Elliptic Curve Parameter Generation for Adaptable Security
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Solution Overview
Problem
The security of elliptic curve cryptography is threatened as computational capacity improves, making it necessary to quickly change the security level, which is challenging due to the fixed group order form used for high-speed pairing computations.
Innovation Solution
An apparatus that generates a prime number r suitable as a group order for an elliptic curve cryptographic processor, allowing for easy adjustment of security levels by utilizing a prime number generation unit, group order suitability judgment unit, and outputting a group order candidate, enabling high-speed pairing computations with adaptable security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If a fixed group order form is used to achieve high-speed pairing computations, then computational speed is improved, but the ability to easily change security levels deteriorates
Solution Approach 1:
The patent applies dynamics by making the group order adaptable rather than fixed. The cryptographic processor is designed to accept and process elliptic curve parameters with variable group orders, allowing the security level to be adjusted by changing the prime number r while maintaining the same high-speed computation architecture. This resolves the contradiction by enabling both speed and adaptability.
Solution Approach 2:
The patent applies parameter changes by allowing the group order parameter (prime number r) to be changed independently while keeping the computational architecture unchanged. The system can switch between different security levels by simply changing the cryptographic parameters (the prime number r) without requiring hardware modifications, thus maintaining high computation speed while achieving security level adjustability.
2Reliability
If the bit number of group order is increased to improve security, then security level is improved, but computational capacity requirements increase
Solution Approach 1:
The patent applies parameter changes by allowing flexible selection of the prime number r's bit length. The system can choose appropriate security levels by selecting different bit lengths for r based on the required security strength and available computational resources. This enables security to be adjusted without necessarily increasing computational capacity, as the parameter can be optimized for the specific application context.
Data Source
AI summary
A prime number generation unit 110 generates an integer r having a form suitable for fast elliptic curve pairing computation, by using a processing device (S302 to S303). The prime number generation unit 110 judges whether the integer r is a prime number or not, by using the processing device (S304). When the integer r is a prime number, the prime number generation unit 110 judges whether the prime number r is a group order capable of easily changing the level of security or not, by using the processing device (S305). Thereby, it is possible to generate an elliptic curve parameter which is settable to an elliptic curve cryptographic processor that performs elliptic curve pairing computation using an algorithm capable of performing fast computation even by using a processing device with low computational capacity and which is capable of easily changing the level of security.