Elliptic Curve Cryptography Key Generation Using Linear Combinations

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Solution Overview

Problem

Existing methods for generating elliptic curve cryptography keys are slow and require more powerful processors, limiting their efficiency and scalability for digital signatures and key agreements.

Innovation Solution

A method that generates N pairs of elliptic curve cryptography keys using a linear combination of previously-generated key pairs, where the linear combination involves addition operations, allowing for faster key generation and implementation on less powerful processors, utilizing a Vandermonde matrix for enhanced security.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Speed

If traditional methods are used to generate elliptic curve cryptography keys, then security is maintained, but the key generation process is slow and requires powerful processors

Engineering Contradiction:
Improvekey generation speedVSAvoidprocessor requirements
Core Design Contradiction:
SpeedVSDevice complexity

Solution Approach 1:

The patent pre-generates a set of base key pairs (P1, P2, ..., PK) in advance and stores them. When N keys are needed, they are generated by combining these pre-existing base keys through linear combinations, avoiding the need to generate each key from scratch and significantly reducing computation time during actual use.

Inventive Principle:
Principle #10Preliminary action

Solution Approach 2:

The patent divides the key generation process into two phases: a preliminary phase where base key pairs are generated and stored, and an operational phase where required keys are generated by linear combinations of stored base keys. This segmentation allows computationally intensive operations to be performed once rather than repeatedly.

Inventive Principle:
Principle #1Segmentation

2Productivity

If traditional key generation methods are used, then cryptographic security is ensured, but the process requires excessive computational resources and time

Engineering Contradiction:
Improvekey generation efficiencyVSAvoidtime for signature and key agreement processes
Core Design Contradiction:
ProductivityVSLoss of time

Solution Approach 1:

Base key pairs are generated and stored in advance, so that during signature and key agreement operations, only linear combination operations are needed, dramatically reducing the time required for these cryptographic operations.

Inventive Principle:
Principle #10Preliminary action

Solution Approach 2:

The patent changes the approach from generating each key independently through full cryptographic protocols to generating keys as linear combinations of base keys. This parameter change in the generation methodology reduces computational complexity from O(N) full generations to O(1) combination operations after initial setup.

Inventive Principle:
Principle #35Parameter changes

Data Source

PatentEP3993314B1Keys for elliptic curve cryptography
Publication Date: 2023.11.29 STMICROELECTRONICS SRL
  • EP3993314B1 patent drawingFigure 1~2
  • EP3993314B1 patent drawingFigure 3~4
  • EP3993314B1 patent drawing

AI summary

The present disclosure relates to a method of generation of N first pairs of ECC keys for elliptic curve cryptography, wherein each first pair of keys is a linear combination of previously-generated second pairs of elliptic curve cryptography keys.