exponentiation.exponent module

Module containing all logic for securely performing exponentiation using the MPyC framework.

exponentiation.exponent.convert_exponents_to_other_base(old_base, new_base, exponents)

Convert the exponent of a given exponentiation for a given new base so that the result is the same.

More specifically, the following invariant is preserved: \(base_{old}\^exponent == base_{new}\^return_value\)

Parameters:

• old_base (Union[int, float]) – Original base of the exponentiation.

• new_base (float) – Desired base of the exponentiation.

• exponents (List[TypeVar(SecureNumberType, bound= SecureNumber)]) – List of original exponents.

Return type:

List[TypeVar(SecureNumberType, bound= SecureNumber)]

Returns:

List of exponents that satisfy the stated invariant.

exponentiation.exponent.maximal_exponent(base, stype)

Returns largest exponent x such that base**x fits within the precision of the field.

Parameters:

• base (float) – base of the exponentiation

• stype (Union[Type[SecureFixedPoint], Type[SecureInteger]]) – SecureNumberType class

Return type:

int

Returns:

largest exponent x such that base**x fits within the precision of the given types field

exponentiation.exponent.minimal_exponent(base, stype)

Returns smallest exponent x such that base**x fits within the precision of the field.

Parameters:

• base (float) – base of the exponentiation

• stype (Union[Type[SecureFixedPoint], Type[SecureInteger]]) – SecureNumberType class

Return type:

int

Returns:

smallest exponent x such that base**x fits within the precision of the given types field

exponentiation.exponent.secure_pow(base, exponents, trunc_to_domain=False, lower=None, upper=None, bit_precision=None)

Secure exponentiation.

Computes approximate secret-sharing of base**x for all given secret-shared x in [lower, upper]. May additionally enforce that x is truncated to fit in [lower, upper].

The exponentiation is approximate since it splits the computation into an exact integral computation and a approximate non-integral computation. The approximated part leverages Taylor series.

If exponents are truncated to the feasible domain, for a exponent \(x\), the function returns \(base^{upper}\) if \(x > upper\), \(base^x\) if \(x\in [lower, upper]\), and \(0\) if \(x < lower\).

Parameters:

• base (float) – Base of the exponentiation.

• exponents (Union[SecureInteger, SecureFixedPoint, TypeVar(SecureObjectsContainerTV, List[SecureInteger], List[SecureFixedPoint])]) – Exponents of the base.

• lower (Optional[float]) – Lower bound of exponents range, maximized for type(exponents[0]) if None.

• upper (Optional[float]) – Upper bound of exponents range, maximized for type(exponents[0]) if None.

• trunc_to_domain (bool) – Truncates exponents so that they fall in the given range at cost of additional resources. Additionally ensures that base**[lower] evaluates to [0].

• bit_precision (Optional[int]) – Bound on relative error of approximation, set to half of fractional bits if None.

Return type:

Union[SecureInteger, SecureFixedPoint, TypeVar(SecureObjectsContainerTV, List[SecureInteger], List[SecureFixedPoint])]

Returns:

Secret-shared value of the exponentiation for every exponent provided.

Raises:

NotImplementedError – Raised when size of domain is greater than twice the size of the maximum upper bound.