group

type Group ¶

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
}

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 Marshaling ¶

type Marshaling interface {
	encoding.BinaryMarshaler
	encoding.BinaryUnmarshaler

	// String returns the human readable string representation of the object.
	String() string

	// Encoded length of this object in bytes.
	MarshalSize() int
}

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.

type Point ¶

type Point interface {
	Marshaling

	// Equality test for two Points derived from the same Group.
	Equal(s2 Point) bool

	// Null sets the receiver to the neutral identity element.
	Null() Point

	// Base sets the receiver to this group's standard base point.
	Base() Point

	// Pick sets the receiver to a fresh random or pseudo-random Point.
	Pick(rand cipher.Stream) Point

	// Set sets the receiver equal to another Point p.
	Set(p Point) Point

	// Clone clones the underlying point.
	Clone() Point

	// Add points so that their scalars add homomorphically.
	Add(a, b Point) Point

	// Subtract points so that their scalars subtract homomorphically.
	Sub(a, b Point) Point

	// Set to the negation of point a.
	Neg(a Point) Point

	// Multiply point p by the scalar s.
	// If p == nil, multiply with the standard base point Base().
	Mul(s Scalar, p Point) Point
}

Point represents an element of a public-key cryptographic Group. For example, this is a number modulo the prime P in a DSA-style Schnorr group, or an (x, y) point on an elliptic curve. A Point can contain a Diffie-Hellman public key, an ElGamal ciphertext, etc.

type Scalar ¶

type Scalar interface {
	Marshaling

	// Equality test for two Scalars derived from the same Group.
	Equal(s2 Scalar) bool

	// Clone creates a new Scalar with the same value.
	Clone() Scalar

	// SetInt64 sets the receiver to a small integer value.
	SetInt64(v int64) Scalar

	// Set to the additive identity (0).
	Zero() Scalar

	// Set to the modular sum of scalars a and b.
	Add(a, b Scalar) Scalar

	// Set to the modular difference a - b.
	Sub(a, b Scalar) Scalar

	// Set to the modular negation of scalar a.
	Neg(a Scalar) Scalar

	// Set to the multiplicative identity (1).
	One() Scalar

	// Set to the modular product of scalars a and b.
	Mul(a, b Scalar) Scalar

	// Set to the modular division of scalar a by scalar b.
	Div(a, b Scalar) Scalar

	// Set to the modular inverse of scalar a.
	Inv(a Scalar) Scalar

	// Set to a fresh random or pseudo-random scalar.
	Pick(rand cipher.Stream) Scalar

	// SetBytes sets the scalar from a byte-slice,
	// reducing if necessary to the appropriate modulus.
	// The endianess of the byte-slice is determined by the
	// implementation.
	SetBytes([]byte) Scalar
}

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.