floating_point.basic_functions module

Module that extends the functions available for secure integers, fixed-point numbers and floating-point numbers.

floating_point.basic_functions.anorm(to_reduce, apply_sign=True)

Secure function that securely calculates 1/2**k, k for k such that to_reduce / 2**k is in the domain [0.5, 1)

Parameters:

• to_reduce (TypeVar(SecureNumberT, bound= SecureNumber)) – the number to be normalized.

• apply_sign (bool) – whether the normalization factor should preserve the sign.

Return type:

tuple[TypeVar(SecureNumberT, bound= SecureNumber), TypeVar(SecureNumberT, bound= SecureNumber)]

Returns:

A tuple containing the secret-shared normalization factor 1/2**k and the secret-shared bit length k.

Raises:

ValueError – When the secure type has not been initialized properly.

floating_point.basic_functions.exp2_fxp_integral(exponent, int_size=None)

Secure base-2 exponentiation of the input.

Parameters:

• exponent (SecureFixedPoint) – exponent of the exponentiation. It is assumed that the value is integer. if a non-integer fixed-point number is provided as input, there is a chance the wrong answer is returned.

• int_size (int | None) – upper-bound on the bit length of the input value. This helps make the calculations more efficient.

Return type:

SecureFixedPoint

Returns:

The base-2 exponentation of the exponent.

floating_point.basic_functions.exp2_int(exponent, int_size=None)

Secure base-2 exponentiation of the input.

Parameters:

• exponent (SecureInteger) – Exponent of the exponentiation. It is assumed that the value is a secure Integer. If the value is negative, the multiplicative inverse of 2**(-exponent) is calculated.

• int_size (int | None) – Upper bound on the bit length of the input value. This helps make the calculations more efficient.

Return type:

SecureInteger

Returns:

The base-2 exponentation of the exponent.

floating_point.basic_functions.exp2_int_pos(exponent, int_size=None)

Secure base-2 exponentiation of the input.

Parameters:

• exponent (SecureInteger) – exponent of the exponentiation. It is assumed that the value is integer and positive. if a non-integer fixed-point number is provided as input, there is a chance the wrong answer is returned. If a negative value is provided as input, the answer will be wrong.

• int_size (int | None) – upper-bound on the bit length of the input value. This helps make the calculations more efficient.

Return type:

SecureInteger

Returns:

The base-2 exponentation of the exponent.

floating_point.basic_functions.integer(value)

Function that securely truncates a number to its integer part.

Parameters:

value (TypeVar(SecureNumberT, bound= SecureNumber)) – The secure number.

Return type:

TypeVar(SecureNumberT, bound= SecureNumber)

Returns:

the floor function securely applied to value (similar to int).

floating_point.basic_functions.ln_small(value)

Secure natural logarithm approximation of the input value in the domain [0.5, 1).

Parameters:

value (SecureFixedPoint) – Secure fixed point number in the range [0.5, 1)

Return type:

SecureFixedPoint

Returns:

secure fixed point containing an approximation of the natural logarithm of the provided input value

floating_point.basic_functions.log_flp(secure_flp, secfxp_type)

Base-2 logarithm of a secure floating point number. This method abuses the structure of secure floating point numbers to obtain a more efficient solution than the Taylor approximation. During this process, the significand needs to be converted from a secure integer to a secure fixed point to enable a base-2 logarithm subroutine for fixed points.

Parameters:

• secure_flp (SecureFloatingPoint) – Secure floating point number.

• secfxp_type (type[SecureFixedPoint]) – Secure fixed point type that is used in the conversion.

Return type:

SecureFloatingPoint

Returns:

Secure floating point number containing the base-2 logarithm of the input value.

Raises:

ValueError – Significand has smaller bit length than exponent.

floating_point.basic_functions.log_fxp(value, base)

Secure logarithm of a secure fixed point number in a public base

Parameters:

• base (int | float) – plaintext base of the logarithm.

• value (SecureFixedPoint) – Secure fixed point number of which the logarithm is taken with respect to the base.

Return type:

SecureFixedPoint

Returns:

Secure fixed point number containing the natural logarithm of the input in the given base

floating_point.basic_functions.natural_log(value)

Secure natural logarithm of a secure fixed point.

Parameters:

value (SecureFixedPoint) – Secure fixed point number

Return type:

SecureFixedPoint

Returns:

Secure fixed point number containing the natural logarithm of the input

floating_point.basic_functions.parity(value)

Function that securely calculates the parity of the integer part of the given secure number.

Parameters:

value (TypeVar(SecureNumberT, bound= SecureNumber)) – The secure number.

Return type:

TypeVar(SecureNumberT, bound= SecureNumber)

Returns:

The parity of the integer part of the secure number.

floating_point.basic_functions.poly_approximation(coefficients, value)

Function for securely approximating a certain function using a polynomial

Parameters:

• coefficients (list[int] | list[float]) – List of polynomial coefficients. The coefficients go from degree zero upward. e.g. coefficients[i] correspond to the term of degree i.

• value (TypeVar(SecureNumberT, bound= SecureNumber)) – value to be evaluated

Return type:

TypeVar(SecureNumberT, bound= SecureNumber)

Returns:

The polynomial evaluation of value with respect to the coefficients.

Raises:

TypeError – When the first coefficient is not compatible with the secure type.

floating_point.basic_functions.sqrt_flp(secure_flp, secfxp_type)

Square root of a secure floating point number. This method abuses the structure of secure floating point numbers to obtain a more efficient solution than the Taylor approximation. During this process, the significand needs to be converted from a secure integer to a secure fixed point to enable a square root subroutine for fixed points.

Parameters:

• secure_flp (SecureFloatingPoint) – Secure floating point number.

• secfxp_type (type[SecureFixedPoint]) – Secure fixed point type that is used in the conversion.

Return type:

SecureFloatingPoint

Returns:

Secure floating point number containing the square root of the input value.

floating_point.basic_functions.sqrt_fxp(value)

Secure square root of the input value.

Parameters:

value (SecureFixedPoint) – Secure fixed point number

Return type:

SecureFixedPoint

Returns:

secure fixed point number containing the square root of the input

floating_point.basic_functions.sqrt_small(value)

Secure approximation of the square root in the domain [0.5,1).

Parameters:

value (SecureFixedPoint) – Secure fixed point number

Return type:

SecureFixedPoint

Returns:

secure fixed point number containing an approximation of the square root of the input value