Pseudo Randomness (in digital system) PRESENTED BY GROUP 8 SHU-YU HUANG, FONG-JHENG LIN

Outline  Pseudo randomness  Example: M-Sequence  Application  Summary

Pseudo randomness  True RNG (Random Number Generator) Physical Source Sensor, Converter Transformer Numbers Unpredictable Irreproducible coin, dice, human guess, your girlfriend/boyfriend/mom * The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, 3rd ed. by Donald E. Knuth. Reading, MA: Addison-Wesley, 1997

Pseudo randomness  True RNG (Random Number Generator) Physical Source Sensor, Converter Transformer Numbers Unpredictable Irreproducible quantum phenomena, radioactive decay * The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, 3rd ed. by Donald E. Knuth. Reading, MA: Addison-Wesley, 1997

Pseudo randomness  Pros & Cons of True RNG ProsCons No periodicitiesSlow UnpredictableIrreproducible no dependencies presentNot portable High level of securityCostly Need no algorithmCould be manipulated * RANDOM.ORG

Pseudo randomness  Story of Caesar * X(n)=X(n)+3 A->D B->E C->F ANDY->DQGB

Pseudo randomness  Pseudo RNG Seed Function, Algorithm Number Series * The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, 3rd ed. by Donald E. Knuth. Reading, MA: Addison-Wesley, 1997 ANDYDQGB X(n)=X(n)+3

Pseudo randomness  Pseudo RNG Seed Function, Algorithm Number Series Deterministic Periodic Reproducible testing set, simulation set, gaming parameters * The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, 3rd ed. by Donald E. Knuth. Reading, MA: Addison-Wesley, 1997 usually truly random ,312,231,123…

Pseudo randomness  Pseudo RNG True Random Number * The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, 3rd ed. by Donald E. Knuth. Reading, MA: Addison-Wesley, 1997 Number Pseudo Random Numbers

Pseudo randomness  True RNG vs Pseudo RNG (512*512 pixal) * True Pseudo

Pseudo randomness * RANDOM.ORG

Pseudo randomness * NIST (National Institute of Standards and Technology), A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. 2001

Pseudo randomness  Frequency test (for pseudorandom number with n bits) * K. M. Ramachandran, C. P. Tsokos, Mathematical Statistics with Applications, 1 st editionpublished by ELSEVIER, 2009

Pseudo randomness  Frequency test (for pseudorandom number with n bits) … … * NIST (National Institute of Standards and Technology), A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. 2001

Pseudo randomness  Frequency test (for pseudorandom number with n bits) * NIST (National Institute of Standards and Technology), A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications For computer

Example: M-Sequence  Maximum length sequence

Example: M-Sequence  Calculation of pi

Summary of Pseudorandom Variables  Pros:  Accelerates the generation of patterns  Generate the same results  Cons:  Could be deciphered  Periodic

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