Truncated Polynomial Ring One-Way Functions for Low Latency Cryptography
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Solution Overview
Problem
Conventional hash-based cryptographic systems experience high latency and processing loads due to the large number of hash cycles required for key generation, making them inefficient for use in mobile devices and other conventional computing systems.
Innovation Solution
The implementation of faster one-way functions using truncated polynomial rings, which reduce processor load and latency by requiring fewer computational cycles, while maintaining strong one-wayness and resistance to quantum computing attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional hash-based cryptographic functions are used for key generation, then strong encryption security is achieved, but high latency and processing load occur due to large number of hash cycles
Solution Approach 1:
The patent changes the fundamental parameter of the cryptographic function from conventional hashing to polynomial computation in truncated polynomial rings. This parameter change maintains cryptographic security through the hardness of polynomial factorization and related mathematical problems, while dramatically reducing the number of computational cycles needed for key generation, thereby resolving the latency issue.
Solution Approach 2:
The patent substitutes the mechanical hashing process with a mathematically equivalent but computationally more efficient polynomial-based system. Instead of repeatedly applying hash functions, the system uses polynomial operations in truncated polynomial rings, which have similar security properties but require fewer computational steps, thus reducing processing load and latency.
2Reliability
If conventional hash-based cryptographic functions are used for key generation, then strong encryption security is achieved, but excessive processor load occurs due to large number of hash cycles
Solution Approach 1:
The patent changes the computational parameter from iterative hashing to polynomial computation in truncated polynomial rings. This parameter change maintains the cryptographic security through the mathematical hardness of the underlying problems, while significantly reducing the computational complexity and processor load required for key generation operations.
Solution Approach 2:
The patent replaces the mechanical iterative hashing process with a more efficient polynomial-based cryptographic system. The substitution uses polynomial operations in truncated polynomial rings that achieve equivalent or superior security with fewer computational operations, thereby reducing processor load and improving productivity.
3Productivity
If polynomial computation with truncated polynomial rings is used, then processor load and latency are reduced, but implementation complexity increases
Solution Approach 1:
The patent segments the polynomial computation process into distinct modular operations: polynomial multiplication in truncated polynomial rings, key generation steps, and cryptographic function applications. This segmentation allows each component to be optimized and implemented independently, reducing overall implementation complexity while maintaining processing efficiency.
Solution Approach 2:
The patent creates a universal polynomial-based cryptographic framework that can serve multiple functions: key generation, encryption, and authentication. This multi-functional approach reduces implementation complexity by using a single mathematical foundation for multiple cryptographic operations, rather than requiring separate implementations for each function.
Data Source
AI summary
Methods for applying one-way functions for the purposes of cryptography and authentication are disclosed. The methods may be used in cryptographic systems relying on physical unclonable functions or the measurement of biological objects where repeated, sequential applications of one-way functions is required. Under the method, an input bitstream is received. The bitstream may optionally be expanded with a binary nonce and may be optionally transformed into a balanced ternary stream. A polynomial is generated having coefficients that are the values encoded in the stream. The polynomial is raised to a power to generate a second polynomial, and the coefficients of the second polynomial are read as an output stream.