Pseudorandom String Generator Using Dynamic Coefficient Regeneration
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Solution Overview
Problem
Current pseudorandom generators, such as those using linear feedback registers, require excessive computation resources and memory, making them unsuitable for integration into low-cost electronic systems like hardwired logic chips due to the large number of coefficients needed for multivariate quadratic polynomials, which hinders their industrial-scale application.
Innovation Solution
The generator regenerates coefficients on each iteration, using a small number of parameters to reduce memory size and maintains high-speed operation by limiting polynomials to second degree, employing a coefficient generator module like a linear or nonlinear shift register, and optimizing calculation order to minimize the number of factors calculated.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If coefficients are stored for multivariate quadratic polynomials in a pseudorandom generator, then security is improved, but memory size and device complexity increase excessively
Solution Approach 1:
The patent applies dynamics by transitioning from static coefficient storage to dynamic coefficient generation. Instead of storing all coefficients of multivariate quadratic polynomials in memory, the system regenerates coefficients on-demand during each iteration of the pseudorandom number generation process. This is achieved through a coefficient generation module that produces new coefficients based on the current state variables, reducing memory requirements while maintaining the security properties of the generator.
Solution Approach 2:
The patent changes the parameter approach by replacing fixed stored coefficients with dynamically generated coefficients. The coefficient generation module transforms the system from using static parameters (stored coefficients) to dynamic parameters (regenerated coefficients based on current state). This parameter transformation allows the system to maintain security through complex polynomial relationships while using minimal memory resources.
2Reliability
If coefficients are stored for multivariate quadratic polynomials, then security is improved, but device complexity and number of electronic gates increase
Solution Approach 1:
The system replaces static coefficient storage with dynamic coefficient generation, reducing the number of electronic gates required. Instead of implementing large memory arrays to store all coefficients, the patent uses a coefficient generation module that computes coefficients on-demand using a small number of state variables and logical operations. This dynamic approach significantly reduces device complexity while maintaining security.
Solution Approach 2:
The patent extracts the coefficient storage function from the main system, separating it into a dedicated coefficient generation module. This module generates coefficients externally based on current state variables, eliminating the need for large internal memory structures. By taking out the coefficient storage requirement and replacing it with a generation mechanism, the system reduces electronic gate requirements while preserving security properties.
3Device complexity
If a small number of state variables is used, then device complexity is reduced, but the speed of pseudorandom string generation decreases
Solution Approach 1:
The patent changes the parameter generation approach by using a small number of state variables that are updated efficiently in each iteration. The coefficient generation module computes new coefficients based on these few state variables using optimized operations. This parameter approach allows the system to maintain low device complexity while achieving high generation speed through efficient computation rather than relying on large state spaces.
Data Source
AI summary
The invention relates to a method of generating a pseudorandom string of terms belonging to a finite body K of cardinal q≧2 intended to be used in a cryptography procedure, said method comprising the iterative calculation of a system (Γ) of m polynomials with n variables belonging to the finite body K. According to the invention, the coefficients of these m polynomials are regenerated at each iteration. The invention also relates to pseudorandom string generator intended to implement this method.