Introduction Random number generators (RNGs) are important to modern science and information technology. Project Objective q In this project, a new parallel random number generator that can run in parallel is purposed. The underlying algorithm that drives randomness is the ZUC algorithm. q NIST randomness test suite is invoked to test multiple aspects of random streams generated. ZUC Random Number Generator Zeyang Gao Earlham College Methodology ZUC algorithm is an encryption algorithm which has three logical layers. One can reassemble the keystream output to get new sets of inputs to feed the ZUC algorithm again and then pass them into a new process of ZUC algorithm so that it will generate random numbers in parallel. Results 50 random number streams generated by ZUC algorithm are tested by NIST and yield the following result under the test hypothesis: Discussions Performance Comparison Bar Chart SPRNG (Scalable library for Pseudo-Random Number Generation) is a library of pseudo random number generation algorithms developed in 1998. In this experiment, q Each algorithm needs to generate 10 million random numbers. q “–p” means the algorithm runs in parallel with two processors. ZUC random number generator is slightly slower than SPRNG, but it adds more randomness to the stream than SPRNG if tested against NIST. References [1] A. Rukhin et al., “A statistical test suite for random and pseudorandom number generators for statistical applications,” NIST Special Publication in Computer Security, pp. 800-822, 2001. [2] ETSI/SAGE Specification “Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128- EIA3.Document 2: 128-EEA3 and 128-EIA3 Specification version: 1.6,” 2011. [3] Michael Mascagni and Ashok Srinivasan. 2000. Algorithm 806: SPRNG: a scalable library for pseudorandom number generation. ACM Trans. Math. Softw. 26, 3 (September 2000), 436-461. With a significance level =0.01, all p-values are greater than . Thus there is not enough evidence to reject H 0 , which means ZUC random number generator produces reliable random streams that are random enough under NIST standards. Acknowledgments I would like to thank Charlie Peck from Earlham College for his inspiration during the topic development. I would also like to thank Dave Barbella and Ajit Chavan from Earlham College for their advice and help on my project. Test Hypothesis

ZUC Random Number Generator

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IntroductionRandom number generators (RNGs) are important to modern

science and information technology.

Project Objectiveq In this project, a new parallel random number generator that can

run in parallel is purposed. The underlying algorithm that drivesrandomness is the ZUC algorithm.

q NIST randomness test suite is invoked to test multiple aspects ofrandom streams generated.

ZUCRandomNumberGeneratorZeyangGaoEarlhamCollege

MethodologyZUC algorithm is an encryption algorithm which has three logical layers.

One can reassemble the keystream output to get new sets of inputs tofeed the ZUC algorithm again and then pass them into a new process ofZUC algorithm so that it will generate random numbers in parallel.

Results50 random number streams generated by ZUC algorithm are tested by

NIST and yield the following result under the test hypothesis:

DiscussionsPerformance Comparison Bar Chart

SPRNG (Scalable library for Pseudo-Random Number Generation) is a library of pseudo random number generation algorithms developed in 1998. In this experiment,

q Each algorithm needs to generate 10 million random numbers. q “–p” means the algorithm runs in parallel with two processors.

ZUC random number generator is slightly slower than SPRNG, but it adds more randomness to the stream than SPRNG if tested against NIST.

References[1] A. Rukhin et al., “A statistical test suite for random and

pseudorandom number generators for statistical applications,” NIST Special Publication in Computer Security, pp. 800-822, 2001.

[2] ETSI/SAGE Specification “Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3.Document 2: 128-EEA3 and 128-EIA3 Specification version: 1.6,” 2011.

[3] Michael Mascagni and Ashok Srinivasan. 2000. Algorithm 806: SPRNG: a scalable library for pseudorandom number generation. ACM Trans. Math. Softw. 26, 3 (September 2000), 436-461.

With a significance level 𝛂=0.01, all p-values are greater than 𝛂. Thus there is not enough evidence to reject H0, which means ZUC random number generator produces reliable random streams that are random enough under NIST standards.

AcknowledgmentsI would like to thank Charlie Peck from Earlham College for his

inspiration during the topic development. I would also like to thankDave Barbella and Ajit Chavan from Earlham College for theiradvice and help on my project.

Test Hypothesis