Struct num_modular::Montgomery

pub struct Montgomery<I, M>(_, _);

A modular reducer based on Montgomery form, only supports odd modulus.

The generic type T represents the underlying integer representation for modular inverse -m^-1 mod R, and R=2^B will be used as the auxiliary modulus, where B is automatically selected based on the size of T.

Trait Implementations

impl<I: Clone, M: Clone> Clone for Montgomery<I, M>

fn clone(&self) -> Montgomery<I, M>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<I: Debug, M: Debug> Debug for Montgomery<I, M>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Reducer<u128> for Montgomery<u128, u128>

fn transform(&self, target: u128) -> u128

Transform a normal integer into reduced form

fn residue(&self, target: u128) -> u128

Transform a reduced form back to normal integer

fn mul(&self, lhs: u128, rhs: u128) -> u128

Calculate (lhs * rhs) mod m in reduced form

fn square(&self, target: u128) -> u128

Calculate target^2 mod m in reduced form

fn new(m: &u128) -> Self

Create a reducer for a modulus m

fn modulus(&self) -> u128

Get the modulus in original integer type

fn is_zero(&self, target: &u128) -> bool

Test if the residue() == 0

fn add(&self, lhs: u128, rhs: u128) -> u128

Calculate (lhs + rhs) mod m in reduced form

fn double(&self, target: u128) -> u128

Calculate 2*target mod m

fn sub(&self, lhs: u128, rhs: u128) -> u128

Calculate (lhs - rhs) mod m in reduced form

fn neg(&self, target: u128) -> u128

Calculate -monty mod m in reduced form

fn inv(&self, target: u128) -> Option<u128>

Calculate target^-1 mod m in reduced form, it may return None when there is no modular inverse.

fn pow(&self, base: u128, exp: u128) -> u128

Calculate base ^ exp mod m in reduced form

impl Reducer<u16> for Montgomery<u16, u16>

fn new(m: &u16) -> Self

Create a reducer for a modulus m

fn modulus(&self) -> u16

Get the modulus in original integer type

fn is_zero(&self, target: &u16) -> bool

Test if the residue() == 0

fn add(&self, lhs: u16, rhs: u16) -> u16

Calculate (lhs + rhs) mod m in reduced form

fn double(&self, target: u16) -> u16

Calculate 2*target mod m

fn sub(&self, lhs: u16, rhs: u16) -> u16

Calculate (lhs - rhs) mod m in reduced form

fn neg(&self, target: u16) -> u16

Calculate -monty mod m in reduced form

fn inv(&self, target: u16) -> Option<u16>

Calculate target^-1 mod m in reduced form, it may return None when there is no modular inverse.

fn pow(&self, base: u16, exp: u16) -> u16

Calculate base ^ exp mod m in reduced form

fn transform(&self, target: u16) -> u16

Transform a normal integer into reduced form

fn residue(&self, target: u16) -> u16

Transform a reduced form back to normal integer

fn mul(&self, lhs: u16, rhs: u16) -> u16

Calculate (lhs * rhs) mod m in reduced form

fn square(&self, target: u16) -> u16

Calculate target^2 mod m in reduced form

impl Reducer<u32> for Montgomery<u32, u32>

fn new(m: &u32) -> Self

Create a reducer for a modulus m

fn modulus(&self) -> u32

Get the modulus in original integer type

fn is_zero(&self, target: &u32) -> bool

Test if the residue() == 0

fn add(&self, lhs: u32, rhs: u32) -> u32

Calculate (lhs + rhs) mod m in reduced form

fn double(&self, target: u32) -> u32

Calculate 2*target mod m

fn sub(&self, lhs: u32, rhs: u32) -> u32

Calculate (lhs - rhs) mod m in reduced form

fn neg(&self, target: u32) -> u32

Calculate -monty mod m in reduced form

fn inv(&self, target: u32) -> Option<u32>

Calculate target^-1 mod m in reduced form, it may return None when there is no modular inverse.

fn pow(&self, base: u32, exp: u32) -> u32

Calculate base ^ exp mod m in reduced form

fn transform(&self, target: u32) -> u32

Transform a normal integer into reduced form

fn residue(&self, target: u32) -> u32

Transform a reduced form back to normal integer

fn mul(&self, lhs: u32, rhs: u32) -> u32

Calculate (lhs * rhs) mod m in reduced form

fn square(&self, target: u32) -> u32

Calculate target^2 mod m in reduced form

impl Reducer<u64> for Montgomery<u64, u64>

fn new(m: &u64) -> Self

Create a reducer for a modulus m

fn modulus(&self) -> u64

Get the modulus in original integer type

fn is_zero(&self, target: &u64) -> bool

Test if the residue() == 0

fn add(&self, lhs: u64, rhs: u64) -> u64

Calculate (lhs + rhs) mod m in reduced form

fn double(&self, target: u64) -> u64

Calculate 2*target mod m

fn sub(&self, lhs: u64, rhs: u64) -> u64

Calculate (lhs - rhs) mod m in reduced form

fn neg(&self, target: u64) -> u64

Calculate -monty mod m in reduced form

fn inv(&self, target: u64) -> Option<u64>

Calculate target^-1 mod m in reduced form, it may return None when there is no modular inverse.

fn pow(&self, base: u64, exp: u64) -> u64

Calculate base ^ exp mod m in reduced form

fn transform(&self, target: u64) -> u64

Transform a normal integer into reduced form

fn residue(&self, target: u64) -> u64

Transform a reduced form back to normal integer

fn mul(&self, lhs: u64, rhs: u64) -> u64

Calculate (lhs * rhs) mod m in reduced form

fn square(&self, target: u64) -> u64

Calculate target^2 mod m in reduced form

impl Reducer<u8> for Montgomery<u8, u8>

fn new(m: &u8) -> Self

Create a reducer for a modulus m

fn modulus(&self) -> u8

Get the modulus in original integer type

fn is_zero(&self, target: &u8) -> bool

Test if the residue() == 0

fn add(&self, lhs: u8, rhs: u8) -> u8

Calculate (lhs + rhs) mod m in reduced form

fn double(&self, target: u8) -> u8

Calculate 2*target mod m

fn sub(&self, lhs: u8, rhs: u8) -> u8

Calculate (lhs - rhs) mod m in reduced form

fn neg(&self, target: u8) -> u8

Calculate -monty mod m in reduced form

fn inv(&self, target: u8) -> Option<u8>

Calculate target^-1 mod m in reduced form, it may return None when there is no modular inverse.

fn pow(&self, base: u8, exp: u8) -> u8

Calculate base ^ exp mod m in reduced form

fn transform(&self, target: u8) -> u8

Transform a normal integer into reduced form

fn residue(&self, target: u8) -> u8

Transform a reduced form back to normal integer

fn mul(&self, lhs: u8, rhs: u8) -> u8

Calculate (lhs * rhs) mod m in reduced form

fn square(&self, target: u8) -> u8

Calculate target^2 mod m in reduced form

impl<I: Copy, M: Copy> Copy for Montgomery<I, M>