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Overview ¶
Package curve25519 contains several implementations of Twisted Edwards Curves, from general and unoptimized to highly specialized and optimized.
Twisted Edwards curves are elliptic curves satisfying the equation:
ax^2 + y^2 = c^2(1 + dx^2y^2)
for some scalars c, d over some field K. We assume K is a (finite) prime field for a large prime p. We also assume c == 1 because all curves in the generalized form are isomorphic to curves having c == 1.
For details see Bernstein et al, "Twisted Edwards Curves", http://eprint.iacr.org/2008/013.pdf
Index ¶
- type ExtendedCurve
- func (c *ExtendedCurve) Init(p *Param, fullGroup bool) *ExtendedCurve
- func (c *ExtendedCurve) IsPrimeOrder() bool
- func (c *ExtendedCurve) NewKey(stream cipher.Stream) kyber.Scalar
- func (c *ExtendedCurve) Point() kyber.Point
- func (c *ExtendedCurve) PointLen() int
- func (c *ExtendedCurve) Scalar() kyber.Scalar
- func (c *ExtendedCurve) ScalarLen() int
- func (c *ExtendedCurve) String() string
- type Param
- type ProjectiveCurve
- func (c *ProjectiveCurve) Init(p *Param, fullGroup bool) *ProjectiveCurve
- func (c *ProjectiveCurve) IsPrimeOrder() bool
- func (c *ProjectiveCurve) NewKey(stream cipher.Stream) kyber.Scalar
- func (c *ProjectiveCurve) Point() kyber.Point
- func (c *ProjectiveCurve) PointLen() int
- func (c *ProjectiveCurve) Scalar() kyber.Scalar
- func (c *ProjectiveCurve) ScalarLen() int
- func (c *ProjectiveCurve) String() string
- type SuiteCurve25519
- func (s *SuiteCurve25519) Hash() hash.Hash
- func (c *SuiteCurve25519) IsPrimeOrder() bool
- func (s *SuiteCurve25519) New(t reflect.Type) interface{}
- func (c *SuiteCurve25519) NewKey(stream cipher.Stream) kyber.Scalar
- func (c *SuiteCurve25519) PointLen() int
- func (s *SuiteCurve25519) RandomStream() cipher.Stream
- func (s *SuiteCurve25519) Read(r io.Reader, objs ...interface{}) error
- func (c *SuiteCurve25519) Scalar() kyber.Scalar
- func (c *SuiteCurve25519) ScalarLen() int
- func (c *SuiteCurve25519) String() string
- func (s *SuiteCurve25519) Write(w io.Writer, objs ...interface{}) error
- func (s *SuiteCurve25519) XOF(seed []byte) kyber.XOF
Constants ¶
This section is empty.
Variables ¶
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Functions ¶
This section is empty.
Types ¶
type ExtendedCurve ¶
type ExtendedCurve struct {
// contains filtered or unexported fields
}
ExtendedCurve implements Twisted Edwards curves using the Extended Coordinate representation specified in: Hisil et al, "Twisted Edwards Curves Revisited", http://eprint.iacr.org/2008/522
This implementation is designed to work with all Twisted Edwards curves, foregoing the further optimizations that are available for the special case with curve parameter a=-1. We leave the task of hyperoptimization to curve-specific implementations such as the ed25519 package.
func (*ExtendedCurve) Init ¶
func (c *ExtendedCurve) Init(p *Param, fullGroup bool) *ExtendedCurve
Init initializes the curve with given parameters.
func (*ExtendedCurve) IsPrimeOrder ¶
func (c *ExtendedCurve) IsPrimeOrder() bool
func (*ExtendedCurve) NewKey ¶
NewKey returns a formatted curve25519 key (avoiding subgroup attack by requiring it to be a multiple of 8). NewKey implements the kyber/util/key.Generator interface.
func (*ExtendedCurve) Point ¶
func (c *ExtendedCurve) Point() kyber.Point
Point creates a new Point on this curve.
func (*ExtendedCurve) PointLen ¶
func (c *ExtendedCurve) PointLen() int
Returns the size in bytes of an encoded Point on this curve. Uses compressed representation consisting of the y-coordinate and only the sign bit of the x-coordinate.
type Param ¶
type Param struct {
Name string // Name of curve
P big.Int // Prime defining the underlying field
Q big.Int // Order of the prime-order base point
R int // Cofactor: Q*R is the total size of the curve
A, D big.Int // Edwards curve equation parameters
FBX, FBY big.Int // Standard base point for full group
PBX, PBY big.Int // Standard base point for prime-order subgroup
Elligator1s big.Int // Optional s parameter for Elligator 1
Elligator2u big.Int // Optional u parameter for Elligator 2
}
Param defines a Twisted Edwards curve (TEC).
func Param1174 ¶
func Param1174() *Param
Param1174 defines Curve1174, as specified in: Bernstein et al, "Elligator: Elliptic-curve points indistinguishable from uniform random strings" http://elligator.cr.yp.to/elligator-20130828.pdf
func Param25519 ¶
func Param25519() *Param
Param25519 defines the Edwards version of Curve25519, as specified in: Bernstein et al, "High-speed high-security signatures", http://ed25519.cr.yp.to/ed25519-20110926.pdf
func Param41417 ¶
func Param41417() *Param
Param41417 defines the Curve41417 curve, as specified in: Bernstein et al, "Curve41417: Karatsuba revisited", http://eprint.iacr.org/2014/526.pdf
func ParamE382 ¶
func ParamE382() *Param
ParamE382 defines the E-382 curve specified in: Aranha et al, "A note on high-security general-purpose elliptic curves", http://eprint.iacr.org/2013/647.pdf
and more recently in:
"Additional Elliptic Curves for IETF protocols" http://tools.ietf.org/html/draft-ladd-safecurves-02 (this I-D is now expired)
func ParamE521 ¶
func ParamE521() *Param
ParamE521 defines the E-521 curve specified in: Aranha et al, "A note on high-security general-purpose elliptic curves", http://eprint.iacr.org/2013/647.pdf
and more recently included in: "Additional Elliptic Curves for IETF protocols" http://tools.ietf.org/html/draft-ladd-safecurves-02
type ProjectiveCurve ¶
type ProjectiveCurve struct {
// contains filtered or unexported fields
}
ProjectiveCurve implements Twisted Edwards curves using projective coordinate representation (X:Y:Z), satisfying the identities x = X/Z, y = Y/Z. This representation still supports all Twisted Edwards curves and avoids expensive modular inversions on the critical paths. Uses the projective arithmetic formulas in: http://cr.yp.to/newelliptic/newelliptic-20070906.pdf
func (*ProjectiveCurve) Init ¶
func (c *ProjectiveCurve) Init(p *Param, fullGroup bool) *ProjectiveCurve
Init initializes the curve with given parameters.
func (*ProjectiveCurve) IsPrimeOrder ¶
func (c *ProjectiveCurve) IsPrimeOrder() bool
func (*ProjectiveCurve) NewKey ¶
NewKey returns a formatted curve25519 key (avoiding subgroup attack by requiring it to be a multiple of 8). NewKey implements the kyber/util/key.Generator interface.
func (*ProjectiveCurve) Point ¶
func (c *ProjectiveCurve) Point() kyber.Point
Point creates a new Point on this curve.
func (*ProjectiveCurve) PointLen ¶
func (c *ProjectiveCurve) PointLen() int
Returns the size in bytes of an encoded Point on this curve. Uses compressed representation consisting of the y-coordinate and only the sign bit of the x-coordinate.
type SuiteCurve25519 ¶
type SuiteCurve25519 struct {
ProjectiveCurve
}
SuiteCurve25519 is the suite for the 25519 curve
func NewBlakeSHA256Curve25519 ¶
func NewBlakeSHA256Curve25519(fullGroup bool) *SuiteCurve25519
NewBlakeSHA256Curve25519 returns a cipher suite based on package go.dedis.ch/kyber/xof/blake2xb, SHA-256, and Curve25519.
If fullGroup is false, then the group is the prime-order subgroup.
The scalars created by this group implement kyber.Scalar's SetBytes method, interpreting the bytes as a big-endian integer, so as to be compatible with the Go standard library's big.Int type.
func (*SuiteCurve25519) Hash ¶
func (s *SuiteCurve25519) Hash() hash.Hash
Hash returns the instance associated with the suite
func (*SuiteCurve25519) IsPrimeOrder ¶
func (c *SuiteCurve25519) IsPrimeOrder() bool
func (*SuiteCurve25519) New ¶
func (s *SuiteCurve25519) New(t reflect.Type) interface{}
New implements the kyber.encoding interface
func (*SuiteCurve25519) NewKey ¶
NewKey returns a formatted curve25519 key (avoiding subgroup attack by requiring it to be a multiple of 8). NewKey implements the kyber/util/key.Generator interface.
func (*SuiteCurve25519) PointLen ¶
func (c *SuiteCurve25519) PointLen() int
Returns the size in bytes of an encoded Point on this curve. Uses compressed representation consisting of the y-coordinate and only the sign bit of the x-coordinate.
func (*SuiteCurve25519) RandomStream ¶
func (s *SuiteCurve25519) RandomStream() cipher.Stream
RandomStream returns a cipher.Stream that returns a key stream from crypto/rand.
func (*SuiteCurve25519) Read ¶
func (s *SuiteCurve25519) Read(r io.Reader, objs ...interface{}) error
func (*SuiteCurve25519) ScalarLen ¶
func (c *SuiteCurve25519) ScalarLen() int
Returns the size in bytes of an encoded Scalar for this curve.
Source Files