Overview of this Presentation

1. Validation of Pseudo Random Numbers through Graphical AnalysisAndrew CronwrightSupervisor: Barry Irwin

2. Overview of this Presentation • Randomness Defined • PRNG’s Introduced • Application of PRNG’s • Focus of PRNG’s in this Project • ISN’s Introduced • Results • Hardware RNG • Conclusion

3. What is randomness? • A function or process not affected by any input or state • Independent of previous results • Example • Flipping an unbiased coin • Rolling die • Quantum effects

4. PRNG’s • Mathematical function • Deterministic by nature • Simulates true randomness • Produces “random” like output • Used in many application

5. Applications of PRNG’s • PRNG’s for different applications have different needs • Cryptography • TCP Initial Sequence Numbers • Physical Simulations • Games / Gambling (Lotto)

6. Cryptography • Secret key must be random • If not random, can be easily guessed • Made random by collecting entropy

7. Physical Simulations • Monte Carlo experiments require random numbers • Provided by PRNG

8. Initial Sequence Numbers • On the creation of a TCP connection • A unique sequence number is used • Used to identify packets belonging to a specific connection.

9. Initial Sequence Numbers, the problem • T, trusted host • C, client • X, nasty person • X can cause connections to be dropped • X can hijack connections and introduce malicious code

10. Initial Sequence Numbers, the solution • RFC 793 proposed linear method for ISN • New standards introduced after security issues ISN = M + F(localhostIP + localport + remotehost + remoteportIP) or ISN = M + R(t) or ISN = R(t)

11. The problem • Many computer systems need random numbers • Provided by a PRNG • PRNG’s can cause problems if not up to standard

12. Random Event Validation • Will use graphical methods to identify randomness • Use the NIST test suite to support findings • Investigate Initial Sequence Numbers (ISNs) • Build hardware RNG

13. A graphical view • Method of delayed coordinates plotted in a phase space • Convert 1-D to 3-D by: X[n] = s[n-2] – s[n-3] Y[n] = s[n-1] – s[n - 2] Z[n] = s[n] – s[n-1] • Higher dimensions are possible • Acts as a “comb”

14. Example

15. Lattice view X[n] = s[n] Y[n] = s[n-1] Z[n] = s[n-2] • This will highlight any lattice structure in the sequence

16. Example

17. Spherical view Θ[n] = 2 * PI * s[n-2] φ[n] = PI * s[n-1] r[n] = √( s[n] ) X[n] = r * Cos(θ) * Sin(φ) Y[n] = r * Sin(θ) * Sin(φ) Z[n] = r * Cos(φ) • Very similar to above method • Will also highlight dependencies in the data sequnce

18. Example

19. Colour – A higher dimension • Colour added using the HSV colour model • Assign first number in sequence a colour, and pass through the spectrum assigning colours to each element • Highlights whether sequence was created in a temporal manner

20. Results – Win XP

21. Win XP – SP1

22. Win XP – SP2

23. Cisco – IOS 12.1

24. Fedora Core 3

25. Hardware RNG

26. Hardware RNG - Results

27. Conclusion • PRNG’s are important, and should be carefully selected for an application • ISN’s should be implemented using a good quality PRNG • A hardware RNG is easy to implement, can be easily incorperated in PC’s hardware

28. Conclusion cont. • Provided a graphical method for testing random numbers • Easier and faster than statistical testing • Will show / identify attractors in data quickly • Size of data set to test?