if_helper

cryptographic_estimators.IFEstimator.if_helper.Lfunction(alpha, beta, logN)

Implements the exponent of the L-function L[alpha, beta] = exp((beta)*logN**alpha * log(logN)**(1-alpha) )

Parameters:

• alpha (float) – main constant in the L-function

• beta (float) – another constant in the L-function

• logN (float) – ln(N) of the number to factor

Returns:

the exponent of the L-function

Return type:

float

Examples

>>> from cryptographic_estimators.IFEstimator.if_helper import Lfunction
>>> n = 1024
>>> Lfunction(0.5, 1, n)
84.2486031274931

cryptographic_estimators.IFEstimator.if_helper.division_complexity(n)

Computes the time complexity of dividing a 2n-bit integer by an n-bit integer.

See Thm. 1.4.2 in [BZ10] https://arxiv.org/pdf/1004.4710

Parameters:

n (int) – bit length of the divisor

Returns:

the time complexity of the division operation

Return type:

float

Examples

>>> from cryptographic_estimators.IFEstimator.if_helper import division_complexity
>>> n = 1024
>>> division_complexity(n)
1051648

cryptographic_estimators.IFEstimator.if_helper.multipication_complexity(n)

Computes the time complexity of multiplying two n-bit integers.

Parameters:

n (int) – bit length of the integers to multiply

Returns:

the time complexity of the multiplication operation

Return type:

float

Examples

>>> from cryptographic_estimators.IFEstimator.if_helper import multipication_complexity
>>> n = 1024
>>> multipication_complexity(n)
1048576

cryptographic_estimators.IFEstimator.if_helper.pifunction(x)

Implements the prime counting function π(x) which counts the number of primes less than or equal to x.

Parameters:

x (float) – the upper limit for counting primes

Returns:

the number of primes less than or equal to x, rounded up

Return type:

int

Examples

>>> from cryptographic_estimators.IFEstimator.if_helper import pifunction
>>> pifunction(127)
27

cryptographic_estimators.IFEstimator.if_helper.primality_testing(n)

Computes the time complexity of the Miller-Rabin primality test for an n-bit integer.

Miller-Rabin primality test with #trials = k = 64 -> n is probably prime with probability at most 2^-2k

Parameters:

n (int) – bit length of the integer to test for primality

Returns:

the time complexity of the Miller-Rabin primality test

Return type:

float

Examples

>>> from cryptographic_estimators.IFEstimator.if_helper import primality_testing
>>> n = 1024
>>> primality_testing(n)
68719476736