Elliptic Curve Cryptosystem Two-Phase Key Generation

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Solution Overview

Problem

Conventional elliptic curve cryptosystems (ECC) require significant time and resources for generating public keys, especially as security standards demand larger keys, necessitating improved methods for digital signing.

Innovation Solution

The method involves generating a first random key and calculating a reference point, which is then used to generate a second, shorter random key to compute a public key for digital signing, reducing the computational burden and signature generation time.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If conventional ECC key generation is used to maintain security with larger keys, then security level is improved, but key generation time and computational resources increase significantly

Engineering Contradiction:

Improvesecurity levelVSAvoidkey generation time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The key generation process is divided into two distinct phases: a preparation phase where a first random key is generated and stored, and a signature phase where a second, shorter random key is generated to compute the public key. This segmentation allows the computationally intensive part to be done once during preparation, while subsequent signature operations use the shorter key for faster computation.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

A first random key and its corresponding public key are generated and stored in advance during the preparation phase. This preliminary action establishes the cryptographic foundation before actual signature operations are needed, allowing faster subsequent operations using the pre-computed values.

Inventive Principle:

Principle #10Preliminary action

2Reliability

If larger keys are used to meet evolving security standards, then security against factorization and discrete logarithm problems is improved, but processing time and hardware requirements increase

Engineering Contradiction:

Improvesecurity against cryptographic attacksVSAvoidprocessing speed

Core Design Contradiction:

ReliabilityVSProductivity

Solution Approach 1:

The cryptographic operations are segmented into two phases with different key sizes. The preparation phase uses a full-length first random key for secure key establishment, while the signature phase uses a shorter second random key for rapid processing, optimizing both security and speed.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent changes the key size parameter dynamically based on the operational phase. A larger key (first random key) is used during preparation for security, while a smaller key (second random key) is used during signature generation for performance, achieving parameter optimization.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS7912216B2Elliptic curve cryptosystem optimization using two phase key generation

Publication Date: 2011.03.22 THALES DIS CPL USA INC

AI summary

A computer-implemented method of generating an elliptic curve cryptosystem (ECC) signature includes the steps of: generating a first random key (k1) having n bits, where n is a natural number; calculating a first ECC point (V) from k1 and a base point; and storing k1 and V securely in a computer-readable medium. To digitally sign electronic data, the method further includes the steps of generating a second random key (k2), where k2 has fewer than n bits; calculating a second ECC point (Q) from V and k2; and digitally signing electronic data using Q.