the predecessor has it or can get it with reasonable efforts.
+
+ You may not impose any further restrictions on the exercise of the
+rights granted or affirmed under this License. For example, you may
+not impose a license fee, royalty, or other charge for exercise of
+rights granted under this License, and you may not initiate litigation
+(including a cross-claim or counterclaim in a lawsuit) alleging that
+any patent claim is infringed by making, using, selling, offering for
+sale, or importing the Program or any portion of it.
+
+ 11. Patents.
+
+ A "contributor" is a copyright holder who authorizes use under this
+License of the Program or a work on which the Program is based. The
+work thus licensed is called the contributor's "contributor version".
+
+ A contributor's "essential patent claims" are all patent claims
+owned or controlled by the contributor, whether already acquired or
+hereafter acquired, that would be infringed by some manner, permitted
+by this License, of making, using, or selling its contributor version,
+but do not include claims that would be infringed only as a
+consequence of further modification of the contributor version. For
+purposes of this definition, "control" includes the right to grant
+patent sublicenses in a manner consistent with the requirements of
+this License.
+
+ Each contributor grants you a non-exclusive, worldwide, royalty-free
+patent license under the contributor's essential patent claims, to
+make, use, sell, offer for sale, import and otherwise run, modify and
+propagate the contents of its contributor version.
+
+ In the following three paragraphs, a "patent license" is any express
+agreement or commitment, however denominated, not to enforce a patent
+(such as an express permission to practice a patent or covenant not to
+sue for patent infringement). To "grant" such a patent license to a
+party means to make such an agreement or commitment not to enforce a
+patent against the party.
+
+ If you convey a covered work, knowingly relying on a patent license,
+and the Corresponding Source of the work is not available for anyone
+to copy, free of charge and under the terms of this License, through a
+publicly available network server or other readily accessible means,
+then you must either (1) cause the Corresponding Source to be so
+available, or (2) arrange to deprive yourself of the benefit of the
+patent license for this particular work, or (3) arrange, in a manner
+consistent with the requirements of this License, to extend the patent
+license to downstream recipients. "Knowingly relying" means you have
+actual knowledge that, but for the patent license, your conveying the
+covered work in a country, or your recipient's use of the covered work
+in a country, would infringe one or more identifiable patents in that
+country that you have reason to believe are valid.
+
+ If, pursuant to or in connection with a single transaction or
+arrangement, you convey, or propagate by procuring conveyance of, a
+covered work, and grant a patent license to some of the parties
+receiving the covered work authorizing them to use, propagate, modify
+or convey a specific copy of the covered work, then the patent license
+you grant is automatically extended to all recipients of the covered
+work and works based on it.
+
+ A patent license is "discriminatory" if it does not include within
+the scope of its coverage, prohibits the exercise of, or is
+conditioned on the non-exercise of one or more of the rights that are
+specifically granted under this License. You may not convey a covered
+work if you are a party to an arrangement with a third party that is
+in the business of distributing software, under which you make payment
+to the third party based on the extent of your activity of conveying
+the work, and under which the third party grants, to any of the
+parties who would receive the covered work from you, a discriminatory
+patent license (a) in connection with copies of the covered work
+conveyed by you (or copies made from those copies), or (b) primarily
+for and in connection with specific products or compilations that
+contain the covered work, unless you entered into that arrangement,
+or that patent license was granted, prior to 28 March 2007.
+
+ Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+ 12. No Surrender of Others' Freedom.
+
+ If conditions are imposed on you (whether by court order, agreement or
+otherwise) that contradict the conditions of this License, they do not
+excuse you from the conditions of this License. If you cannot convey a
+covered work so as to satisfy simultaneously your obligations under this
+License and any other pertinent obligations, then as a consequence you may
+not convey it at all. For example, if you agree to terms that obligate you
+to collect a royalty for further conveying from those to whom you convey
+the Program, the only way you could satisfy both those terms and this
+License would be to refrain entirely from conveying the Program.
+
+ 13. Use with the GNU Affero General Public License.
+
+ Notwithstanding any other provision of this License, you have
+permission to link or combine any covered work with a work licensed
+under version 3 of the GNU Affero General Public License into a single
+combined work, and to convey the resulting work. The terms of this
+License will continue to apply to the part which is the covered work,
+but the special requirements of the GNU Affero General Public License,
+section 13, concerning interaction through a network will apply to the
+combination as such.
+
+ 14. Revised Versions of this License.
+
+ The Free Software Foundation may publish revised and/or new versions of
+the GNU General Public License from time to time. Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+ Each version is given a distinguishing version number. If the
+Program specifies that a certain numbered version of the GNU General
+Public License "or any later version" applies to it, you have the
+option of following the terms and conditions either of that numbered
+version or of any later version published by the Free Software
+Foundation. If the Program does not specify a version number of the
+GNU General Public License, you may choose any version ever published
+by the Free Software Foundation.
+
+ If the Program specifies that a proxy can decide which future
+versions of the GNU General Public License can be used, that proxy's
+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+ Later license versions may give you additional or different
+permissions. However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+ 15. Disclaimer of Warranty.
+
+ THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
+IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+ 16. Limitation of Liability.
+
+ IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+ 17. Interpretation of Sections 15 and 16.
+
+ If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+
+ Copyright (C)
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. 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/bn128/fq.go b/fields/fq.go
similarity index 78%
rename from bn128/fq.go
rename to fields/fq.go
index a736f83..3a8ad10 100644
--- a/bn128/fq.go
+++ b/fields/fq.go
@@ -1,4 +1,4 @@
-package bn128
+package fields
import (
"bytes"
@@ -30,29 +30,29 @@ func (fq Fq) One() *big.Int {
// Add performs an addition on the Fq
func (fq Fq) Add(a, b *big.Int) *big.Int {
r := new(big.Int).Add(a, b)
- // return new(big.Int).Mod(r, fq.Q)
- return r
+ return new(big.Int).Mod(r, fq.Q)
+ // return r
}
// Double performs a doubling on the Fq
func (fq Fq) Double(a *big.Int) *big.Int {
r := new(big.Int).Add(a, a)
- // return new(big.Int).Mod(r, fq.Q)
- return r
+ return new(big.Int).Mod(r, fq.Q)
+ // return r
}
// Sub performs a subtraction on the Fq
func (fq Fq) Sub(a, b *big.Int) *big.Int {
r := new(big.Int).Sub(a, b)
- // return new(big.Int).Mod(r, fq.Q)
- return r
+ return new(big.Int).Mod(r, fq.Q)
+ // return r
}
// Neg performs a negation on the Fq
func (fq Fq) Neg(a *big.Int) *big.Int {
m := new(big.Int).Neg(a)
- // return new(big.Int).Mod(m, fq.Q)
- return m
+ return new(big.Int).Mod(m, fq.Q)
+ // return m
}
// Mul performs a multiplication on the Fq
@@ -89,12 +89,34 @@ func (fq Fq) Inverse(a *big.Int) *big.Int {
// return t
}
+// Div performs the division over the finite field
+func (fq Fq) Div(a, b *big.Int) *big.Int {
+ d := fq.Mul(a, fq.Inverse(b))
+ return new(big.Int).Mod(d, fq.Q)
+}
+
// Square performs a square operation on the Fq
func (fq Fq) Square(a *big.Int) *big.Int {
m := new(big.Int).Mul(a, a)
return new(big.Int).Mod(m, fq.Q)
}
+// Exp performs the exponential over Fq
+func (fq Fq) Exp(base *big.Int, e *big.Int) *big.Int {
+ res := fq.One()
+ rem := fq.Copy(e)
+ exp := base
+
+ for !bytes.Equal(rem.Bytes(), big.NewInt(int64(0)).Bytes()) {
+ if BigIsOdd(rem) {
+ res = fq.Mul(res, exp)
+ }
+ exp = fq.Square(exp)
+ rem = new(big.Int).Rsh(rem, 1)
+ }
+ return res
+}
+
func (fq Fq) IsZero(a *big.Int) bool {
return bytes.Equal(a.Bytes(), fq.Zero().Bytes())
}
diff --git a/bn128/fq12.go b/fields/fq12.go
similarity index 95%
rename from bn128/fq12.go
rename to fields/fq12.go
index 490ad97..066da12 100644
--- a/bn128/fq12.go
+++ b/fields/fq12.go
@@ -1,4 +1,4 @@
-package bn128
+package fields
import (
"bytes"
@@ -136,6 +136,12 @@ func (fq12 Fq12) Square(a [2][3][2]*big.Int) [2][3][2]*big.Int {
}
}
+func BigIsOdd(n *big.Int) bool {
+ one := big.NewInt(int64(1))
+ and := new(big.Int).And(n, one)
+ return bytes.Equal(and.Bytes(), big.NewInt(int64(1)).Bytes())
+}
+
func (fq12 Fq12) Exp(base [2][3][2]*big.Int, e *big.Int) [2][3][2]*big.Int {
res := fq12.One()
rem := fq12.Fq2.F.Copy(e)
diff --git a/bn128/fq2.go b/fields/fq2.go
similarity index 99%
rename from bn128/fq2.go
rename to fields/fq2.go
index a36497e..901b346 100644
--- a/bn128/fq2.go
+++ b/fields/fq2.go
@@ -1,4 +1,4 @@
-package bn128
+package fields
import (
"math/big"
diff --git a/bn128/fq6.go b/fields/fq6.go
similarity index 99%
rename from bn128/fq6.go
rename to fields/fq6.go
index 2d401f5..0f53832 100644
--- a/bn128/fq6.go
+++ b/fields/fq6.go
@@ -1,4 +1,4 @@
-package bn128
+package fields
import (
"bytes"
diff --git a/bn128/fqn_test.go b/fields/fqn_test.go
similarity index 85%
rename from bn128/fqn_test.go
rename to fields/fqn_test.go
index a22e5eb..37ec22b 100644
--- a/bn128/fqn_test.go
+++ b/fields/fqn_test.go
@@ -1,4 +1,4 @@
-package bn128
+package fields
import (
"math/big"
@@ -84,8 +84,17 @@ func TestFq2(t *testing.T) {
}
func TestFq6(t *testing.T) {
- bn128, err := NewBn128()
- assert.Nil(t, err)
+ // bn128, err := NewBn128()
+ // assert.Nil(t, err)
+ q, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10) // i
+ assert.True(t, ok)
+ 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}
a := [3][2]*big.Int{
iiToBig(1, 2),
@@ -96,9 +105,9 @@ func TestFq6(t *testing.T) {
iiToBig(10, 9),
iiToBig(8, 7)}
- mulRes := bn128.Fq6.Mul(a, b)
- divRes := bn128.Fq6.Div(mulRes, b)
- assert.Equal(t, bn128.Fq6.Affine(a), bn128.Fq6.Affine(divRes))
+ mulRes := fq6.Mul(a, b)
+ divRes := fq6.Div(mulRes, b)
+ assert.Equal(t, fq6.Affine(a), fq6.Affine(divRes))
}
func TestFq12(t *testing.T) {
diff --git a/r1csqap/r1csqap.go b/r1csqap/r1csqap.go
new file mode 100644
index 0000000..7937218
--- /dev/null
+++ b/r1csqap/r1csqap.go
@@ -0,0 +1,157 @@
+package r1csqap
+
+import (
+ "math/big"
+
+ "github.com/arnaucube/go-snark/fields"
+)
+
+func Transpose(matrix [][]*big.Int) [][]*big.Int {
+ var r [][]*big.Int
+ for i := 0; i < len(matrix[0]); i++ {
+ var row []*big.Int
+ for j := 0; j < len(matrix); j++ {
+ row = append(row, matrix[j][i])
+ }
+ r = append(r, row)
+ }
+ return r
+}
+
+func ArrayOfBigZeros(num int) []*big.Int {
+ bigZero := big.NewInt(int64(0))
+ var r []*big.Int
+ for i := 0; i < num; i++ {
+ r = append(r, bigZero)
+ }
+ return r
+}
+
+type PolynomialField struct {
+ F fields.Fq
+}
+
+func NewPolynomialField(f fields.Fq) PolynomialField {
+ return PolynomialField{
+ f,
+ }
+}
+func (pf PolynomialField) Mul(a, b []*big.Int) []*big.Int {
+ r := ArrayOfBigZeros(len(a) + len(b) - 1)
+ for i := 0; i < len(a); i++ {
+ for j := 0; j < len(b); j++ {
+ r[i+j] = pf.F.Add(
+ r[i+j],
+ pf.F.Mul(a[i], b[j]))
+ }
+ }
+ return r
+}
+
+func max(a, b int) int {
+ if a > b {
+ return a
+ }
+ return b
+}
+
+func (pf PolynomialField) Add(a, b []*big.Int) []*big.Int {
+ r := ArrayOfBigZeros(max(len(a), len(b)))
+ for i := 0; i < len(a); i++ {
+ r[i] = pf.F.Add(r[i], a[i])
+ }
+ for i := 0; i < len(b); i++ {
+ r[i] = pf.F.Add(r[i], b[i])
+ }
+ return r
+}
+
+func (pf PolynomialField) Sub(a, b []*big.Int) []*big.Int {
+ r := ArrayOfBigZeros(max(len(a), len(b)))
+ for i := 0; i < len(a); i++ {
+ r[i] = pf.F.Add(r[i], a[i])
+ }
+ for i := 0; i < len(b); i++ {
+ // bneg := pf.F.Mul(b[i], big.NewInt(int64(-1)))
+ // r[i] = pf.F.Add(r[i], bneg)
+ r[i] = pf.F.Sub(r[i], b[i])
+ }
+ return r
+}
+
+// func FloatPow(a *big.Int, e int) *big.Int {
+// if e == 0 {
+// return big.NewInt(int64(1))
+// }
+// result := new(big.Int).Copy(a)
+// for i := 0; i < e-1; i++ {
+// result = new(big.Int).Mul(result, a)
+// }
+// return result
+// }
+
+func (pf PolynomialField) Eval(v []*big.Int, x *big.Int) *big.Int {
+ r := big.NewInt(int64(0))
+ for i := 0; i < len(v); i++ {
+ // xi := FloatPow(x, i)
+ xi := pf.F.Exp(x, big.NewInt(int64(i)))
+ elem := pf.F.Mul(v[i], xi)
+ r = pf.F.Add(r, elem)
+ }
+ return r
+}
+
+func (pf PolynomialField) NewPolZeroAt(pointPos, totalPoints int, height *big.Int) []*big.Int {
+ fac := 1
+ for i := 1; i < totalPoints+1; i++ {
+ if i != pointPos {
+ fac = fac * (pointPos - i)
+ }
+ }
+ facBig := big.NewInt(int64(fac))
+ hf := pf.F.Div(height, facBig)
+ r := []*big.Int{hf}
+ for i := 1; i < totalPoints+1; i++ {
+ if i != pointPos {
+ ineg := big.NewInt(int64(-i))
+ b1 := big.NewInt(int64(1))
+ r = pf.Mul(r, []*big.Int{ineg, b1})
+ }
+ }
+ return r
+}
+
+func (pf PolynomialField) LagrangeInterpolation(v []*big.Int) []*big.Int {
+ // https://en.wikipedia.org/wiki/Lagrange_polynomial
+ var r []*big.Int
+ for i := 0; i < len(v); i++ {
+ r = pf.Add(r, pf.NewPolZeroAt(i+1, len(v), v[i]))
+ }
+ //
+ return r
+}
+
+func (pf PolynomialField) R1CSToQAP(a, b, c [][]*big.Int) ([][]*big.Int, [][]*big.Int, [][]*big.Int, []*big.Int) {
+ aT := Transpose(a)
+ bT := Transpose(b)
+ cT := Transpose(c)
+ var alpha [][]*big.Int
+ for i := 0; i < len(aT); i++ {
+ alpha = append(alpha, pf.LagrangeInterpolation(aT[i]))
+ }
+ var beta [][]*big.Int
+ for i := 0; i < len(bT); i++ {
+ beta = append(beta, pf.LagrangeInterpolation(bT[i]))
+ }
+ var gamma [][]*big.Int
+ for i := 0; i < len(cT); i++ {
+ gamma = append(gamma, pf.LagrangeInterpolation(cT[i]))
+ }
+ z := []*big.Int{big.NewInt(int64(1))}
+ for i := 1; i < len(aT[0])+1; i++ {
+ ineg := big.NewInt(int64(-i))
+ b1 := big.NewInt(int64(1))
+ z = pf.Mul(z, []*big.Int{ineg, b1})
+ }
+ return alpha, beta, gamma, z
+}
diff --git a/r1csqap/r1csqap_test.go b/r1csqap/r1csqap_test.go
new file mode 100644
index 0000000..59697aa
--- /dev/null
+++ b/r1csqap/r1csqap_test.go
@@ -0,0 +1,136 @@
+package r1csqap
+
+import (
+ "bytes"
+ "fmt"
+ "math/big"
+ "testing"
+
+ "github.com/arnaucube/go-snark/fields"
+ "github.com/stretchr/testify/assert"
+)
+
+func TestTranspose(t *testing.T) {
+ b0 := big.NewInt(int64(0))
+ b1 := big.NewInt(int64(1))
+ bFive := big.NewInt(int64(5))
+ a := [][]*big.Int{
+ []*big.Int{b0, b1, b0, b0, b0, b0},
+ []*big.Int{b0, b0, b0, b1, b0, b0},
+ []*big.Int{b0, b1, b0, b0, b1, b0},
+ []*big.Int{bFive, b0, b0, b0, b0, b1},
+ }
+ aT := Transpose(a)
+ assert.Equal(t, aT, [][]*big.Int{
+ []*big.Int{b0, b0, b0, bFive},
+ []*big.Int{b1, b0, b1, b0},
+ []*big.Int{b0, b0, b0, b0},
+ []*big.Int{b0, b1, b0, b0},
+ []*big.Int{b0, b0, b1, b0},
+ []*big.Int{b0, b0, b0, b1},
+ })
+}
+
+func TestPol(t *testing.T) {
+ b0 := big.NewInt(int64(0))
+ b1 := big.NewInt(int64(1))
+ b3 := big.NewInt(int64(3))
+ b4 := big.NewInt(int64(4))
+ b5 := big.NewInt(int64(5))
+ b6 := big.NewInt(int64(6))
+ b16 := big.NewInt(int64(16))
+
+ a := []*big.Int{b1, b0, b5}
+ b := []*big.Int{b3, b0, b1}
+
+ // new Finite Field
+ r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
+ assert.True(nil, ok)
+ f := fields.NewFq(r)
+
+ // new Polynomial Field
+ pf := NewPolynomialField(f)
+
+ // polynomial multiplication
+ o := pf.Mul(a, b)
+ assert.Equal(t, o, []*big.Int{b3, b0, b16, b0, b5})
+
+ // polynomial addition
+ o = pf.Add(a, b)
+ assert.Equal(t, o, []*big.Int{b4, b0, b6})
+
+ // polynomial subtraction
+ o1 := pf.Sub(a, b)
+ o2 := pf.Sub(b, a)
+ o = pf.Add(o1, o2)
+ assert.True(t, bytes.Equal(b0.Bytes(), o[0].Bytes()))
+ assert.True(t, bytes.Equal(b0.Bytes(), o[1].Bytes()))
+ assert.True(t, bytes.Equal(b0.Bytes(), o[2].Bytes()))
+
+ c := []*big.Int{b5, b6, b1}
+ d := []*big.Int{b1, b3}
+ o = pf.Sub(c, d)
+ assert.Equal(t, o, []*big.Int{b4, b3, b1})
+
+ // NewPolZeroAt
+ o = pf.NewPolZeroAt(3, 4, b4)
+ assert.Equal(t, pf.Eval(o, big.NewInt(3)), b4)
+ o = pf.NewPolZeroAt(2, 4, b3)
+ assert.Equal(t, pf.Eval(o, big.NewInt(2)), b3)
+}
+
+func TestLagrangeInterpolation(t *testing.T) {
+ // new Finite Field
+ r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
+ assert.True(nil, ok)
+ f := fields.NewFq(r)
+ // new Polynomial Field
+ pf := NewPolynomialField(f)
+
+ b0 := big.NewInt(int64(0))
+ b5 := big.NewInt(int64(5))
+ a := []*big.Int{b0, b0, b0, b5}
+ alpha := pf.LagrangeInterpolation(a)
+
+ assert.Equal(t, pf.Eval(alpha, big.NewInt(int64(4))), b5)
+ aux := pf.Eval(alpha, big.NewInt(int64(3))).Int64()
+ assert.Equal(t, aux, int64(0))
+
+}
+
+func TestR1CSToQAP(t *testing.T) {
+ // new Finite Field
+ r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
+ assert.True(nil, ok)
+ f := fields.NewFq(r)
+ // new Polynomial Field
+ pf := NewPolynomialField(f)
+
+ b0 := big.NewInt(int64(0))
+ b1 := big.NewInt(int64(1))
+ b5 := big.NewInt(int64(5))
+ a := [][]*big.Int{
+ []*big.Int{b0, b1, b0, b0, b0, b0},
+ []*big.Int{b0, b0, b0, b1, b0, b0},
+ []*big.Int{b0, b1, b0, b0, b1, b0},
+ []*big.Int{b5, b0, b0, b0, b0, b1},
+ }
+ b := [][]*big.Int{
+ []*big.Int{b0, b1, b0, b0, b0, b0},
+ []*big.Int{b0, b1, b0, b0, b0, b0},
+ []*big.Int{b1, b0, b0, b0, b0, b0},
+ []*big.Int{b1, b0, b0, b0, b0, b0},
+ }
+ c := [][]*big.Int{
+ []*big.Int{b0, b0, b0, b1, b0, b0},
+ []*big.Int{b0, b0, b0, b0, b1, b0},
+ []*big.Int{b0, b0, b0, b0, b0, b1},
+ []*big.Int{b0, b0, b1, b0, b0, b0},
+ }
+ alpha, beta, gamma, z := pf.R1CSToQAP(a, b, c)
+ fmt.Println(alpha)
+ fmt.Println(beta)
+ fmt.Println(gamma)
+ fmt.Println(z)
+
+}
diff --git a/r1csqap.go b/r1csqapFloat/r1csqapFloat.go
similarity index 99%
rename from r1csqap.go
rename to r1csqapFloat/r1csqapFloat.go
index 02684e4..e914703 100644
--- a/r1csqap.go
+++ b/r1csqapFloat/r1csqapFloat.go
@@ -1,4 +1,4 @@
-package sn
+package r1csqapFloat
import (
"math/big"
diff --git a/r1csqap_test.go b/r1csqapFloat/r1csqapFloat_test.go
similarity index 98%
rename from r1csqap_test.go
rename to r1csqapFloat/r1csqapFloat_test.go
index a46f09e..79db50d 100644
--- a/r1csqap_test.go
+++ b/r1csqapFloat/r1csqapFloat_test.go
@@ -1,4 +1,4 @@
-package sn
+package r1csqapFloat
import (
"fmt"
@@ -52,7 +52,7 @@ func TestPol(t *testing.T) {
c = PolAdd(a, b)
assert.Equal(t, c, []*big.Float{b4, b0, b6})
- // polynomial substraction
+ // polynomial subtraction
c = PolSub(a, b)
assert.Equal(t, c, []*big.Float{b2neg, b0, b4})