mod

Documentation

Overview

Package mod contains a generic implementation of finite field arithmetic on integer fields with a constant modulus.

Index

• type ByteOrder
• type Int
  • func NewInt(v *big.Int, m *big.Int) *Int
  • func NewInt64(v int64, M *big.Int) *Int
  • func NewIntBytes(a []byte, m *big.Int, byteOrder ByteOrder) *Int
  • func NewIntString(n, d string, base int, m *big.Int) *Int
  • func (i *Int) Add(a, b kyber.Scalar) kyber.Scalar
  • func (i *Int) BigEndian(min, max int) []byte
  • func (i *Int) Clone() kyber.Scalar
  • func (i *Int) Cmp(s2 kyber.Scalar) int
  • func (i *Int) Div(a, b kyber.Scalar) kyber.Scalar
  • func (i *Int) Equal(s2 kyber.Scalar) bool
  • func (i *Int) Exp(a kyber.Scalar, e *big.Int) kyber.Scalar
  • func (i *Int) HideDecode(buf []byte)
  • func (i *Int) HideEncode(rand cipher.Stream) []byte
  • func (i *Int) HideLen() int
  • func (i *Int) Init(V *big.Int, m *big.Int) *Int
  • func (i *Int) Init64(v int64, m *big.Int) *Int
  • func (i *Int) InitBytes(a []byte, m *big.Int, byteOrder ByteOrder) *Int
  • func (i *Int) InitString(n, d string, base int, m *big.Int) *Int
  • func (i *Int) Int64() int64
  • func (i *Int) Inv(a kyber.Scalar) kyber.Scalar
  • func (i *Int) Jacobi(as kyber.Scalar) kyber.Scalar
  • func (i *Int) LittleEndian(min, max int) []byte
  • func (i *Int) MarshalBinary() ([]byte, error)
  • func (i *Int) MarshalSize() int
  • func (i *Int) MarshalTo(w io.Writer) (int, error)
  • func (i *Int) Mul(a, b kyber.Scalar) kyber.Scalar
  • func (i *Int) Neg(a kyber.Scalar) kyber.Scalar
  • func (i *Int) Nonzero() bool
  • func (i *Int) One() kyber.Scalar
  • func (i *Int) Pick(rand cipher.Stream) kyber.Scalar
  • func (i *Int) Set(a kyber.Scalar) kyber.Scalar
  • func (i *Int) SetBytes(a []byte) kyber.Scalar
  • func (i *Int) SetInt64(v int64) kyber.Scalar
  • func (i *Int) SetString(n, d string, base int) (*Int, bool)
  • func (i *Int) SetUint64(v uint64) kyber.Scalar
  • func (i *Int) Sqrt(as kyber.Scalar) bool
  • func (i *Int) String() string
  • func (i *Int) Sub(a, b kyber.Scalar) kyber.Scalar
  • func (i *Int) Uint64() uint64
  • func (i *Int) UnmarshalBinary(buf []byte) error
  • func (i *Int) UnmarshalFrom(r io.Reader) (int, error)
  • func (i *Int) Zero() kyber.Scalar

Types

type ByteOrder

type ByteOrder bool

ByteOrder denotes the endianness of the operation.

const (
	// LittleEndian endianness
	LittleEndian ByteOrder = true
	// BigEndian endianness
	BigEndian ByteOrder = false
)

type Int

type Int struct {
	V  big.Int   // Integer value from 0 through M-1
	M  *big.Int  // Modulus for finite field arithmetic
	BO ByteOrder // Endianness which will be used on input and output
}

Int is a generic implementation of finite field arithmetic on integer finite fields with a given constant modulus, built using Go's built-in big.Int package. Int satisfies the kyber.Scalar interface, and hence serves as a basic implementation of kyber.Scalar, e.g., representing discrete-log exponents of Schnorr groups or scalar multipliers for elliptic curves.

Int offers an API similar to and compatible with big.Int, but "carries around" a pointer to the relevant modulus and automatically normalizes the value to that modulus after all arithmetic operations, simplifying modular arithmetic. Binary operations assume that the source(s) have the same modulus, but do not check this assumption. Unary and binary arithmetic operations may be performed on uninitialized target objects, and receive the modulus of the first operand. For efficiency the modulus field M is a pointer, whose target is assumed never to change.

func NewInt

func NewInt(v *big.Int, m *big.Int) *Int

NewInt creaters a new Int with a given big.Int and a big.Int modulus.

func NewInt64

func NewInt64(v int64, M *big.Int) *Int

NewInt64 creates a new Int with a given int64 value and big.Int modulus.

func NewIntBytes

func NewIntBytes(a []byte, m *big.Int, byteOrder ByteOrder) *Int

NewIntBytes creates a new Int with a given slice of bytes and a big.Int modulus.

func NewIntString

func NewIntString(n, d string, base int, m *big.Int) *Int

NewIntString creates a new Int with a given string and a big.Int modulus. The value is set to a rational fraction n/d in a given base.

func (*Int) Add

func (i *Int) Add(a, b kyber.Scalar) kyber.Scalar

Add sets the target to a + b mod M, where M is a's modulus..

func (*Int) BigEndian

func (i *Int) BigEndian(min, max int) []byte

BigEndian encodes the value of this Int into a big-endian byte-slice at least min bytes but no more than max bytes long. Panics if max != 0 and the Int cannot be represented in max bytes.

func (*Int) Clone

func (i *Int) Clone() kyber.Scalar

Clone returns a separate duplicate of this Int.

func (*Int) Cmp

func (i *Int) Cmp(s2 kyber.Scalar) int

Cmp compares two Ints for equality or inequality

func (*Int) Div

func (i *Int) Div(a, b kyber.Scalar) kyber.Scalar

Div sets the target to a * b^-1 mod M, where b^-1 is the modular inverse of b.

func (*Int) Equal

func (i *Int) Equal(s2 kyber.Scalar) bool

Equal returns true if the two Ints are equal

func (*Int) Exp

func (i *Int) Exp(a kyber.Scalar, e *big.Int) kyber.Scalar

Exp sets the target to a^e mod M, where e is an arbitrary big.Int exponent (not necessarily 0 <= e < M).

func (*Int) HideDecode

func (i *Int) HideDecode(buf []byte)

HideDecode a uniform representation of this object from a slice, whose length must be exactly HideLen().

func (*Int) HideEncode

func (i *Int) HideEncode(rand cipher.Stream) []byte

HideEncode a Int such that it appears indistinguishable from a HideLen()-byte string chosen uniformly at random, assuming the Int contains a uniform integer modulo M. For a Int this always succeeds and returns non-nil.

func (*Int) HideLen

func (i *Int) HideLen() int

HideLen returns the length in bytes of a uniform byte-string encoding of this Int, satisfying the requirements of the Hiding interface. For a Int this is always the same length as the normal encoding.

func (*Int) Init

func (i *Int) Init(V *big.Int, m *big.Int) *Int

Init a Int with a given big.Int value and modulus pointer. Note that the value is copied; the modulus is not.

func (*Int) Init64

func (i *Int) Init64(v int64, m *big.Int) *Int

Init64 creates an Int with an int64 value and big.Int modulus.

func (*Int) InitBytes

func (i *Int) InitBytes(a []byte, m *big.Int, byteOrder ByteOrder) *Int

InitBytes init the Int to a number represented in a big-endian byte string.

func (*Int) InitString

func (i *Int) InitString(n, d string, base int, m *big.Int) *Int

InitString inits the Int to a rational fraction n/d specified with a pair of strings in a given base.

func (*Int) Int64

func (i *Int) Int64() int64

Int64 returns the int64 representation of the value. If the value is not representable in an int64 the result is undefined.

func (*Int) Inv

func (i *Int) Inv(a kyber.Scalar) kyber.Scalar

Inv sets the target to the modular inverse of a with respect to modulus M.

func (*Int) Jacobi

func (i *Int) Jacobi(as kyber.Scalar) kyber.Scalar

Jacobi computes the Jacobi symbol of (a/M), which indicates whether a is zero (0), a positive square in M (1), or a non-square in M (-1).

func (*Int) LittleEndian

func (i *Int) LittleEndian(min, max int) []byte

LittleEndian encodes the value of this Int into a little-endian byte-slice at least min bytes but no more than max bytes long. Panics if max != 0 and the Int cannot be represented in max bytes.

func (*Int) MarshalBinary

func (i *Int) MarshalBinary() ([]byte, error)

MarshalBinary encodes the value of this Int into a byte-slice exactly Len() bytes long. It uses i's ByteOrder to determine which byte order to output.

func (*Int) MarshalSize

func (i *Int) MarshalSize() int

MarshalSize returns the length in bytes of encoded integers with modulus M. The length of encoded Ints depends only on the size of the modulus, and not on the the value of the encoded integer, making the encoding is fixed-length for simplicity and security.

func (*Int) MarshalTo

func (i *Int) MarshalTo(w io.Writer) (int, error)

MarshalTo encodes this Int to the given Writer.

func (*Int) Mul

func (i *Int) Mul(a, b kyber.Scalar) kyber.Scalar

Mul sets the target to a * b mod M. Target receives a's modulus.

func (*Int) Neg

func (i *Int) Neg(a kyber.Scalar) kyber.Scalar

Neg sets the target to -a mod M.

func (*Int) Nonzero

func (i *Int) Nonzero() bool

Nonzero returns true if the integer value is nonzero.

func (*Int) One

func (i *Int) One() kyber.Scalar

One sets the Int to the value 1. The modulus must already be initialized.

func (*Int) Pick

func (i *Int) Pick(rand cipher.Stream) kyber.Scalar

Pick a [pseudo-]random integer modulo M using bits from the given stream cipher.

func (*Int) Set

func (i *Int) Set(a kyber.Scalar) kyber.Scalar

Set both value and modulus to be equal to another Int. Since this method copies the modulus as well, it may be used as an alternative to Init().

func (*Int) SetBytes

func (i *Int) SetBytes(a []byte) kyber.Scalar

SetBytes set the value value to a number represented by a byte string. Endianness depends on the endianess set in i.

func (*Int) SetInt64

func (i *Int) SetInt64(v int64) kyber.Scalar

SetInt64 sets the Int to an arbitrary 64-bit "small integer" value. The modulus must already be initialized.

func (*Int) SetString

func (i *Int) SetString(n, d string, base int) (*Int, bool)

SetString sets the Int to a rational fraction n/d represented by a pair of strings. If d == "", then the denominator is taken to be 1. Returns (i,true) on success, or (nil,false) if either string fails to parse.

func (*Int) SetUint64

func (i *Int) SetUint64(v uint64) kyber.Scalar

SetUint64 sets the Int to an arbitrary uint64 value. The modulus must already be initialized.

func (*Int) Sqrt

func (i *Int) Sqrt(as kyber.Scalar) bool

Sqrt computes some square root of a mod M of one exists. Assumes the modulus M is an odd prime. Returns true on success, false if input a is not a square.

func (*Int) String

func (i *Int) String() string

Return the Int's integer value in hexadecimal string representation.

func (*Int) Sub

func (i *Int) Sub(a, b kyber.Scalar) kyber.Scalar

Sub sets the target to a - b mod M. Target receives a's modulus.

func (*Int) Uint64

func (i *Int) Uint64() uint64

Uint64 returns the uint64 representation of the value. If the value is not representable in an uint64 the result is undefined.

func (*Int) UnmarshalBinary

func (i *Int) UnmarshalBinary(buf []byte) error

UnmarshalBinary tries to decode a Int from a byte-slice buffer. Returns an error if the buffer is not exactly Len() bytes long or if the contents of the buffer represents an out-of-range integer.

func (*Int) UnmarshalFrom

func (i *Int) UnmarshalFrom(r io.Reader) (int, error)

UnmarshalFrom tries to decode an Int from the given Reader.

func (*Int) Zero

func (i *Int) Zero() kyber.Scalar

Zero set the Int to the value 0. The modulus must already be initialized.