GPU随机数生成：Tiny Encryption Algorithm的应用

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"GPU Random Numbers via the Tiny Encryption Algorithm (2010)" 是一篇关于在图形处理器（GPU）上实现随机数生成的论文。该研究由Fahad Zafar、Marc Olano和Aaron Curtis在200y年发表于某期刊的第z期，讨论了随着GPU计算能力的提升，其在非图形应用中的角色日益增强，因此对GPU上的随机数生成器（RNG）提出了更高的需求。文章摘要指出，随机数在GPU的广泛应用中扮演着重要角色，包括但不限于渲染、科学计算以及各种通用和图形应用。理想的GPU RNG应具备以下特性： 1. 可重复性：为了测试和调试，随机数生成器需要能够产生可复现的序列。 2. 随机访问：在任何时候都能获取到任意位置的随机数，而不必依赖先前产生的数字。 3. 多个独立流：支持多个并行计算任务，每个任务都有各自的独立随机数流，以避免相互干扰。 4. 速度：GPU的高性能特性要求RNG能快速生成大量随机数。 5. 无统计偏差：生成的随机数应具有良好的统计均匀性，避免出现可检测到的统计偏差。论文作者假设并非所有算法都要求最高质量的随机数，因此一个好的GPU RNG应该提供速度与质量的折衷选择，用户可以根据具体需求调整，以获得快速但质量较低或慢速但质量较高的随机数。论文提出使用Tiny Encryption Algorithm（TEA）作为GPU伪随机数生成器的一种解决方案。TEA是一种轻量级的加密算法，以其相对简单的结构和较高的计算效率而知名。作者将他们的方法与前人的工作进行了比较，并提供了评估结果，以证明TEA在满足GPU随机数生成需求方面的有效性。通过这种方式，论文为GPU上的高效随机数生成提供了一种新途径，这对于那些依赖于随机性且对性能有严格要求的应用（如模拟、加密、物理计算等）至关重要。此外，通过提供可调整的质量和速度选项，该方法还允许开发者根据应用场景灵活地优化其随机数生成策略。

Volume xx (200y), Number z, pp. 1–9

GPU Random Numbers via the Tiny Encryption Algorithm

Fahad Zafar, Marc Olano, Aaron Curtis

University of Maryland, Baltimore County

Abstract

Random numbers are extensively used on the GPU. As more computation is ported to the GPU, it can no longer

be treated as rendering hardware alone. Random number generators (RNG) are expected to cater general purpose

and graphics applications alike. Such diversity adds to expected requirements of a RNG. A good GPU RNG should

be able to provide repeatability, random access, multiple independent streams, speed, and random numbers free

from detectable statistical bias. A speciﬁc application may require some if not all of the above characteristics at

one time. In particular, we hypothesize that not all algorithms need the highest-quality random numbers, so a good

GPU RNG should provide a speed quality tradeoff that can be tuned for fast low quality or slower high quality

random numbers.

We propose that the Tiny Encryption Algorithm satisﬁes all of the requirements of a good GPU Pseudo Random

Number Generator. We compare our technique against previous approaches, and present an evaluation using

standard randomness test suites as well as Perlin noise and a Monte-Carlo shadow algorithm. We show that the

quality of random number generation directly affects the quality of the noise produced, however, good quality

noise can still be produced with a lower quality random number generator.

Categories and Subject Descriptors (according to ACM CCS): G.3 [Probability and Statistics]: Random number

generation— I.3.7 [Computer Graphics]: Three-dimensional Graphics and Realism—Color, shading, shadowing,

and texture E.2 [Data Encryption]: —

Keywords: cryptographic hash, noise, shadows

1. Introduction

Random numbers have many uses in computer graphics,

from Monte-Carlo sampling for realistic image synthesis to

noise generation for artistic shader construction. The mod-

ern Graphics Processing Unit (GPU) is a high performance

programmable parallel processor. While many randomized

shading effects can be accomplished through textures, the

increasing bias of GPUs towards computation over texture

lookups, especially potentially uncorrelated texture lookups,

leads to a desire for more computational solutions.

In particular, generation of random numbers on the GPU

should not require valuable texture storage and texture band-

width. Since changes in random sampling can introduce

dancing or shimmering artifacts, we need the same ran-

dom numbers from the RNG given the same seed position

in space or on a surface. Additionally we require indepen-

dent parallel streams of random numbers. For some appli-

cations, these streams are per-GPU thread, while for oth-

ers they are based on either position in space or on the sur-

face, with a single GPU thread potentially pulling numbers

from several streams. For spatial streams, several threads

may access numbers from the same stream, and should get

the same results. The numbers should be statistically inde-

pendent within each stream and between streams. Multiple

calls should also not halt for some shared memory object

that maintains the state of the RNG.

This leads to a set of desired properties for GPU random

number generation: repeatability to avoid frame-to-frame

coherence artifacts, independent random streams and ran-

dom access within the stream for parallel consistency, ran-

dom numbers free from noticeable statistical bias, and gen-

erator speed. Like other authors, we ﬁnd a cryptographic

function satisﬁes all of these requirements [TW08]. By run-

ning a seed and possible sequence number through the cryp-

tographic function, we get repeatable, randomly accessible

parallel streams of random numbers. One of the primary

submitted to COMPUTER GRAPHICS Forum (5/2010).

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