Documentation
¶
Overview ¶
This package contains several implementations of Twisted Edwards Curves, from general and unoptimized to highly specialized and optimized.
Twisted Edwards curves (TEC's) 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 ¶
- func NewAES128SHA256Ed25519(fullGroup bool) abstract.Suite
- type ExtendedCurve
- type Param
- type ProjectiveCurve
- func (c *ProjectiveCurve) Init(p *Param, fullGroup bool) *ProjectiveCurve
- func (c *ProjectiveCurve) Point() abstract.Point
- func (c *ProjectiveCurve) PointLen() int
- func (c *ProjectiveCurve) PrimeOrder() bool
- func (c *ProjectiveCurve) Scalar() abstract.Scalar
- func (c *ProjectiveCurve) ScalarLen() int
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
func NewAES128SHA256Ed25519 ¶
Ciphersuite based on AES-128, SHA-256, and the Ed25519 curve.
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
Initialize the curve with given parameters.
func (*ExtendedCurve) Point ¶
func (c *ExtendedCurve) Point() abstract.Point
Create 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.
func (*ExtendedCurve) PrimeOrder ¶
func (c *ExtendedCurve) PrimeOrder() bool
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
}
Parameters defining a Twisted Edwards curve (TEC).
func Param1174 ¶
func Param1174() *Param
Parameters defining 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
Parameters defining 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
Parameters for Curve41417, as specified in: Bernstein et al, "Curve41417: Karatsuba revisited", http://eprint.iacr.org/2014/526.pdf
func ParamE382 ¶
func ParamE382() *Param
Parameters for 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
func ParamE521 ¶
func ParamE521() *Param
Parameters for 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
Initialize the curve with given parameters.
func (*ProjectiveCurve) Point ¶
func (c *ProjectiveCurve) Point() abstract.Point
Create 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.
func (*ProjectiveCurve) PrimeOrder ¶
func (c *ProjectiveCurve) PrimeOrder() bool
Source Files