Key Derivation Function Using XOR and AND Operations

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Solution Overview

Problem

Security microprocessors face vulnerabilities in maintaining the confidentiality of cryptographic keys due to side-channel attacks, which can determine the key value by observing auxiliary channels like power consumption and electromagnetic radiation, even with existing protective measures.

Innovation Solution

A method for generating derived cryptographic keys using a key derivation function that combines random and complementary operations with a symmetric block cipher algorithm, specifically F(K,X,S) = F(K,X,T) ⊕ F(K,X,∼T), where T is randomly chosen from S or its complement, to produce a key that is independent of the choice duration and resistant to side-channel attacks.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If a master key is used for multiple cryptographic operations, then productivity is improved, but reliability deteriorates due to increased vulnerability to side-channel attacks

Engineering Contradiction:
Improvekey generation efficiencyVSAvoidkey confidentiality
Core Design Contradiction:
ProductivityVSReliability

Solution Approach 1:

The patent segments the key derivation process into multiple independent cryptographic operations (first encryption operation with first operand, second encryption operation with second operand). Each operation is isolated and contributes to the final derived key, preventing side-channel attacks from compromising the entire key through a single operation.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The patent introduces random operands as intermediaries in the key derivation process. These random values are combined with the master key through cryptographic operations to produce derived keys, acting as mediators that prevent direct observation of the master key through side-channel attacks while maintaining derivation efficiency.

Inventive Principle:
Principle #24Intermediary (Mediator)

2Reliability

If protective measures against side-channel attacks are implemented, then reliability is improved, but device complexity increases

Engineering Contradiction:
Improveside-channel resistanceVSAvoidcryptographic operation complexity
Core Design Contradiction:
ReliabilityVSDevice complexity

Solution Approach 1:

The patent changes the parameters of the cryptographic operations by varying the operands (first operand, second operand) in different derivation operations. This parameter variation ensures that each operation has a unique execution profile, making side-channel analysis ineffective while using the same underlying cryptographic algorithm, thus avoiding increased device complexity.

Inventive Principle:
Principle #35Parameter changes

3Ease of operation

If the same cryptographic algorithm is used for key derivation, then ease of operation is improved, but reliability deteriorates due to predictable operation patterns

Engineering Contradiction:
Improvealgorithm consistencyVSAvoidattack resistance
Core Design Contradiction:
Ease of operationVSReliability

Solution Approach 1:

The patent introduces dynamic elements into the key derivation process by using random operands that change with each derivation operation. While the underlying cryptographic algorithm remains consistent (maintaining ease of operation), the actual operations become dynamic and unpredictable, preventing attackers from using predictable patterns in side-channel analysis.

Inventive Principle:
Principle #15Dynamics

Data Source

PatentEP2738974B1Method for deriving multiple cryptographic keys from a master key in a security microprocessor
Publication Date: 2020.08.12 SPIRTECH SOCIETE A RESPONSABILITE LIMITEE
  • EP2738974B1 patent drawingFigure 1~2
  • EP2738974B1 patent drawingFigure 3
  • EP2738974B1 patent drawingFigure 4~5

AI summary

The method involves determining a derivation key function (KDF) from a permanent main key (K), a variable parameter (X) and a public or private key (S), where the key function comprises a cryptographic function controlled by the main key. A commutative operation is performed on two operands, where the operation comprises an exclusive OR operation and an AND operation. The derivation key function is calculated by selecting the variable parameter, calculating two keys using a cryptographic calculation unit of a safety microprocessor and combining the keys to produce a derived key (K').