from public import public from scipy.stats import pearsonr import numpy as np from numpy.typing import NDArray from ...ec.mult import ScalarMultiplier from ...ec.point import Point from ...ec.context import DefaultContext, local from ...ec.params import DomainParameters from ...ec.mod import Mod from ..trace import Trace from ..trace.plot import plot_trace from ..attack.leakage_model import LeakageModel @public class CPA: traces: NDArray points: list[Point] mult: ScalarMultiplier params: DomainParameters leakage_model: LeakageModel correlations: dict[str, list[list[float]]] def __init__( self, points: list[Point], traces: list[Trace], leakage_model: LeakageModel, mult: ScalarMultiplier, params: DomainParameters, ): """ :param points: Points on which scalar multiplication with secret scalar was performed :param traces: Power traces corresponding to the scalar multiplication for each of the points :param mult: Scalar multiplier used :param params: Domain parameters used """ self.points = points self.traces = np.array([trace.samples for trace in traces]).transpose() self.mult = mult self.params = params self.leakage_model = leakage_model self.correlations = {"guess_one": [], "guess_zero": []} def compute_intermediate_value( self, guessed_scalar: int, target_bit: int, point: Point ) -> Mod: with local(DefaultContext()) as ctx: self.mult.init(self.params, point) self.mult.multiply(guessed_scalar) action_index = -1 for bit in bin(guessed_scalar)[2 : target_bit + 2]: if bit == "1": action_index += 2 elif bit == "0": action_index += 1 result = ctx.actions.get_by_index([0, action_index])[0] return result.output_points[0].X def compute_correlation_trace( self, guessed_scalar: int, target_bit: int ) -> list[float]: correlation_trace = [] intermediate_values = [] for i in range(len(self.points)): intermediate_value = self.compute_intermediate_value( guessed_scalar, target_bit, self.points[i] ) intermediate_values.append(self.leakage_model(intermediate_value)) for trace in self.traces: correlation_trace.append(pearsonr(intermediate_values, trace)[0]) return correlation_trace def plot_correlations(self, ct): return plot_trace(Trace(np.array(ct))).opts(width=950, height=600) def recover_bit( self, recovered_scalar: int, target_bit: int, scalar_bit_length: int, real_pub_key: Point, ) -> int: if target_bit == scalar_bit_length - 1: self.mult.init(self.params, self.params.generator) if real_pub_key == self.mult.multiply(recovered_scalar): return recovered_scalar return recovered_scalar | 1 mask = 1 << (scalar_bit_length - target_bit - 1) guessed_scalar_0 = recovered_scalar guessed_scalar_1 = recovered_scalar | mask correlation_trace_0 = self.compute_correlation_trace( guessed_scalar_0, target_bit ) correlation_trace_1 = self.compute_correlation_trace( guessed_scalar_1, target_bit ) self.correlations["guess_zero"].append(correlation_trace_0) self.correlations["guess_one"].append(correlation_trace_1) if np.nanmax(np.abs(correlation_trace_0)) > np.nanmax( np.abs(correlation_trace_1) ): return guessed_scalar_0 return guessed_scalar_1 def perform(self, scalar_bit_length: int, real_pub_key: Point) -> int: recovered_scalar = 1 << (scalar_bit_length - 1) for target_bit in range(1, scalar_bit_length): recovered_scalar = self.recover_bit( recovered_scalar, target_bit, scalar_bit_length, real_pub_key ) return recovered_scalar