go-dedis-kyber/docs/group.md

Introduction

Group interface represents a mathematical group usable for Diffie-Hellman key exchange, ElGamal encryption, and the related body of public-key cryptographic algorithms and zero-knowledge proof methods. The Group interface is designed in particular to be a generic front-end to both traditional DSA-style modular arithmetic groups and ECDSA-style elliptic curves the caller of this interface's methods need not know or care which specific mathematical construction underlies the interface.

The Group interface is essentially just a "constructor" interface enabling the caller to generate the two particular types of objects relevant to DSA-style public-key cryptography; we call these objects Points and Scalars. The caller must explicitly initialize or set a new Point or Scalar object to some value before using it as an input to some other operation involving Point and/or Scalar objects. For example, to compare a point P against the neutral (identity) element, you might use P.Equal(suite.Point().Null()), but not just P.Equal(suite.Point()).

It is expected that any implementation of this interface should satisfy suitable hardness assumptions for the applicable group: e.g., that it is cryptographically hard for an adversary to take an encrypted Point and the known generator it was based on, and derive the Scalar with which the Point was encrypted. Any implementation is also expected to satisfy the standard homomorphism properties that Diffie-Hellman and the associated body of public-key cryptography are based on.

type Group interface {
	String() string

	ScalarLen() int // Max length of scalars in bytes
	Scalar() Scalar // Create new scalar

	PointLen() int // Max length of point in bytes
	Point() Point  // Create new point
}

Functions

String()

Function	Suite.String() string
Parameters	- None
Output	- string : Name of the suite

This function returns the name of the suite, with which the function has been called.

ScalarLen()

Function	Suite.ScalarLen() int
Parameters	- None
Output	- int : Maximum size in bytes of the encoded Scalar

This function returns the maximum size in bytes of the encoded Scalar of the caller suite

Scalar()

Function	Suite.Scalar() Scalar
Parameters	- None
Output	- Scalar : New Scalar instance of the caller suite

This function creates and returns a new Kyber Scalar of the caller suite.

PointLen()

Function	Suite.Point() int
Parameters	- None
Output	- int : Maximum size in bytes of the encoded Point

This function returns the maximum length in bytes of an encoded Point of the caller suite.

Point()

Function	Suite.Point() Point
Parameters	- None
Output	- Point : New Point instance of the caller suite

This function creates and returns a new Kyber Point of the caller suite.