utils.utils module

Useful functions for creating encryption schemes.

utils.utils.extended_euclidean(num_a, num_b)

Perform the extended euclidean algorithm on the input numbers. The method returns gcd, x, y, such that a*x + b*y = gcd.

Parameters:

• num_a (int) – First number a.

• num_b (int) – Second number b.

Return type:

Tuple[int, int, int]

Returns:

Tuple containing gcd, x, and y, such that a*x + b*y = gcd.

utils.utils.is_prime(number)

Check if the input number is a prime number. Uses GMPY2 if available

Parameters:

number (int) – The number to check

Return type:

bool

Returns:

Whether the input is prime or not

utils.utils.lcm(num_a, num_b)

Compute the least common multiple of two input numbers. Uses GMPY2 if available.

Parameters:

• num_a (int) – First number a.

• num_b (int) – Second number b.

Return type:

int

Returns:

Least common multiple of a and b.

utils.utils.mod_inv(value, modulus)

Compute the inverse of a number, given the modulus of the group. Note that the inverse might not exist. Uses GMPY2 if available.

Parameters:

• value (int) – The number to be inverted.

• modulus (int) – The group modulus.

Raises:

ZeroDivisionError – Raised when the inverse of the value does not exist.

Return type:

int

Returns:

The inverse of a under the modulus.

utils.utils.next_prime(low)

Generate the first prime number greater than the given value. Returns GMPY2 MPZ integer if available.

Parameters:

low (int) – Lower bound for the prime.

Return type:

int

Returns:

First prime number strictly greater than low.

utils.utils.pow_mod(base, exponent, modulus)

Compute base**exponent % modulus. Uses GMPY2 if available.

Parameters:

• base (int) – base

• exponent (int) – exponent

• modulus (int) – modulus

Return type:

int

Returns:

base**exponent % modulus

utils.utils.randprime(low, high)

Generate a random prime number in the range [low, high). Returns GMPY2 MPZ integer if available.

Parameters:

• low (int) – Lower bound (inclusive) of the range.

• high (int) – Upper bound (exclusive) of the range.

Return type:

int

Returns:

Random prime number.

Raises:

ValueError – the lower bound should be strictly lower than the upper bound