pyecsca.ec.countermeasures module

Provides several countermeasures against side-channel attacks.

class ScalarMultiplierCountermeasure(mult)[source]

Bases: ABC

A scalar multiplier-based countermeasure.

This class behaves like a scalar multiplier, in fact it wraps one and provides some scalar-splitting countermeasure.

params: Optional[DomainParameters][source]
point: Optional[Point][source]
mult: ScalarMultiplier[source]
init(params, point)[source]

Initialize the countermeasure with the parameters and the point.

abstract multiply(scalar)[source]

Multiply the point with the scalar using the countermeasure.

Note

The countermeasure may compute multiple scalar multiplications internally. Thus, it may call the init method of the scalar multiplier multiple times.

Parameters:

scalar (int) – The scalar to multiply with.

Return type:

Point

Returns:

The result of the multiplication.

class GroupScalarRandomization(mult, rand_bits=32)[source]

Bases: ScalarMultiplierCountermeasure

Group scalar randomization countermeasure.

Samples a random multiple, multiplies the order with it and adds it to the scalar.

\[\begin{split}&r \xleftarrow{\$} \{0, 1, \ldots, 2^{\text{rand_bits}}\} \\ &\textbf{return}\ [k + r n]G\end{split}\]
Parameters:

  • mult (ScalarMultiplier) – The multiplier to use.

  • rand_bits (int) – How many random bits to sample.

rand_bits: int[source]
init(params, point)[source]

Initialize the countermeasure with the parameters and the point.

multiply(scalar)[source]

Multiply the point with the scalar using the countermeasure.

Note

The countermeasure may compute multiple scalar multiplications internally. Thus, it may call the init method of the scalar multiplier multiple times.

Parameters:

scalar (int) – The scalar to multiply with.

Return type:

Point

Returns:

The result of the multiplication.

mult: ScalarMultiplier[source]
params: Optional[DomainParameters][source]
point: Optional[Point][source]
class AdditiveSplitting(mult, add=None)[source]

Bases: ScalarMultiplierCountermeasure

Additive splitting countermeasure.

Splits the scalar into two parts additively, multiplies the point with them and adds the results.

\[\begin{split}&r \xleftarrow{\$} \{0, 1, \ldots, n\} \\ &\textbf{return}\ [k - r]G + [r]G\end{split}\]
Parameters:
add: Optional[AdditionFormula][source]
multiply(scalar)[source]

Multiply the point with the scalar using the countermeasure.

Note

The countermeasure may compute multiple scalar multiplications internally. Thus, it may call the init method of the scalar multiplier multiple times.

Parameters:

scalar (int) – The scalar to multiply with.

Return type:

Point

Returns:

The result of the multiplication.

init(params, point)[source]

Initialize the countermeasure with the parameters and the point.

mult: ScalarMultiplier[source]
params: Optional[DomainParameters][source]
point: Optional[Point][source]
class MultiplicativeSplitting(mult, rand_bits=32)[source]

Bases: ScalarMultiplierCountermeasure

Multiplicative splitting countermeasure.

Splits the scalar into two parts multiplicatively, multiplies the point with them and adds the results.

\[\begin{split}&r \xleftarrow{\$} \{0, 1, \ldots, 2^{\text{rand_bits}}\} \\ &S = [r]G \\ &\textbf{return}\ [k r^{-1} \mod n]S\end{split}\]
Parameters:

  • mult (ScalarMultiplier) – The multiplier to use.

  • rand_bits (int) – How many random bits to sample.

rand_bits: int[source]
multiply(scalar)[source]

Multiply the point with the scalar using the countermeasure.

Note

The countermeasure may compute multiple scalar multiplications internally. Thus, it may call the init method of the scalar multiplier multiple times.

Parameters:

scalar (int) – The scalar to multiply with.

Return type:

Point

Returns:

The result of the multiplication.

init(params, point)[source]

Initialize the countermeasure with the parameters and the point.

mult: ScalarMultiplier[source]
params: Optional[DomainParameters][source]
point: Optional[Point][source]
class EuclideanSplitting(mult, add=None)[source]

Bases: ScalarMultiplierCountermeasure

Euclidean splitting countermeasure.

Picks a random value half the size of the curve, then splits the scalar into the remainder and the quotient of the division by the random value.

\[\begin{split}&r \xleftarrow{\$} \{0, 1, \ldots, 2^{\log_2{(n)}/2}\} \\ &S = [r]G \\ &k_1 = k \mod r \\ &k_2 = \lfloor \frac{k}{r} \rfloor \\ &\textbf{return}\ [k_1]G + [k_2]S\end{split}\]
Parameters:
init(params, point)[source]

Initialize the countermeasure with the parameters and the point.

add: Optional[AdditionFormula][source]
mult: ScalarMultiplier[source]
params: Optional[DomainParameters][source]
point: Optional[Point][source]
multiply(scalar)[source]

Multiply the point with the scalar using the countermeasure.

Note

The countermeasure may compute multiple scalar multiplications internally. Thus, it may call the init method of the scalar multiplier multiple times.

Parameters:

scalar (int) – The scalar to multiply with.

Return type:

Point

Returns:

The result of the multiplication.

class BrumleyTuveri(mult)[source]

Bases: ScalarMultiplierCountermeasure

A countermeasure that fixes the bit-length of the scalar by adding some multiple of the order to it.

Originally proposed in [BT11].

\[\begin{split}&\hat{k}= \begin{cases} k + 2n \quad \text{if } \lceil \log_2(k+n) \rceil = \lceil \log_2 n \rceil\\ k + n \quad \text{otherwise}. \end{cases}\\ &\textbf{return}\ [\hat{k}]G\end{split}\]
mult: ScalarMultiplier[source]
params: Optional[DomainParameters][source]
point: Optional[Point][source]
init(params, point)[source]

Initialize the countermeasure with the parameters and the point.

multiply(scalar)[source]

Multiply the point with the scalar using the countermeasure.

Note

The countermeasure may compute multiple scalar multiplications internally. Thus, it may call the init method of the scalar multiplier multiple times.

Parameters:

scalar (int) – The scalar to multiply with.

Return type:

Point

Returns:

The result of the multiplication.