-
Notifications
You must be signed in to change notification settings - Fork 144
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
Squashed commit of the following: commit ec347f5 Author: armfazh <[email protected]> Date: Fri Jul 24 15:28:34 2020 -0700 Adding decaf group. commit 796b37e Author: armfazh <[email protected]> Date: Wed Jul 22 19:44:07 2020 -0700 Updates internal packages of Ed448. commit f5957e7 Author: armfazh <[email protected]> Date: Wed Jul 22 19:11:15 2020 -0700 Updating Decaf documentation. commit 6f573e6 Author: armfazh <[email protected]> Date: Wed Jul 22 13:56:12 2020 -0700 Updating documentation of ted448 internal package. commit 7e80bfc Author: armfazh <[email protected]> Date: Wed Jun 10 01:56:31 2020 -0700 Adapting ed448 for using the internal ted448 package. commit 44ce6c5 Author: armfazh <[email protected]> Date: Tue Jun 9 23:36:17 2020 -0700 ted448 point public fields. commit 13dd30d Author: armfazh <[email protected]> Date: Tue Jun 9 20:32:32 2020 -0700 Moving twist implementation to an internal package. commit 4cdcb71 Author: armfazh <[email protected]> Date: Mon Jun 1 01:30:22 2020 -0700 Solving scalar constant-time operations. commit 26b9ea4 Author: armfazh <[email protected]> Date: Thu May 21 09:21:36 2020 -0700 Review comments on formulas. commit ff821b5 Author: armfazh <[email protected]> Date: Tue May 19 16:54:36 2020 -0700 Adding tests for detecting decaf/point invalid encodings. commit 3881ea8 Author: armfazh <[email protected]> Date: Fri May 15 15:13:53 2020 -0700 One test for decaf, unmarshaling straight-line code, and check for errors. commit 9b048c0 Author: armfazh <[email protected]> Date: Thu May 14 18:12:57 2020 -0700 Updating interface for decaf and curve. commit a99153c Author: armfazh <[email protected]> Date: Thu May 14 16:10:04 2020 -0700 Adding goldilocks documentation. commit a62d6bd Author: armfazh <[email protected]> Date: Thu May 14 14:15:02 2020 -0700 Adding decaf v1.1 and kat tests. commit c72bdfa Author: armfazh <[email protected]> Date: Wed May 13 13:30:11 2020 -0700 Removing non-used fp functions. commit d4fc865 Author: armfazh <[email protected]> Date: Tue May 12 11:47:57 2020 -0700 Adding some helper functions. commit 6173c83 Author: armfazh <[email protected]> Date: Tue May 12 05:15:55 2020 -0700 Decaf decoding working. More tests needed. commit daa36c1 Author: armfazh <[email protected]> Date: Mon May 11 16:16:16 2020 -0700 Decaf encoding is working, except by the choice of generator. commit 8933f6c Author: armfazh <[email protected]> Date: Thu May 7 01:19:47 2020 -0700 Decaf encoding requires cannon sqrt. commit 9479b45 Author: armfazh <[email protected]> Date: Wed Apr 29 14:51:21 2020 -0700 Adding support for decaf quotient group.
- Loading branch information
Showing
31 changed files
with
1,769 additions
and
1,138 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,28 @@ | ||
| package decaf | ||
|
|
||
| import ( | ||
| "errors" | ||
|
|
||
| fp "github.com/cloudflare/circl/math/fp448" | ||
| ) | ||
|
|
||
| // DecafEncodingSize is the size (in bytes) of an encoded Decaf element. | ||
| const EncodingSize = fp.Size | ||
|
|
||
| // ErrInvalidDecoding alerts of an error during decoding a point. | ||
| var ErrInvalidDecoding = errors.New("invalid decoding") | ||
|
|
||
| var ( | ||
| // aMinusD is paramA-paramD = (-1)-(-39082) = 39081. | ||
| aMinusD = fp.Elt{0xa9, 0x98} | ||
| // sqrtAMinusD is the smallest root of sqrt(paramA-paramD) = sqrt(39081). | ||
| sqrtAMinusD = fp.Elt{ | ||
| 0x36, 0x27, 0x57, 0x45, 0x0f, 0xef, 0x42, 0x96, | ||
| 0x52, 0xce, 0x20, 0xaa, 0xf6, 0x7b, 0x33, 0x60, | ||
| 0xd2, 0xde, 0x6e, 0xfd, 0xf4, 0x66, 0x9a, 0x83, | ||
| 0xba, 0x14, 0x8c, 0x96, 0x80, 0xd7, 0xa2, 0x64, | ||
| 0x4b, 0xd5, 0xb8, 0xa5, 0xb8, 0xa7, 0xf1, 0xa1, | ||
| 0xa0, 0x6a, 0xa2, 0x2f, 0x72, 0x8d, 0xf6, 0x3b, | ||
| 0x68, 0xf7, 0x24, 0xeb, 0xfb, 0x62, 0xd9, 0x22, | ||
| } | ||
| ) |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,191 @@ | ||
| // Package decaf provides a prime-order group derived from a quotient of | ||
| // Edwards curves. | ||
| // | ||
| // Decaf Group | ||
| // | ||
| // Decaf (3) is a prime-order group constructed as a quotient of groups. A Decaf | ||
| // element can be represented by any point in the coset P+J[2], where J is a | ||
| // Jacobi quartic curve and J[2] are its 2-torsion points. | ||
| // Since P+J[2] has four points, Decaf specifies rules to choose one canonical | ||
| // representative, which has a unique encoding. Two representations are | ||
| // equivalent if they belong to the same coset. | ||
| // | ||
| // The types Elt and Scalar provide methods to perform arithmetic operations on | ||
| // the Decaf group. | ||
| // | ||
| // Version | ||
| // | ||
| // This implementation uses Decaf v1.0 of the encoding (see (4,5) for a complete | ||
| // specification). | ||
| // | ||
| // References | ||
| // | ||
| // (1) https://www.shiftleft.org/papers/goldilocks | ||
| // | ||
| // (2) https://tools.ietf.org/html/rfc7748 | ||
| // | ||
| // (3) https://doi.org/10.1007/978-3-662-47989-6_34 and https://www.shiftleft.org/papers/decaf | ||
| // | ||
| // (4) https://sourceforge.net/p/ed448goldilocks/code/ci/v1.0/tree/ | ||
| // | ||
| // (5) https://mailarchive.ietf.org/arch/msg/cfrg/S4YUTt_5eD4kwYbDuhEK0tXT1aM/ | ||
| package decaf | ||
|
|
||
| import ( | ||
| "unsafe" | ||
|
|
||
| "github.com/cloudflare/circl/internal/ted448" | ||
| fp "github.com/cloudflare/circl/math/fp448" | ||
| ) | ||
|
|
||
| // Decaf v1.0 of the encoding. | ||
| const Version = "v1.0" | ||
|
|
||
| // Elt is an element of the Decaf group. It must be always initialized using | ||
| // one of the Decaf functions. | ||
| type Elt struct{ p ted448.Point } | ||
|
|
||
| // Scalar represents a positive integer stored in little-endian order. | ||
| type Scalar = ted448.Scalar | ||
|
|
||
| func (e Elt) String() string { return e.p.String() } | ||
|
|
||
| // IsValid returns True if a is a valid element of the group. | ||
| func IsValid(a *Elt) bool { return ted448.IsOnCurve(&a.p) } | ||
|
|
||
| // Identity returns the identity element of the group. | ||
| func Identity() *Elt { return &Elt{ted448.Identity()} } | ||
|
|
||
| // Generator returns the generator element of the group. | ||
| func Generator() *Elt { return &Elt{ted448.Generator()} } | ||
|
|
||
| // Order returns a scalar with the order of the group. | ||
| func Order() Scalar { return ted448.Order() } | ||
|
|
||
| // Neg calculates c=-a, where - is the inverse of the group operation. | ||
| func Neg(c, a *Elt) { c.p = a.p; c.p.Neg() } | ||
|
|
||
| // Add calculates c=a+b, where + is the group operation. | ||
| func Add(c, a, b *Elt) { q := a.p; q.Add(&b.p); c.p = q } | ||
|
|
||
| // Double calculates c=a+a, where + is the group operation. | ||
| func Double(c, a *Elt) { c.p = a.p; c.p.Double() } | ||
|
|
||
| // Mul calculates c=n*a, where * is scalar multiplication on the group. | ||
| func Mul(c *Elt, n *Scalar, a *Elt) { ted448.ScalarMult(&c.p, n, &a.p) } | ||
|
|
||
| // MulGen calculates c=n*g, where * is scalar multiplication on the group, | ||
| // and g is the generator of the group. | ||
| func MulGen(c *Elt, n *Scalar) { ted448.ScalarBaseMult(&c.p, n) } | ||
|
|
||
| // IsIdentity returns True if e is the identity of the group. | ||
| func (e *Elt) IsIdentity() bool { return fp.IsZero(&e.p.X) && !fp.IsZero(&e.p.Y) && !fp.IsZero(&e.p.Z) } | ||
|
|
||
| // IsEqual returns True if e=a, where = is an equivalence relation. | ||
| func (e *Elt) IsEqual(a *Elt) bool { | ||
| l, r := &fp.Elt{}, &fp.Elt{} | ||
| fp.Mul(l, &e.p.X, &a.p.Y) | ||
| fp.Mul(r, &a.p.X, &e.p.Y) | ||
| fp.Sub(l, l, r) | ||
| return fp.IsZero(l) | ||
| } | ||
|
|
||
| // UnmarshalBinary interprets the first EncodingSize bytes passed in data, and | ||
| // returns a Decaf element. | ||
| func (e *Elt) UnmarshalBinary(data []byte) error { | ||
| if len(data) < EncodingSize { | ||
| return ErrInvalidDecoding | ||
| } | ||
|
|
||
| s := &fp.Elt{} | ||
| copy(s[:], data[:EncodingSize]) | ||
| p := fp.P() | ||
| isLessThanP := isLessThan(s[:], p[:]) | ||
| isPositiveS := fp.Parity(s) == 0 | ||
|
|
||
| den, num := &fp.Elt{}, &fp.Elt{} | ||
| isr, altx, t0 := &fp.Elt{}, &fp.Elt{}, &fp.Elt{} | ||
| x, y := &fp.Elt{}, &fp.Elt{} | ||
| one := fp.One() | ||
| paramD := ted448.ParamD() | ||
| fp.Sqr(t0, s) // t0 = s^2 | ||
| fp.Sub(den, &one, t0) // den = 1 + a*s^2 | ||
| fp.Add(y, &one, t0) // y = 1 - a*s^2 | ||
| fp.Mul(num, t0, ¶mD) // num = d*s^2 | ||
| fp.Add(num, num, num) // = 2*d*s^2 | ||
| fp.Add(num, num, num) // = 4*d*s^2 | ||
| fp.Sqr(t0, den) // t0 = den^2 = (1 + a*s^2)^2 | ||
| fp.Sub(num, t0, num) // num = den^2 - 4*d*s^2 | ||
| fp.Mul(t0, t0, num) // t0 = den^2*num | ||
| isQR := fp.InvSqrt(isr, &one, t0) // isr = 1/(den*sqrt(num)) | ||
| fp.Mul(altx, isr, den) // altx = isr*den | ||
| fp.Mul(altx, altx, s) // = s*isr*den | ||
| fp.Add(altx, altx, altx) // = 2*s*isr*den | ||
| fp.Mul(altx, altx, &sqrtAMinusD) // = 2*s*isr*den*sqrt(A-D) | ||
| isNegX := fp.Parity(altx) // isNeg = sgn(altx) | ||
| fp.Neg(t0, isr) // t0 = -isr | ||
| fp.Cmov(isr, t0, uint(isNegX)) // if altx is negative then isr = -isr | ||
| fp.Mul(t0, isr, den) // t0 = isr*den | ||
| fp.Mul(x, t0, isr) // x = isr^2*den | ||
| fp.Mul(x, x, num) // x = isr^2*den*num | ||
| fp.Mul(x, x, s) // x = s*isr^2*den*num | ||
| fp.Add(x, x, x) // x = 2*s*isr^2*den*num | ||
| fp.Mul(y, y, t0) // y = (1 - a*s^2)*isr*den | ||
|
|
||
| isValid := isPositiveS && isLessThanP && isQR | ||
| b := uint(*((*byte)(unsafe.Pointer(&isValid)))) | ||
| fp.Cmov(&e.p.X, x, b) | ||
| fp.Cmov(&e.p.Y, y, b) | ||
| fp.Cmov(&e.p.Ta, x, b) | ||
| fp.Cmov(&e.p.Tb, y, b) | ||
| fp.Cmov(&e.p.Z, &one, b) | ||
| if !isValid { | ||
| return ErrInvalidDecoding | ||
| } | ||
| return nil | ||
| } | ||
|
|
||
| // MarshalBinary returns a unique encoding of the element e. | ||
| func (e *Elt) MarshalBinary() ([]byte, error) { | ||
| var encS [EncodingSize]byte | ||
| err := e.marshalBinary(encS[:]) | ||
| return encS[:], err | ||
| } | ||
|
|
||
| func (e *Elt) marshalBinary(enc []byte) error { | ||
| x, ta, tb, z := &e.p.X, &e.p.Ta, &e.p.Tb, &e.p.Z | ||
| t, t2, s := &fp.Elt{}, &fp.Elt{}, &fp.Elt{} | ||
| one := fp.One() | ||
| fp.Mul(t, ta, tb) // t = ta*tb | ||
| t0, t1 := *x, *t // (t0,t1) = (x,t) | ||
| fp.AddSub(&t0, &t1) // (t0,t1) = (x+t,x-t) | ||
| fp.Mul(&t1, &t0, &t1) // t1 = num = (x+t)*(x-t) = x^2*(z^2-y^2)/z^2 | ||
| fp.Mul(&t0, &t1, &aMinusD) // t0 = (a-d)*(x+t)*(x-t) = (a-d)*x^2*(z^2-y^2)/z^2 | ||
| fp.Sqr(t2, x) // t2 = x^2 | ||
| fp.Mul(&t0, &t0, t2) // t0 = x^2*(a-d)*(x+t)*(x-t) = (a-d)*x^4*(z^2-y^2)/z^2 | ||
| fp.InvSqrt(&t0, &one, &t0) // t0 = isr = z/(x^2*sqrt((a-d)*(z^2-y^2))) | ||
| fp.Mul(&t1, &t1, &t0) // t1 = ratio = (z^2-y^2)/(z*sqrt((a-d)*(z^2-y^2))) | ||
| fp.Mul(t2, &t1, &sqrtAMinusD) // t2 = altx = sqrt((z^2-y^2))/z | ||
| isNeg := fp.Parity(t2) // isNeg = sgn(t2) | ||
| fp.Neg(t2, &t1) // t2 = -t1 | ||
| fp.Cmov(&t1, t2, uint(isNeg)) // if t2 is negative then t1 = -t1 | ||
| fp.Mul(s, &t1, z) // s = t1*z | ||
| fp.Sub(s, s, t) // s = t1*z - t | ||
| fp.Mul(s, s, x) // s = x*(t1*z - t) | ||
| fp.Mul(s, s, &t0) // s = isr*x*(t1*z - t) | ||
| fp.Mul(s, s, &aMinusD) // s = (a-d)*isr*x*(t1*z - t) | ||
| isNeg = fp.Parity(s) // isNeg = sgn(s) | ||
| fp.Neg(&t0, s) // t0 = -s | ||
| fp.Cmov(s, &t0, uint(isNeg)) // if s is negative then s = -s | ||
| return fp.ToBytes(enc[:], s) | ||
| } | ||
|
|
||
| // isLessThan returns true if 0 <= x < y, and assumes that slices are of the | ||
| // same length and are interpreted in little-endian order. | ||
| func isLessThan(x, y []byte) bool { | ||
| i := len(x) - 1 | ||
| for i > 0 && x[i] == y[i] { | ||
| i-- | ||
| } | ||
| return x[i] < y[i] | ||
| } |
Oops, something went wrong.