Struct Int 

pub struct Int {
    pub bo: ByteOrder,
    /* private fields */
}

Int is a generic implementation of finite field arithmetic on integer finite fields with a given constant modulus, built using num_bigint_dig crate. The Scalar trait is implemented for Int, and hence serves as a basic implementation of Scalar, e.g., representing discrete-log exponents of Schnorr groups or scalar multipliers for elliptic curves.

Int offers an API similar to and compatible with BigInt, but “carries around” the relevant modulus and automatically normalizes the value to that modulus after all arithmetic operations, simplifying modular arithmetic. Binary operations assume that the source(s) have the same modulus, but do not check this assumption. Unary and binary arithmetic operations may be performed on uninitialized target objects, and receive the modulus of the first operand. For efficiency the modulus field m is a pointer, whose target is assumed never to change.

Fields

bo: ByteOrder

endianness which will be used on input and output

Implementations

impl Int

pub fn init64(self, v: i64, m: BigInt) -> Self

[init64()] creates an Int with an i64 value and BigInt modulus.

pub fn little_endian(&self, min: usize, max: usize) -> Result<Vec<u8>, IntError>

[little_endian()] encodes the value of this Int into a little-endian byte-slice at least min bytes but no more than max bytes long. Panics if max != 0 and the Int cannot be represented in max bytes.

pub fn new_int(v: BigInt, m: BigInt) -> Int

[new_int()] creates a new Int with a given BigInt and a BigInt modulus.

pub fn new_int64(v: i64, m: BigInt) -> Int

[new_int64()] creates a new Int with a given i64 value and BigInt modulus.

pub fn new_int_bytes(a: &[u8], m: &BigInt, byte_order: ByteOrder) -> Int

[new_int_bytes()] creates a new Int with a given slice of bytes and a BigInt modulus.

pub fn new_int_string(n: String, d: String, base: i32, m: &BigInt) -> Int

[new_int_string()] creates a new Int with a given String and a BigInt modulus. The value is set to a rational fraction n/d in a given base.

pub fn equal(&self, s2: &Self) -> bool

[equal()] returns true if the two ints are equal

pub fn cmpr(&self, s2: &Self) -> Ordering

[cmpr()] compares two ints for equality or inequality

pub fn init_bytes(self, a: &[u8], m: &BigInt, byte_order: ByteOrder) -> Self

[init_bytes()] init the Int to a number represented in a big-endian byte string.

pub fn set_string( self, n: String, d: String, base: i32, ) -> Result<Self, IntError>

[set_string()] sets the Int to a rational fraction n/d represented by a pair of strings. If d == "", then the denominator is taken to be 1. Returns the Int on success or an Error if the string failed to parse

impl Int

pub fn nonzero(&self) -> bool

[nonzero()] returns true if the integer value is nonzero.

pub fn int64(&self) -> i64

[int64()] returns the i64 representation of the value. If the value is not representable in an i64 the result is undefined.

pub fn set_uint64(&self, v: u64) -> Self

[set_uint64()] sets the Int to an arbitrary u64 value. The modulus must already be initialized.

pub fn uint64(&self) -> u64

[uint64()] returns the u64 representation of the value. If the value is not representable in an u64 the result is undefined.

pub fn exp(self, a: &Self, e: &BigInt) -> Self

[exp()] sets the target to a^e mod m, where e is an arbitrary BigInt exponent (not necessarily 0 <= e < m).

pub fn jacobi(&self, a_s: &Self) -> Self

jacobi() computes the Jacobi symbol of (a/m), which indicates whether a is zero (0), a positive square in m (1), or a non-square in m (-1).

pub fn sqrt(&mut self, a_s: &Self) -> Result<(), IntError>

[sqrt()] computes some square root of a mod m of ONE exists. Assumes the modulus m is an odd prime. Returns true on success, false if input a is not a square.

pub fn big_endian(&self, min: usize, max: usize) -> Result<Vec<u8>, IntError>

[big_endian()] encodes the value of this Int into a big-endian byte-slice at least min bytes but no more than max bytes long. Returns an Error if max != 0 and the Int cannot be represented in max bytes.

Trait Implementations

impl<'a, 'b> Add<&'a Int> for &'b Int

type Output = Int

The resulting type after applying the + operator.

fn add(self, rhs: &Int) -> Self::Output

Performs the + operation.

impl<'a> Add<&'a Int> for Int

type Output = Int

The resulting type after applying the + operator.

fn add(self, rhs: &Int) -> Self::Output

Performs the + operation.

impl<'a> Add<Int> for &'a Int

type Output = Int

The resulting type after applying the + operator.

fn add(self, rhs: Int) -> Self::Output

Performs the + operation.

impl Add for Int

type Output = Int

The resulting type after applying the + operator.

fn add(self, rhs: Int) -> Self::Output

Performs the + operation.

impl BinaryMarshaler for Int

fn marshal_binary(&self) -> Result<Vec<u8>, MarshallingError>

[marshal_binary()] encodes the value of this Int into a byte-slice exactly [self.marshal_size()] bytes long. It uses i’s ByteOrder to determine which byte order to output.

impl BinaryUnmarshaler for Int

fn unmarshal_binary(&mut self, data: &[u8]) -> Result<(), MarshallingError>

[unmarshal_binary()] tries to decode a Int from a byte-slice buffer. Returns an Error if the buffer is not exactly [self.marshal_size()] bytes long or if the contents of the buffer represents an out-of-range integer.

impl Clone for Int

fn clone(&self) -> Int

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Int

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

Formats the value using the given formatter.

impl Default for Int

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Int

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for Int

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

Formats the value using the given formatter.

impl LowerHex for Int

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

Formats the value using the given formatter.

impl Marshaling for Int

fn marshal_size(&self) -> usize

[marshal_size()] returns the length in bytes of encoded integers with modulus m. The length of encoded ints depends only on the size of the modulus, and not on the the value of the encoded integer, making the encoding is fixed-length for simplicity and security.

fn marshal_to(&self, w: &mut impl Write) -> Result<(), MarshallingError>

Encode the contents of this object and write it to an io::Write.

fn unmarshal_from(&mut self, r: &mut impl Read) -> Result<(), MarshallingError>

Decode the content of this object by reading from a io::Read. If r is an [XOF], it uses r to pick a valid object pseudo-randomly, which may entail reading more than len bytes due to retries.

fn unmarshal_from_random(&mut self, r: &mut (impl Read + Stream))

fn marshal_id(&self) -> [u8; 8]

[marshal_id()] returns the type tag used in encoding/decoding

impl<'a, 'b> Mul<&'a Int> for &'b Int

type Output = Int

The resulting type after applying the * operator.

fn mul(self, rhs: &Int) -> Self::Output

Performs the * operation.

impl<'a> Mul<&'a Int> for Int

type Output = Int

The resulting type after applying the * operator.

fn mul(self, rhs: &Int) -> Self::Output

Performs the * operation.

impl<'a> Mul<Int> for &'a Int

type Output = Int

The resulting type after applying the * operator.

fn mul(self, rhs: Int) -> Self::Output

Performs the * operation.

impl Mul for Int

type Output = Int

The resulting type after applying the * operator.

fn mul(self, rhs: Int) -> Self::Output

Performs the * operation.

impl Ord for Int

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for Int

fn eq(&self, other: &Self) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for Int

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Scalar for Int

fn set(self, a: &Self) -> Self

[set()] sets both value and modulus to be equal to another Int. Since this method copies the modulus as well,

fn set_int64(self, v: i64) -> Self

[set_int64()] sets the Int to an arbitrary 64-bit “small integer” value. The modulus must already be initialized.

fn zero(self) -> Self

[zero()] set the Int to the value 0. The modulus must already be initialized.

fn sub(self, a: &Self, b: &Self) -> Self

[sub()] sets the target to a - b mod m. Target receives a’s modulus.

fn pick(self, rand: &mut impl Stream) -> Self

[pick()] a pseudo-random integer modulo m using bits from the given stream cipher.

fn set_bytes(self, a: &[u8]) -> Self

[set_bytes()] set the value value to a number represented by a byte string. Endianness depends on the endianess set in i.

fn one(self) -> Self

[one()] sets the Int to the value 1. The modulus must already be initialized.

fn div(self, a: &Self, b: &Self) -> Self

[div()] sets the target to a * b^-1 mod m, where b^-1 is the modular inverse of b.

fn inv(self, a: &Self) -> Self

[inv()] sets the target to the modular inverse of a with respect to modulus m.

fn neg(self, a: &Self) -> Self

[neg()] sets the target to -a mod m.

impl Serialize for Int

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl UpperHex for Int

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

Formats the value using the given formatter.

impl Eq for Int