Elliptic Curve Key Generation Using Shared Knowledge

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Solution Overview

Problem

Existing asymmetric cryptosystems, particularly elliptic curve cryptography (ECC), face challenges in securely generating and managing cryptographic keys, especially when multiple parties need to communicate securely and differentiate their communications, and in scenarios requiring multiple digital signatures with the same private key but different public keys.

Innovation Solution

The method involves transforming the initial generating point of an elliptic curve into a new generating point using shared knowledge as a deterministic function, allowing the same private key to be used for multiple public-private key pairs and digital signatures, with the new generating point being substituted in the key generation and signature processes, and ensuring secure storage and deletion to prevent key compromise.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If the same private key is used for multiple public-private key pairs, then key management efficiency is improved, but the complexity of generating and managing multiple public keys increases

Engineering Contradiction:

Improvekey management efficiencyVSAvoidcomplexity of generating and managing multiple public keys

Core Design Contradiction:

ProductivityVSDevice complexity

Solution Approach 1:

The patent segments the key management process by separating the private key (kept secret and reused) from multiple public keys (distributed to different parties). This allows one private key to generate multiple public keys through different transforming functions, improving efficiency while maintaining security.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The private key serves multiple functions by being used to generate multiple public keys for different communication parties. The same private key can authenticate with multiple recipients, each receiving a unique public key, thus achieving multi-functionality without requiring multiple private keys.

Inventive Principle:

Principle #6Universality (Multi-functionality)

2Reliability

If different transforming functions are used to generate public keys from the same private key, then security is improved, but the complexity of the key generation process increases

Engineering Contradiction:

ImprovesecurityVSAvoidcomplexity of the key generation process

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent applies asymmetry by using different transforming functions (different elliptic curve generating points) to generate public keys from the same private key. Each party receives a public key generated with a unique transforming function, ensuring that compromising one public key does not compromise others, thus enhancing security through asymmetric transformation.

Inventive Principle:

Principle #4Asymmetry

3Adaptability or versatility

If multiple public keys are generated for the same private key, then adaptability in communication is improved, but the time required for key generation and management increases

Engineering Contradiction:

Improveadaptability in communicationVSAvoidtime required for key generation and management

Core Design Contradiction:

Adaptability or versatilityVSLoss of time

Solution Approach 1:

The patent implements preliminary action by pre-generating multiple public keys from a single private key using different transforming functions. These public keys are stored and ready for immediate use with different communication parties, eliminating the need to generate new keys each time communication is needed, thus reducing time loss while maintaining adaptability.

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS7593527B2Providing digital signature and public key based on shared knowledge

Publication Date: 2009.09.22 FIRST DATA CORP

AI summary

A public key and digital signature is provided using a private key of a public-private key pair in an elliptic curve digital signature algorithm (ECDSA) by: identifying domain parameters of an elliptic curve for use in elliptic curve cryptography, the domain parameters including an initial generating point; transforming the generating point into a new generating point as a deterministic function; generating the public key as a deterministic function of the private key and the domain parameters, in which the new generating point is substituted for the initial generating point; and generating the digital signature as a function of the private key and the domain parameters, in which the new generating point is substituted for the initial generating point.