fe25519 module

Pure-Python data structure for working with Ed25519 (and Ristretto) field elements and operations.

class fe25519(ns: Sequence[int])

Bases: object

Class for creating and operating on field elements. The public interface of this class is determined primarily by the needs of the ge25519 library. However, use of some built-in Python operators is supported via special methods.

d = fe25519([929955233495203, 466365720129213, 1662059464998953, 2033849074728123, 1442794654840575])

d2 = fe25519([1859910466990425, 932731440258426, 1072319116312658, 1815898335770999, 633789495995903])

sqrtm1 = fe25519([1718705420411056, 234908883556509, 2233514472574048, 2117202627021982, 765476049583133])

invsqrtamd = fe25519([278908739862762, 821645201101625, 8113234426968, 1777959178193151, 2118520810568447])

onemsqd = fe25519([1136626929484150, 1998550399581263, 496427632559748, 118527312129759, 45110755273534])

sqdmone = fe25519([1507062230895904, 1572317787530805, 683053064812840, 317374165784489, 1572899562415810])

sqrtadm1 = fe25519([2241493124984347, 425987919032274, 2207028919301688, 1220490630685848, 974799131293748])

curve25519_A = fe25519([486662, 0, 0, 0, 0])

static zero() → fe25519

Constant corresponding to the zero element.

>>> fe25519.zero() + fe25519.one() == fe25519.one()
True

static one() → fe25519

Constant corresponding to the multiplicative identity element.

>>> fe25519.one() * fe25519.one() == fe25519.one()
True

copy() → fe25519

Create a copy of this element instance.

>>> fe25519.one().copy() == fe25519.one()
True

reduce() → fe25519

Reduce this element to a canonical representation.

>>> (~fe25519.one()).reduce()
fe25519([1, 0, 0, 0, 0])

__add__(other: fe25519) → fe25519

Compute the sum of this element and another element.

>>> fe25519.zero() + fe25519.zero() == fe25519.zero()
True

__neg__() → fe25519

Compute the negation of this element.

>>> fe25519.one().cneg(1) != fe25519.one()
True

cmov(g: fe25519, b: int) → fe25519

Conditionally select this element or another based on a boolean integer.

cneg(b: int) → fe25519

Compute the conditional negation of this element.

>>> fe25519.one().cneg(0) == fe25519.one()
True
>>> (fe25519.one().cneg(1) + fe25519.one()).is_zero()
1

__abs__() → fe25519

Compute the absolute value of this element.

>>> abs(-fe25519.one()).is_negative()
0

__sub__(other: fe25519) → fe25519

Compute the result of subtracting another element from this element.

>>> fe25519.zero() - fe25519.one() == fe25519.one().cneg(1)
True

__mul__(other: fe25519) → fe25519

Compute the product of this element and another element.

>>> fe25519.one() * fe25519.zero() == fe25519.zero()
True

sq() → fe25519

Compute the square of this element.

>>> two = fe25519.one() + fe25519.one()
>>> four = two + two
>>> two.sq() == four
True

sq2() → fe25519

Compute the element that is twice the square of this element.

>>> two = fe25519.one() + fe25519.one()
>>> two.sq2() == two.sq() + two.sq()
True

pow22523() → fe25519

Compute the result of the exponentiation of this element by a special fixed exponent.

invert() → fe25519

Compute the multiplicative inverse of this element.

>>> two = fe25519.one() + fe25519.one()
>>> (two.invert() * two).reduce() == fe25519.one()
True

__invert__() → fe25519

Compute the multiplicative inverse of this element.

>>> two = fe25519.one() + fe25519.one()
>>> (((~two) * two) - fe25519.one()).is_zero()
1

__pow__(e: int) → fe25519

Exponentiation is a synonym for squaring and inversion.

>>> two = fe25519.one() + fe25519.one()
>>> two**2 == two * two == two.sq()
True
>>> ~fe25519.one() == fe25519.one() ** (-1)
True

sqrt_ratio_m1_ristretto255(v: fe25519) → Tuple[fe25519, int]

Compute the result of a specialized root operation.

chi25519() → fe25519

Compute the result of a specialized root operation (for elligator).

__eq__(other: fe25519) → bool

Determine whether this element and another are equivalent.

>>> fe25519.zero() == fe25519.one()
False
>>> fe25519.one() == fe25519.one()
True

is_zero() → int

Determine whether this element is zero.

>>> fe25519.zero().is_zero()
1
>>> fe25519.one().is_zero()
0

is_negative() → int

Determine whether the negation bit is set in this element.

>>> fe25519.zero().is_negative()
0

static from_bytes(bs: bytes) → fe25519

Assemble an element instance from its byte representation.

>>> s = '0100000000000000000000000000000000000000000000000000000000000000'
>>> fe25519.from_bytes(bytes.fromhex(s))
fe25519([1, 0, 0, 0, 0])

to_bytes() → bytes

Build the byte representation of this element.

>>> fe25519.one().to_bytes().hex()
'0100000000000000000000000000000000000000000000000000000000000000'

__bytes__() → bytes

Build the byte representation of this element.

>>> bytes(fe25519.one()).hex()
'0100000000000000000000000000000000000000000000000000000000000000'

__str__() → str

Obtain the string representation of an element.

>>> str(fe25519.one())
'fe25519([1, 0, 0, 0, 0])'

__repr__() → str

Obtain the string representation of an element.