Random Number Generation System Selecting Discrete Gaussian Sampling Method
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Solution Overview
Problem
Existing methods for generating random numbers according to discrete Gaussian distribution on a multidimensional lattice face challenges with high memory cost due to the accumulation method and low computation efficiency due to the rejection sampling method, particularly when dealing with varying centers of one-dimensional discrete Gaussian distributions.
Innovation Solution
A random number generation system that selects between the accumulation method and rejection sampling method based on a uniform random number's probability value, using the accumulation method for values within a certain probability range and the rejection sampling method for higher values, thereby reducing memory and computation costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the accumulation method is used to generate random numbers according to discrete Gaussian distribution, then computation efficiency is improved, but memory cost increases significantly
Solution Approach 1:
The patent divides the discrete Gaussian distribution generation into two segments: (1) generate a random number according to a coarse discrete distribution with limited support (low memory requirement), and (2) adjust this random number to achieve the target discrete Gaussian distribution. This segmentation allows using a simplified distribution table that requires minimal memory while still achieving accurate Gaussian sampling through subsequent adjustment steps.
Solution Approach 2:
The patent changes the parameter representation by using a mixture model approach where the discrete Gaussian distribution is approximated as a combination of several discrete distributions with different variances and weights. This parameter transformation allows achieving accurate Gaussian sampling without storing the entire high-resolution Gaussian table, thereby reducing memory cost while maintaining computation efficiency.
2Quantity of substance
If the rejection sampling method is used to generate random numbers, then memory cost is reduced, but computation efficiency decreases
Solution Approach 1:
The patent performs preliminary action by pre-computing and storing only the essential parameters of discrete distributions (such as means, variances, and weights of mixture components) rather than the complete probability distribution table. This preliminary preparation enables efficient sampling without requiring large memory storage, achieving both low memory cost and high computation efficiency.
Solution Approach 2:
The patent introduces an intermediary discrete distribution that serves as a bridge between the uniform random number generator and the target discrete Gaussian distribution. This intermediary distribution has limited support requiring minimal memory and can be efficiently sampled, then transformed to achieve the final Gaussian distribution, thereby avoiding the inefficiency of direct rejection sampling while maintaining low memory usage.
3Adaptability or versatility
If discrete Gaussian distribution with varying centers is used on multidimensional lattice, then cryptographic functionality is improved, but both memory and computation costs increase
Solution Approach 1:
The patent develops a universal sampling framework that can handle discrete Gaussian distributions with any center and variance parameters using the same underlying algorithmic structure. By using a mixture model approach and preliminary parameter pre-computation, the system achieves cryptographic functionality with varying centers without proportionally increasing memory and computation costs, as the core algorithm remains efficient and reusable across different parameter settings.
Data Source
AI summary
A generation means 11 generates a uniform random number between 0 and a first probability, which is a probability of a stochastic variable becoming a value within a predetermined interval in a positive range in the first discrete distribution. When a uniform random number less than or equal to a second probability is generated, the second probability being a probability of the stochastic variable becoming a value within a predetermined interval in a second discrete distribution, which is a discrete Gaussian distribution on a one-dimensional lattice the center of which is the origin, the selection means 12 selects, as a random number generation method, an accumulation method in which a functional value defining the second discrete distribution is used. When a uniform random number greater than the second probability is generated, the selection means 12 selects a rejection sampling method as the random number generation method.