Identity Based Encryption Using Pre-Computed Tate Pairing
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Solution Overview
Problem
Conventional identity-based elliptic curve cryptography is computationally intensive, making it unsuitable for devices with limited processing power, memory, and battery resources, such as mobile phones and sensor nodes, due to the need for complex Tate pairing operations.
Innovation Solution
A method where a central server generates and publishes pre-computed public parameters, including a Tate pairing value, allowing devices to encrypt data efficiently without performing intensive Tate pairing computations, using a friendly prime and torsion group prime order to facilitate quick cryptographic operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional identity-based elliptic curve cryptography is implemented with Tate pairing operations, then security is maintained, but computational resources and processing time are excessively consumed
Solution Approach 1:
The patent pre-computes the Tate pairing value during system initialization and stores it in a lookup table. When encryption is needed, the device simply retrieves the pre-computed value instead of performing the intensive Tate pairing operation in real-time, thus resolving the contradiction between maintaining security and achieving computational efficiency
Solution Approach 2:
The patent pre-determines friendly prime numbers and torsion group parameters during system setup. These pre-selected parameters optimize subsequent cryptographic operations, enabling devices with limited processing power to perform encryption efficiently while maintaining security standards
2Reliability
If Tate pairing operations are performed in real-time during encryption, then cryptographic security is ensured, but battery power and processing resources are depleted rapidly
Solution Approach 1:
The system performs the energy-intensive Tate pairing computation once during initialization and caches the result. All subsequent encryption operations use this cached value, reducing battery consumption from O(n) to O(1) where n is the number of encryption operations, thus resolving the energy efficiency contradiction while maintaining security
3Adaptability or versatility
If complex cryptographic computations are performed on devices with limited capabilities, then identity-based encryption can be implemented, but device complexity and resource requirements increase
Solution Approach 1:
The patent divides the cryptographic system into two parts: a setup phase that performs complex computations to generate pre-computed parameters, and an encryption phase that uses these parameters with simple operations. This segmentation allows lightweight devices to perform encryption without needing full cryptographic computation capabilities, resolving the contradiction between adaptability and device complexity
Solution Approach 2:
The patent introduces pre-computed parameters and lookup tables as intermediaries between the cryptographic protocol and the device hardware. These intermediaries absorb the computational complexity, allowing devices with limited processing power to implement identity-based encryption without directly performing complex Tate pairing operations
Data Source
AI summary
Method and system for identity based encryption are described. The method comprises obtaining public parameters and a public key set from a central server, where the public parameters include a friendly prime, a torsion group prime order, an super-singular elliptic curve, a first torsion group, a pre-computed Tate pairing value, a first elliptic curve point and a second elliptic curve point, and a distortion map, and where the pre-computed Tate pairing value is generated by the central server. Further, a receiver key set of elliptic curve points based on a receiver identity of a receiver is determined, where the receiver key set is a subset of the public key set. Further a receiver public key based on the receiver key set is computed. Further, the data is encrypted using the Tate pairing value and an encryption component, wherein the encryption component is computed based on the receiver public key set.