scalar

package
v0.0.0-...-1f23a7b Latest Latest
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 Go to latest Published: Sep 4, 2023 License: BSD-3-Clause Imports: 9 Imported by: 1

Documentation

Overview

Package scalar implements arithmetic on scalars (integers mod the group order).

Index

Constants

View Source 
const (
	// ScalarSize is the size of a scalar in bytes.
	ScalarSize = 32

	// ScalarWideSize is the size of a wide scalar in bytes.
	ScalarWideSize = 64
)

Variables

View Source 
var (

	// BASEPOINT_ORDER is the order of the Ed25519 basepoint and the Ristretto
	// group.
	BASEPOINT_ORDER = func() *Scalar {

		s, err := NewFromBits([]byte{
			0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
			0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
			0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
			0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10,
		})
		if err != nil {
			panic("curve/scalar: failed to define basepoint order constant: " + err.Error())
		}
		return s
	}()
)

Functions

func ScMinimalVartime 

func ScMinimalVartime(scalar []byte) bool

ScMinimalVartime returns true if the given byte-encoded scalar is less than the order of the curve, in variable-time.

This method is intended for verification applications, and is significantly faster than deserializing the scalar and calling IsCanonical.

func ToRadix2wSizeHint 

func ToRadix2wSizeHint(w uint) uint

ToRadix2wSizeHint returns a size hint indicating how many entries of the return value of ToRadix2w are nonzero.

Types

type Scalar 

type Scalar struct {
	disalloweq.DisallowEqual //nolint:unused
	// contains filtered or unexported fields
}

Scalar holds an integer s < 2^255 which represents an element of Z/L.

func New 

func New() *Scalar

New returns a scalar set to zero.

func NewFromBits 

func NewFromBits(in []byte) (*Scalar, error)

NewFromBits constructs a scalar from the low 255 bits of a 256-bit integer.

This function is intended for applications like X25519 which require specific bit-patterns when performing scalar multiplication.

func NewFromBytesModOrder 

func NewFromBytesModOrder(in []byte) (*Scalar, error)

NewFromBytesModOrder constructs a scalar by reducing a 256-bit little-endian integer modulo the group order L.

func NewFromBytesModOrderWide 

func NewFromBytesModOrderWide(in []byte) (*Scalar, error)

NewFromBytesModOrderWide constructs a scalar by reducing a 512-bit little-endian integer modulo the group order L.

func NewFromCanonicalBytes 

func NewFromCanonicalBytes(in []byte) (*Scalar, error)

NewFromCanonicalBytes attempts to construct a scalar from a canoical byte representation.

func NewFromUint64 

func NewFromUint64(x uint64) *Scalar

NewFromUint64 returns a scalar set to the given uint64.

func One 

func One() *Scalar

One returns a scalar set to 1.

func (*Scalar) Add 

func (s *Scalar) Add(a, b *Scalar) *Scalar

Add sets `s= a + b (mod l)`, and returns s.

func (*Scalar) BatchInvert 

func (s *Scalar) BatchInvert(inputs []*Scalar) *Scalar

BatchInvert computes the inverses of slice of `Scalar`s in a batch, and sets s to the product of all inverses, and returns s. Each element of the input slice is replaced by its inverse.

WARNING: The input scalars MUST be nonzero. If you cannot prove that this is the case you MUST not use this function.

func (*Scalar) Bits 

func (s *Scalar) Bits() [8 * ScalarSize]byte

Bits gets the bits of the scalar.

func (*Scalar) ConditionalSelect 

func (s *Scalar) ConditionalSelect(a, b *Scalar, choice int)

ConditionalSelect sets s to a iff choice == 0 and b iff choice == 1.

func (*Scalar) Equal 

func (s *Scalar) Equal(t *Scalar) int

Equal returns 1 iff the s and t are equal, 0 otherwise. This function will execute in constant-time.

func (*Scalar) Invert 

func (s *Scalar) Invert(t *Scalar) *Scalar

Invert sets s to the multiplicative inverse of the nonzero scalar t, and returns s.

WARNING: The scalar MUST be nonzero. If you cannot prove that this is the case you MUST not use this function.

func (*Scalar) IsCanonical 

func (s *Scalar) IsCanonical() bool

IsCanonical checks if this scalar is the canonical representative mod L.

This is intended for uses like input validation, where variable-time code is acceptable.

func (*Scalar) MarshalBinary 

func (s *Scalar) MarshalBinary() ([]byte, error)

MarshalBinary encodes the scalar into a binary form and returns the result.

func (*Scalar) Mul 

func (s *Scalar) Mul(a, b *Scalar) *Scalar

Mul sets `s = a * b (mod l)`, and returns s.

func (*Scalar) Neg 

func (s *Scalar) Neg(t *Scalar) *Scalar

Neg `s = -t`, and returns s.

func (*Scalar) NonAdjacentForm 

func (s *Scalar) NonAdjacentForm(w uint) [256]int8

NonAdjacentForm returns a width-w "Non-Adjacent Form" of this scalar.

func (*Scalar) One 

func (s *Scalar) One() *Scalar

One sets s to one, and returns s.

func (*Scalar) Product 

func (s *Scalar) Product(values []*Scalar) *Scalar

Product sets s to the product of values, and returns s.

func (*Scalar) Reduce 

func (s *Scalar) Reduce(t *Scalar) *Scalar

Reduce reduces t modulo L, and returns s.

func (*Scalar) Set 

func (s *Scalar) Set(t *Scalar) *Scalar

Set sets s to t, and returns s.

func (*Scalar) SetBits 

func (s *Scalar) SetBits(in []byte) (*Scalar, error)

SetBits constructs a scalar from the low 255 bits of a 256-bit integer.

This function is intended for applications like X25519 which require specific bit-patterns when performing scalar multiplication.

func (*Scalar) SetBytesModOrder 

func (s *Scalar) SetBytesModOrder(in []byte) (*Scalar, error)

SetBytesModOrder sets s to the scalar constructed by reducing a 256-bit little-endian integer modulo the group order L.

func (*Scalar) SetBytesModOrderWide 

func (s *Scalar) SetBytesModOrderWide(in []byte) (*Scalar, error)

SetBytesModOrderWide sets s to the scalar constructed by reducing a 512-bit little-endian integer modulo the group order L.

func (*Scalar) SetCanonicalBytes 

func (s *Scalar) SetCanonicalBytes(in []byte) (*Scalar, error)

SetCanonicalBytes sets s from a canonical byte representation.

func (*Scalar) SetRandom 

func (s *Scalar) SetRandom(rng io.Reader) (*Scalar, error)

SetRandom sets s to a scalar chosen uniformly at random using entropy from the user-provided io.Reader. If rng is nil, the runtime library's entropy source will be used.

func (*Scalar) SetUint64 

func (s *Scalar) SetUint64(x uint64) *Scalar

SetUint64 sets s to the given uint64, and returns s.

func (*Scalar) Sub 

func (s *Scalar) Sub(a, b *Scalar) *Scalar

Sub sets `s = a - b (mod l)`, and returns s.

func (*Scalar) Sum 

func (s *Scalar) Sum(values []*Scalar) *Scalar

Sum sets s to the sum of values, and returns s.

func (*Scalar) ToBytes 

func (s *Scalar) ToBytes(out []byte) error

ToBytes packs the scalar into 32 bytes.

func (*Scalar) ToRadix16 

func (s *Scalar) ToRadix16() [64]int8

ToRadix16 returns the scalar in radix 16, with coefficients in [-8,8).

func (*Scalar) ToRadix2w 

func (s *Scalar) ToRadix2w(w uint) [43]int8

ToRadix2w returns a representation of a scalar in radix 64, 128, or 256.

func (*Scalar) UnmarshalBinary 

func (s *Scalar) UnmarshalBinary(data []byte) error

UnmarshalBinary decodes a binary serialized scalar.

func (*Scalar) Zero 

func (s *Scalar) Zero() *Scalar

Zero sets s to zero, and returns s.

Source Files

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