Bijective Algorithm Authentication via Partial Reverse Computation

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Solution Overview

Problem

Existing authentication methods using bijective algorithms are vulnerable to attacks, particularly 'Differential Power Analysis by the end' (DPA by the end), which allow attackers to deduce the predetermined key by comparing the computed reference code byte by byte with the received code, making it difficult to secure message authentication.

Innovation Solution

A control method and device that authenticates received codes without computing reference codes by applying a bijective algorithm partially from the starting step and reversing it partially from the ending step, comparing intermediate results to determine authenticity, thereby preventing attackers from exploiting the final comparison.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If the complete bijective algorithm is applied to compute reference codes for authentication, then authentication accuracy is improved, but vulnerability to DPA by the end attacks increases

Engineering Contradiction:
Improveauthentication accuracyVSAvoidvulnerability to DPA attacks
Core Design Contradiction:
ReliabilityVSObject-affected harmful factors

Solution Approach 1:

The authentication process is segmented into two independent paths: the authenticator computes a reference code using the complete bijective algorithm, while the verifier computes an intermediate result using only a partial application of the algorithm. This segmentation allows authentication to proceed without the verifier needing to compute the complete reference code, thereby preventing DPA by the end attacks while maintaining authentication accuracy through the comparison of the intermediate result with a corresponding portion of the received code.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The vulnerable final comparison step that computes the complete reference code is extracted and replaced. Instead of computing the full reference code at the verifier side, only an intermediate result from a partial algorithm application is computed and compared. This extraction removes the attack surface for DPA by the end attacks while preserving the essential authentication function.

Inventive Principle:
Principle #2Taking out (Extraction)

2Reliability

If the bijective algorithm is applied completely to generate and verify codes, then message authentication is ensured, but key security is compromised due to byte-by-byte comparison

Engineering Contradiction:
Improvemessage authenticationVSAvoidkey security
Core Design Contradiction:
ReliabilityVSLoss of information

Solution Approach 1:

The verification process performs only a partial application of the bijective algorithm, computing an intermediate result rather than the complete reference code. This partial action is sufficient for authentication purposes when compared with the corresponding portion of the received code, while avoiding the excessive computation that would expose the key through complete reference code generation and byte-by-byte comparison.

Inventive Principle:
Principle #16Partial or excessive action

3Measurement precision

If reference codes are computed and compared byte by byte, then code authenticity is verified, but attackers can deduce the predetermined key from physical effect variations

Engineering Contradiction:
Improvecode authenticity verificationVSAvoidkey deduction from physical effects
Core Design Contradiction:
Measurement precisionVSObject-affected harmful factors

Solution Approach 1:

The harmful byte-by-byte comparison operation that enables key deduction is extracted and replaced with a comparison of intermediate results from partial algorithm application. This extraction eliminates the physical effect variations that attackers exploit while preserving the essential functionality of verifying code authenticity through comparison.

Inventive Principle:
Principle #2Taking out (Extraction)

Solution Approach 2:

An intermediate result from partial algorithm application serves as a mediator between the received code and the authentication decision. This intermediary value allows verification of code authenticity without requiring the computation or comparison of complete reference codes, thereby preventing attackers from deducing the predetermined key through physical effect analysis.

Inventive Principle:
Principle #24Intermediary (Mediator)

Data Source

PatentEP2918036B1Control method and device for controlling authenticity of codes resulting from application of a bijective algorithm to messages
Publication Date: 2019.01.02 THALES DIS FRANCE SA
  • EP2918036B1 patent drawingFigure 1~2

AI summary

A device (CD) is intended for controlling authenticity of a code received with a message by an electronic device (ED2) and resulting from application to this message of a bijective algorithm with at least one predetermined key. This device (CD) comprises i) a first computation means (CM1) arranged for applying partly this bijective algorithm with this predetermined key, from a starting step to a chosen intermediate step, to the received message, in order to get a first result, ii) a second computation means (CM2) arranged for applying partly in a reverse manner the bijective algorithm with the predetermined key, from an ending step to this chosen intermediate step, to the received code while using the received message, in order to get a second result, and iii) a comparison means (CM3) arranged for comparing these first and second results and for outputting an information representative of the authenticity of the received code when the first and second results are identical.