Finite Field Polynomial Pseudo Random Bit Generation
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Solution Overview
Problem
Conventional Blum-Blum-Shub pseudo random number generators rely on large integers for security, which can be computationally expensive and limit the generation of pseudo random bits per cycle, restricting their cryptographic efficiency.
Innovation Solution
The method employs finite field polynomials to generate pseudo random bits, leveraging faster polynomial operations over GF(2) to produce cryptographic keys, enhancing the speed and efficiency of key generation compared to integer-based systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If large integers are used in conventional BBS pseudo random number generators, then security is improved, but computational cost increases and generation speed decreases
Solution Approach 1:
The patent changes the mathematical parameter from large integers to finite field polynomials. Specifically, it uses polynomials over GF(2) with coefficients in a finite field, which allows for more efficient computational operations while maintaining cryptographic security. This parameter transformation enables faster pseudo random number generation without sacrificing security.
Solution Approach 2:
The patent replaces the integer-based arithmetic system with a polynomial arithmetic system over finite fields. By substituting the conventional integer multiplication and modular arithmetic with polynomial operations in GF(2), the system achieves more efficient computation and faster generation speeds while preserving the cryptographic properties required for security.
2Reliability
If the size of n is increased in BBS generators, then security is improved, but the number of bits generated per cycle increases requiring larger computational operations
Solution Approach 1:
The patent changes from using large integer n to using polynomials over finite fields. This allows the system to generate pseudo random bits more efficiently by leveraging the algebraic structure of finite fields, reducing the computational complexity required for each generation operation while maintaining security through the difficulty of inverting polynomial operations.
3Productivity
If polynomial operations over GF(2) are used, then generation speed is improved, but the complexity of the system increases
Solution Approach 1:
The patent substitutes conventional integer-based cryptographic operations with polynomial operations over finite fields. This substitution, while introducing new mathematical concepts, enables significantly faster computation and pseudo random number generation by exploiting the efficient arithmetic properties of GF(2) and finite field polynomial multiplication.
Data Source
AI summary
Some embodiments of a method and an apparatus to generate pseudo random bits from polynomials have been presented. In one embodiment, a set of finite field polynomials is used to generate a series of pseudo random bits in one or more cycles. Then a cryptographic key is generated from the series of pseudo random bits.