go-dedis-kyber/docs/scalar.md

Introduction

Scalar represents a scalar value by which a Point (group element) may be encrypted to produce another Point. This is an exponent in DSA-style groups, in which security is based on the Discrete Logarithm assumption, and a scalar multiplier in elliptic curve groups.

type Scalar interface {
	Marshaling
	
	Equal(s2 Scalar) bool
	Set(a Scalar) Scalar
	Clone() Scalar
	SetInt64(v int64) Scalar
	Zero() Scalar
	Add(a, b Scalar) Scalar
	Sub(a, b Scalar) Scalar
	Neg(a Scalar) Scalar
	One() Scalar
	Mul(a, b Scalar) Scalar
	Div(a, b Scalar) Scalar
	Inv(a Scalar) Scalar
	Pick(rand cipher.Stream) Scalar
	SetBytes([]byte) Scalar
}

Data Members

Marshalling

Marshaling is a basic interface representing fixed-length (or known-length) cryptographic objects or structures having a built-in binary encoding. Implementors must ensure that calls to these methods do not modify the underlying object so that other users of the object can access it concurrently.

Functions

Equal()

Function	Scalar.Equal(Scalar) bool
Parameters	- Scalar : The Scalar with which the equality has to be checked with
Output	- Boolean : Answer to the equality of the points

This function is used to check the equality of two Scalars derived from the same group. The functions return a true/false indicating wether the Points are equal or not.

Set()

Function	Scalar.Set(Scalar) Scalar
Parameters	- Scalar : Scalar whose value has to be set to the current Scalar
Output	- Scalar : Caller Scalar with same value as the parametric Scalar

This function sets the receiver object's value to the Scalar specified by another object passed as a parameter to the function.

Clone()

Function	Scalar.Clone() Scalar
Parameters	- None
Output	- Scalar : A new Scalar which is a clone of the caller Scalar

This function returns a new Scalar with the same value as the Scalar which called the function.

SetInt64()

Function	Scalar.SetInt64(int64) Scalar
Parameters	- int64 : Value which is to be assigned to the Scalar
Output	- Scalar : Caller Scalar with value equal to the paramter

This function sets the value of the calling object to a small integer value, which is passed to the function as a parameter.

Zero()

Function	Scalar.Zero() Scalar
Parameters	- None
Output	- Scalar : Caller Scalar with value equal to the group's addtive identity

This function sets the value of the calling object equal to the additive identity.

One()

Function	Scalar.One() Scalar
Parameters	- None
Output	- Scalar : Caller Scalar with value equal to the group's multiplicative identity

This function sets the value of the calling object equal to the multiplicative identity.

Add()

Function	Scalar.Add(Scalar, Scalar) Scalar
Parameters	- Scalar, Scalar : The two Scalars which have to be added
Output	- Scalar : Caller Scalar with value equal to the sum of the parametric Scalars

This function sets the receiving object to the modular sum of scalars passed to the function as parameters.

Sub()

Function	Scalar.Sub(Scalar, Scalar) Scalar
Parameters	- Scalar, Scalar : The two Scalars which have to be substracted
Output	- Scalar : Caller Scalar with value equal to the difference of the parametric Scalars

This function sets the receiving object to the modular difference (Scalar 1 - Scalar 2) of the scalars passed as parameters.

Neg()

Function	Scalar.Neg(Scalar) Scalar
Parameters	- Scalar : The Scalar whose value has to be negated
Output	- Scalar : Caller Scalar with value equal to the neagtion of the value of the given Scalar

This function sets the receiving object to the modular negation of the Scalar passed to the function as parameter.

Mul()

Function	Scalar.Mul(Scalar, Scalar) Scalar
Parameters	- Scalar, Scalar : The two Scalars which have to be multiplied
Output	- Scalar : Caller Scalar with value equal to the product of the paramtetric Scalars

This function sets the receiving object to the modular product of the Scalars passed to the function as parameters.

Div()

Function	Scalar.Div(Scalar, Scalar) Scalar
Parameters	- Scalar, Scalar : Two Scalars which have to be divided
Output	- Scalar : Caller Scalar with value equal to Scalar 1 / Scalar 2

This function sets the receiving object to the modular division (Scalar 1 / Scalar 2) of the two Scalars passed to the function as parameters.

Inv()

Function	Scalar.Inv(Scalar) Scalar
Parameters	- Scalar : The Scalar whose value has to be inverted
Output	- Scalar : Caller Scalar with value equal to the inverse of parametric Scalar

This function sets the receiving object to the modular inverse of the Scalar passed to the function as parameter.

Pick()

Function	Scalar.Pick(cipher.Stream) Scalar
Parameters	- cipher.Stream : Source from random / pseudo-random values are picked
Output	- Scalar : Caller Scalar with value equal to some random / pseudo-random value

This functions sets the receiver object to a random or pseudo-random Scalar, which is extracted with the help of the cipher.Stream which is passed as a parameter to the function.

SetBytes()

Function	Scalar.SetBytes([]byte) Scalar
Parameters	- []byte : Byte encoding of the value to be assigned in little endian format
Output	- Scalar : Caller scalar with value corresponding to the given byte encoding

SetBytes sets the value of the scalar from a byte-slice, reducing if necessary to the appropriate modulus. The endianess of the byte-slice is determined by the implementation. For example - In the case of the ED25519 curve the endianess is Little Endianess.