ffrs.GFi16

class ffrs.GFi16

Finite-field operations for prime fields <= 65537

Methods

GFi16.__init__	Instantiate type for operations over \(GF(65537)\)
GFi16.add	Addition: \(\text{lhs} + \text{rhs}\)
GFi16.div	Division: \(\frac{\text{num}}{\text{den}}\)
GFi16.exp	Exponential function: \(a^{\text{value}}\)
GFi16.inv	Reciprocal: \(\frac{1}{\text{value}}\)
GFi16.log	Logarithm: \(\log_a (\text{value})\)
GFi16.mul	Multiplication: \(\text{lhs} \times \text{rhs}\)
GFi16.pow	Power: \(\text{base}^\text{exponent}\)
GFi16.sub	Subtraction: \(\text{lhs} - \text{rhs}\)

Attributes

GFi16.field_elements	\(p\)
GFi16.power	Always 1
GFi16.prime	\(p\)
GFi16.primitive	Primitive value used to generate the field

__init__(self: libffrs.GFi16, primitive: SupportsInt | SupportsIndex) → None

Instantiate type for operations over \(GF(65537)\)

Parameters:

primitive – \(a\) – primitive value used to generate the field

add(self: libffrs.GFi16, lhs: SupportsInt | SupportsIndex, rhs: SupportsInt | SupportsIndex) → int

Addition: \(\text{lhs} + \text{rhs}\)

div(self: libffrs.GFi16, num: SupportsInt | SupportsIndex, den: SupportsInt | SupportsIndex) → int

Division: \(\frac{\text{num}}{\text{den}}\)

exp(self: libffrs.GFi16, value: SupportsInt | SupportsIndex) → int

Exponential function: \(a^{\text{value}}\)

inv(self: libffrs.GFi16, value: SupportsInt | SupportsIndex) → int

Reciprocal: \(\frac{1}{\text{value}}\)

log(self: libffrs.GFi16, value: SupportsInt | SupportsIndex) → int

Logarithm: \(\log_a (\text{value})\)

mul(self: libffrs.GFi16, lhs: SupportsInt | SupportsIndex, rhs: SupportsInt | SupportsIndex) → int

Multiplication: \(\text{lhs} \times \text{rhs}\)

pow(self: libffrs.GFi16, base: SupportsInt | SupportsIndex, exponent: SupportsInt | SupportsIndex) → int

Power: \(\text{base}^\text{exponent}\)

sub(self: libffrs.GFi16, lhs: SupportsInt | SupportsIndex, rhs: SupportsInt | SupportsIndex) → int

Subtraction: \(\text{lhs} - \text{rhs}\)