Galois Extension Field Block Cipher for Power-Constrained IoT

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Solution Overview

Problem

IoT devices face security challenges due to limited standardization of protocols and hardware, leading to low security measures that are not widely accepted and validated, primarily because of cost, size, weight, power, and time-to-market constraints, which result in the use of custom protocols that are not robust.

Innovation Solution

Adaptation of the Galois Extension Fields (GEF) combination technique for block encryption, utilizing a pseudo-random number generator (PRNG) to form a key matrix, applying GEF operations to map elements to higher-order fields, and combining plaintext and key matrices using extension field matrix multiplication, with operations optimized for efficient encryption and decryption processes.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If standard security protocols are implemented in IoT devices, then security reliability is improved, but device complexity and power consumption increase

Engineering Contradiction:

Improvesecurity reliabilityVSAvoiddevice complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent transforms the cryptographic operations from standard finite field arithmetic to Galois Extension Field arithmetic, changing the mathematical parameters of the encryption algorithm. This parameter change enables more efficient computation that is better suited for resource-constrained IoT devices while maintaining security standards

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces traditional cryptographic mechanical operations with optimized mathematical operations in Galois Extension Fields. By substituting the computational mechanism with field-based arithmetic operations, the system achieves better performance on low-power processors without sacrificing security reliability

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Reliability

If standard security protocols are implemented in IoT devices, then security reliability is improved, but power consumption increases

Engineering Contradiction:

Improvesecurity reliabilityVSAvoidpower consumption

Core Design Contradiction:

ReliabilityVSUse of energy by moving object

Solution Approach 1:

The patent changes the computational parameters from standard cryptographic operations to Galois Extension Field operations, which require fewer computational steps and less energy processing. This parameter transformation maintains security while reducing the energy cost of encryption and decryption operations

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent substitutes energy-intensive traditional cryptographic computations with more efficient field arithmetic operations. This mechanical substitution reduces power consumption by replacing heavy computational mechanisms with lighter, field-based arithmetic operations suitable for battery-powered IoT devices

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

3Ease of manufacture

If custom protocols are used to meet SWaP-C constraints, then ease of manufacture is improved, but security reliability deteriorates

Engineering Contradiction:

Improveease of manufactureVSAvoidsecurity reliability

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

The patent creates a universal cryptographic solution based on Galois Extension Fields that can be applied across different IoT devices and protocols. This universal approach allows custom protocols to maintain security reliability by using a proven mathematical foundation rather than ad-hoc security measures

Inventive Principle:

Principle #6Universality (Multi-functionality)

Solution Approach 2:

The patent enables IoT devices to perform cryptographic operations independently using optimized Galois Extension Field arithmetic. This self-service capability allows devices to implement secure custom protocols without relying on external security infrastructure, maintaining both ease of manufacture and security reliability

Inventive Principle:

Principle #25Self-service

4Ease of operation

If computational complexity is reduced for IoT devices, then ease of operation is improved, but security strength deteriorates

Engineering Contradiction:

Improveease of operationVSAvoidsecurity strength

Core Design Contradiction:

Ease of operationVSStrength

Solution Approach 1:

The patent changes the computational parameters to Galois Extension Field arithmetic, which simplifies the mathematical operations required for encryption and decryption. This parameter change makes the system easier to operate on IoT devices while maintaining cryptographic strength through the mathematical properties of extension fields

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS12445266B2Galois extension field-based block cipher

Publication Date: 2025.10.14 VIRGINIA TECH INTELLECTUAL PROPERTIES INC

AI summary

Various examples are provided related to a block cipher adaptation of the Galois Extension Fields (GEF) combination technique. In one example, a GEF-based block encryption includes forming an output from a PRNG into a key matrix, where the key matrix is formatted as an invertible square matrix; applying a GEF operation to the key matrix to map elements to a closed subset in a higher-order GEF space; mapping plaintext to a plaintext matrix; applying a GEF operation to the plaintext matrix to map elements to the higher-order GEF space; combining the plaintext matrix and the key matrix to produce a vector of ciphertext in the higher-order GEF space; reducing the vector to a reduced vector of ciphertext using an inverse of the GEF operation; and during the reducing, applying a ceiling operation to bijectively map elements in the reduced vector to a closed subset. Another example includes GEF-based block decryption.