nacl.ristretto¶

The classes Ristretto255Scalar and Ristretto255Point provide a high-level abstraction around the low-level bindings to libsodium. Several functions are accessible through operator overloading.

See Finite field arithmetic for high-level documentation.

class nacl.ristretto.Ristretto255Scalar(value: Union[nacl.ristretto.Ristretto255Scalar, bytes, int, fractions.Fraction])[source]¶

Scalar field modulo prime ORDER. Each element is a scalar value.

Variables

ZERO – Scalar with value 0
ONE – Scalar with value 1
MINUS_ONE – Scalar with value -1 (modulo ORDER)
SIZE – Size of Scalars in bytes (32)
NONREDUCED_SIZE – Size of non reduced scalar (64); see reduce().
ORDER – Group order (2 ** 252 + 27742317777372353535851937790883648493)

__add__(other: Union[nacl.ristretto.Ristretto255Scalar, bytes, int, fractions.Fraction]) → nacl.ristretto.Ristretto255Scalar[source]¶

Add two scalars.

Parameters: other – Any of the types supported by the constructor
Returns: Sum of self and other reduced modulo ORDER

__bool__() → bool[source]¶

Check if scalar is non-zero.

Returns: True if non-zero, False otherwise

__bytes__() → bytes[source]¶

Get byte representation of scalar.

Returns: Value of scalar in little-endian encoding

__eq__(other: object) → bool[source]¶

Check if two scalars are identical. Comparing with other types such as int will return False.

Returns: True if equal, False otherwise

__init__(value: Union[nacl.ristretto.Ristretto255Scalar, bytes, int, fractions.Fraction]) → None[source]¶

Create a new Ristretto255Scalar.

Parameters: value – Value of the scalar. Will be converted according to its type.
Raises: exc.TypeError – Type not supported

Value can be one of:

Ristretto255Scalar: Create a new object with the same value.
bytes: value must be SIZE bytes in little-endian order.
int: value will be reduced modulo ORDER.
Fraction: Numerator of value multiplied with the inverse of its denominator.

__int__() → int[source]¶

Get integer representation of scalar.

Returns: Value of scalar reduced modulo ORDER

__mul__(other: Union[nacl.ristretto.Ristretto255Scalar, bytes, int, fractions.Fraction]) → nacl.ristretto.Ristretto255Scalar[source]¶

Multiply two scalars.

Parameters: other – Any of the types supported by the constructor
Returns: Product of self and other modulo ORDER

__neg__() → nacl.ristretto.Ristretto255Scalar[source]¶

Get the additive inverse such that -x + x == Ristretto255Scalar.ZERO.

Returns: Additive inverse

__sub__(other: Union[nacl.ristretto.Ristretto255Scalar, bytes, int, fractions.Fraction]) → nacl.ristretto.Ristretto255Scalar[source]¶

Subtract other from self.

Parameters: other – Any of the types supported by the constructor
Returns: Difference of self and other reduced modulo ORDER

__truediv__(other: Union[nacl.ristretto.Ristretto255Scalar, bytes, int, fractions.Fraction]) → nacl.ristretto.Ristretto255Scalar[source]¶

Divide two scalars.

Parameters: other – Any of the types supported by the constructor
Returns: Product of self and inverse of other modulo ORDER

property complement: nacl.ristretto.Ristretto255Scalar¶

Get the complement such that x.complement + x == Ristretto255Scalar.ONE.

Note that this is not the two’s complement where ~x + x == -1.

Returns: Complemental value reduced modulo ORDER

property inverse: nacl.ristretto.Ristretto255Scalar¶

Get multiplicative inverse such that x.inverse * x == Ristretto255Scalar.ONE.

Returns: Multiplicative inverse reduced modulo ORDER

classmethod random() → nacl.ristretto.Ristretto255Scalar[source]¶

Create non-zero random scalar.

Returns: Random scalar

classmethod random_zero() → nacl.ristretto.Ristretto255Scalar[source]¶

Create a random scalar that could be zero.

Returns: Ristretto255Scalar: Random scalar

classmethod reduce(value: bytes) → nacl.ristretto.Ristretto255Scalar[source]¶

Reduce a larger value, e.g. the output of a hash function, to a scalar. There should be at least 317 bits to ensure almost uniformity.

Parameters: value – NONREDUCED_SIZE bytes in little-endian encoding
Returns: Value reduced modulo ORDER

class nacl.ristretto.Ristretto255Point(value: bytes, _assume_valid: bool = False)[source]¶

Ristretto255 group. Each element is a curve point.

Variables

ORDER – Group order
SIZE – Size of Points in bytes (32)
HASH_SIZE – Size input for from_hash() (64).
ZERO – Neutral element

__add__(other: nacl.ristretto.Ristretto255Point) → nacl.ristretto.Ristretto255Point[source]¶

Add two points.

Parameters: other – A group point
Returns: Sum of self and other

__bool__() → bool[source]¶

Check if this is not the zero / neutral / identity point.

Returns: False if zero point, True otherwise

__bytes__() → bytes[source]¶

Get byte representation of point.

Returns: Little-endian byte representation of point

__eq__(other: object) → bool[source]¶

Compare this point to another point.

Parameters: other – Other point to compare to
Returns: True if same point, False otherwise or if not a Ristretto255Scalar

__mul__(other: Union[nacl.ristretto.Ristretto255Scalar, bytes, int, fractions.Fraction]) → nacl.ristretto.Ristretto255Point[source]¶

Multiply the non-zero scalar other with the point.

Parameters: other – Scalar value, any type supported by Ristretto255Scalar.
Returns: Product of self and other

__neg__() → nacl.ristretto.Ristretto255Point[source]¶

Get inverse element such that -self + self == Ristretto255Point.ZERO.

Returns: Inverse of self

__sub__(other: nacl.ristretto.Ristretto255Point) → nacl.ristretto.Ristretto255Point[source]¶

Subtract two points.

Parameters: other – A group point
Returns: Difference of self and other

classmethod base_mul(n: Union[nacl.ristretto.Ristretto255Scalar, bytes, int, fractions.Fraction]) → nacl.ristretto.Ristretto255Point[source]¶

Multiply the non-zero scalar n with the Ed25519 base point.

Parameters: n – Scalar value, any type supported by Ristretto255Scalar.
Returns: Product of the Ed25519 base point and n

classmethod from_hash(value: bytes) → nacl.ristretto.Ristretto255Point[source]¶

Map 64 bytes of input, e.g. the result of a hash function, to a group point. This might be the zero point, e.g. if hash value is all zeros.

Parameters: value – HASH_SIZE bytes in little-endian encoding
Returns: Point created from value

classmethod random() → nacl.ristretto.Ristretto255Point[source]¶

Generate a random Ristretto255 point. This might be, although astronomically unlikely, the zero point.

Returns: Random point