Cryptographic Exponentiation Side-Channel Protection

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Solution Overview

Problem

Existing cryptographic exponentiation algorithms are vulnerable to side-channel attacks, such as Single Power Analysis (SPA), which can reveal sensitive information about the exponent through electrical consumption patterns, and are not optimized for execution speed.

Innovation Solution

An iterative calculation method that performs exponentiation using only multiplications of identical large variables, decomposing multiplications of different variables into combinations of identical variable multiplications, and employing simultaneous execution of multiplications to maintain regularity and avoid dummy operations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Loss of time

If the SQUARE function is used for multiplying identical large variables and the MULT function for multiplying different large variables, then the execution time is optimized, but the electrical consumption pattern reveals information about the exponent bits through SPA analysis

Engineering Contradiction:

Improveexecution timeVSAvoidexponent information leakage

Core Design Contradiction:

Loss of timeVSLoss of information

Solution Approach 1:

The patent applies homogeneity by ensuring that all multiplication operations in the exponentiation algorithm are performed using the same function (MULT), rather than distinguishing between SQUARE for identical variables and MULT for different variables. This creates a uniform operation pattern that prevents SPA attacks while maintaining execution efficiency through optimized multiplication routines

Inventive Principle:

Principle #33Homogeneity

2Loss of information

If only the MULT function is used for all multiplications without the SQUARE function, then SPA protection is improved, but the execution time increases due to loss of optimization

Engineering Contradiction:

Improveexponent information leakageVSAvoidexecution time

Core Design Contradiction:

Loss of informationVSLoss of time

Solution Approach 1:

The patent changes the operational parameter by using a single MULT function for all multiplications instead of switching between SQUARE and MULT functions. This parameter change maintains security by creating uniform power consumption patterns while preserving performance through efficient multiplication algorithm implementation

Inventive Principle:

Principle #35Parameter changes

3Loss of information

If dummy multiplications are inserted to create regularity in the algorithm, then SPA protection is improved, but the execution time increases due to unnecessary operations

Engineering Contradiction:

Improveexponent information leakageVSAvoidexecution speed

Core Design Contradiction:

Loss of informationVSProductivity

Solution Approach 1:

The patent extracts and eliminates the need for dummy multiplications by using a unified MULT function approach that inherently provides regularity in operation patterns. This removes unnecessary computational steps while maintaining the security benefits of regular power consumption patterns

Inventive Principle:

Principle #2Taking out (Extraction)

Data Source

PatentEP2492804B1Encryption method comprising an exponentiation operation

Publication Date: 2013.09.04 INSIDE SECURE

Figure 1~4
Figure 5A~6B

AI summary

The invention relates to a method and a device (DV1) protected against side-channel attacks, for computing the result of the exponentiation of a data m by an exponent d. The method and the device are configured to perform only multiplications of identical large variables by decomposing any multiplication of different large variables x, y into a combination of multiplications of identical large variables.