Struct num_modular::Montgomery

pub struct Montgomery<T> { /* private fields */ }

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.

Implementations

impl Montgomery<u8>

pub const fn new(m: u8) -> Self

impl Montgomery<u16>

pub const fn new(m: u16) -> Self

impl Montgomery<u32>

pub const fn new(m: u32) -> Self

impl Montgomery<u64>

pub const fn new(m: u64) -> Self

impl Montgomery<u128>

pub const fn new(m: u128) -> Self

impl Montgomery<usize>

pub const fn new(m: usize) -> Self

Trait Implementations

impl<T: Clone> Clone for Montgomery<T>

fn clone(&self) -> Montgomery<T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug> Debug for Montgomery<T>

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

Formats the value using the given formatter.

impl Reducer<u128> for Montgomery<u128>

fn new(m: &u128) -> Self

Create a reducer for a modulus m

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

Transform a normal integer into reduced form

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

Check whether target is a valid reduced form

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

Transform a reduced form back to normal integer

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

Calculate (lhs * rhs) mod m in reduced form

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

Calculate target^2 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

fn add_in_place(&self, lhs: &mut T, rhs: &T)

fn sub_in_place(&self, lhs: &mut T, rhs: &T)

fn mul_in_place(&self, lhs: &mut T, rhs: &T)

impl Reducer<u16> for Montgomery<u16>

fn new(m: &u16) -> Self

Create a reducer for a modulus m

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

Transform a normal integer into reduced form

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

Check whether target is a valid reduced form

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

Transform a reduced form back to normal integer

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

Calculate (lhs * rhs) mod m in reduced form

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

Calculate target^2 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 add_in_place(&self, lhs: &mut T, rhs: &T)

fn sub_in_place(&self, lhs: &mut T, rhs: &T)

fn mul_in_place(&self, lhs: &mut T, rhs: &T)

impl Reducer<u32> for Montgomery<u32>

fn new(m: &u32) -> Self

Create a reducer for a modulus m

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

Transform a normal integer into reduced form

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

Check whether target is a valid reduced form

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

Transform a reduced form back to normal integer

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

Calculate (lhs * rhs) mod m in reduced form

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

Calculate target^2 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 add_in_place(&self, lhs: &mut T, rhs: &T)

fn sub_in_place(&self, lhs: &mut T, rhs: &T)

fn mul_in_place(&self, lhs: &mut T, rhs: &T)

impl Reducer<u64> for Montgomery<u64>

fn new(m: &u64) -> Self

Create a reducer for a modulus m

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

Transform a normal integer into reduced form

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

Check whether target is a valid reduced form

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

Transform a reduced form back to normal integer

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

Calculate (lhs * rhs) mod m in reduced form

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

Calculate target^2 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 add_in_place(&self, lhs: &mut T, rhs: &T)

fn sub_in_place(&self, lhs: &mut T, rhs: &T)

fn mul_in_place(&self, lhs: &mut T, rhs: &T)

impl Reducer<u8> for Montgomery<u8>

fn new(m: &u8) -> Self

Create a reducer for a modulus m

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

Transform a normal integer into reduced form

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

Check whether target is a valid reduced form

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

Transform a reduced form back to normal integer

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

Calculate (lhs * rhs) mod m in reduced form

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

Calculate target^2 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 add_in_place(&self, lhs: &mut T, rhs: &T)

fn sub_in_place(&self, lhs: &mut T, rhs: &T)

fn mul_in_place(&self, lhs: &mut T, rhs: &T)

impl Reducer<usize> for Montgomery<usize>

fn new(m: &usize) -> Self

Create a reducer for a modulus m

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

Transform a normal integer into reduced form

fn check(&self, target: &usize) -> bool

Check whether target is a valid reduced form

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

Transform a reduced form back to normal integer

fn modulus(&self) -> usize

Get the modulus in original integer type

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

Test if the residue() == 0

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

Calculate (lhs + rhs) mod m in reduced form

fn dbl(&self, target: usize) -> usize

Calculate 2*target mod m

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

Calculate (lhs - rhs) mod m in reduced form

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

Calculate -monty mod m in reduced form

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

Calculate (lhs * rhs) mod m in reduced form

fn sqr(&self, target: usize) -> usize

Calculate target^2 mod m in reduced form

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

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

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

Calculate base ^ exp mod m in reduced form

fn add_in_place(&self, lhs: &mut T, rhs: &T)

fn sub_in_place(&self, lhs: &mut T, rhs: &T)

fn mul_in_place(&self, lhs: &mut T, rhs: &T)

impl<T: Copy> Copy for Montgomery<T>