Modular Reduction Algorithm for SPA-Resistant Inverse Computation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing cryptographic algorithms, such as the extended Euclidean algorithm, are susceptible to Simple Power Analysis (SPA) attacks due to their reliance on integer division, which reveals sensitive information about processed numbers, potentially exposing secret keys.
Innovation Solution
The algorithm is modified to replace integer division with modular reduction, incorporating an enlargement parameter and modular shift operations to obscure the division result, thereby enhancing security against SPA attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the extended Euclidean algorithm is used to compute modular multiplicative inverse, then the computation is efficient and straightforward, but the algorithm becomes vulnerable to Simple Power Analysis (SPA) attacks due to the division operation revealing side-channel information
Solution Approach 1:
The patent introduces an intermediary transformation by replacing the direct division operation with a sequence of modular reduction operations. The division step q = a/b is transformed into intermediate calculations involving modular reductions (a mod b, a mod 2b, etc.) that do not directly expose the quotient value through power consumption patterns, thus protecting against SPA attacks while maintaining computational efficiency
Solution Approach 2:
The patent changes the computational parameters by replacing the division operation with modular reduction operations. Instead of directly computing q = a/b, the algorithm computes equivalent results through modular arithmetic operations (a mod b, a mod 2b, etc.), which have different power consumption characteristics that do not leak sensitive information about the quotient
2Ease of operation
If integer division is implemented using iteration loops with shifting and subtracting, then the division can be realized on microprocessors, but the current or power consumption and time consumption depend on the numbers processed, enabling SPA attacks
Solution Approach 1:
The patent introduces modular reduction as an intermediary operation that replaces direct division. The modular reduction operations serve as a mediator that achieves the same computational goal (obtaining quotient and remainder) without directly exposing the division result through power consumption patterns that would reveal information about the operands
Solution Approach 2:
The patent makes the algorithm dynamic by using conditional logic that adapts the number of iterations and operations based on the relationship between operands. The modular reduction approach allows the algorithm to dynamically adjust its execution path without creating predictable power consumption patterns that would leak information about the specific numbers being processed
Data Source
AI summary
A device for determining an inverse of an initial value related to a modulus, comprising a unit configured to process an iterative algorithm in a plurality of iterations, wherein an iteration includes two modular reductions and has, as an iteration loop result, values obtained by an iteration loop of an extended Euclidean algorithm.