This chapter examined NIST test results from the OTP prototype encoder. The out- put binary sequences from each chaos source were combined in different configura- tions, but the final solution was to take a binary digit from each chaos source and form dibits. Applying a VN algorithm to the dibits maximised the entropy in the fi- nal sequence which was then exported for randomness testing. Various randomness tests carried out on the prototype were discussed but the main test for randomness was the NIST suite of fifteen tests where each test had a certain length and parameter requirements, as discussed in 9.2.
A sequence of 157 Mbits from the prototype was divided into 1000 bits and tested using a NIST test executable program called ASSESS. This was repeated ten times and the data was exported to Excel, where the results were plotted to observe the uniformity of the p-values. Thus, the fifteen tests produced p-values (statistical probability bands of randomness) for short and large sequences and the uniformity of the p-values was consistent with very good randomness.
Another test was developed during the research to evaluate the entropy for the best Padé delay added to each chaos source. The delay value which maximised the entropy was found by varying the Padé potentiometer over a range of resistance values and observing the average of the analogue x-signal closest to the zero axis.
10 Conclusion and Future work
“Out of chaos comes order.” Friedrich Nietzsche10.1
Conclusions and Future Work
The thesis aims and objectives involved methods for answering the research ques- tion, “How can stored Cloud data be made unreadable using chaos encoding?”. The research commenced with a review of methods for creating random binary se- quences for encoding data locally by the client. The research question was finally answered by creating a prototype one-time pad (OTP) encoder which incorporated a novel application of an analogue Padé delay added to the two analogue chaos sources. Adding delays in this manner converted the third-order chaos sources to novel fourth-order hyper-chaos systems and produced binary sequences with greater entropy.
The VN algorithm applied to binary streams from each chaos source max- imised the entropy of the final OTP. Furthermore, the Lorenz and Chua chaos oscil- lators were seeded by a novel sampled electronic noise from a 433 MHz data receiver to provide the necessary keys with which to start the two chaos sources. This ini- tialising method ensured the chaos trajectories started from a random key each time they were generated and hence adversaries could not successfully cryptanalyse in- tercepted data. OTP encoding according to Vladimir Kotelnikov in 1941 and Claude Shannon in 1945, is a theoretically-perfect, and unbreakable system, if OTP rules are adhered to [Molotkov, 2006], [Sachkov, 2006].
Techniques using evolutionary computing for evolving noise-producing chaos-initialising functions from true noise were also investigated. Since noise is stochastic this is a highly speculative idea, nevertheless, evolved functions which, with some post-processing, produced pseudo-random binary sequences. More im- portantly, a prototype constructed from analogue circuits ensured the binary se- quences produced had an infinite cycle length, unlike the previous digital platform method. This alternative method used a true noise source to produce true random binary sequences and was more effective at securing sensitive data and classified the encoder as a true source of randomness.
Currently, the main objection to OTP encoding for localised encryption of data be- fore storing in the Cloud, concerns the distribution of the OTP between two par- ties, the so-called key-distribution problem (KDP). However, the research examined in this thesis proposed one-to-cloud specialised applications where this was not a problem because only the cloud client was involved with the encoding-decoding process.
A substantial part of the research applied the linear PSpice circuit simulator to exploit aspects of chaos for maximising the entropy of the OTP true random bit sequences (TRBS) for achieving true secrecy in the Cloud. This necessitated creat- ing new simulation parts, simulation tools and meters, for examining phenomenon such as bifurcation to ensure the encoder operated in the chaos region. However, in this region, many PSpice convergence problems occurred because of the nonlin- ear nature of chaos systems but a simple novel application of PSpice parts enabled a range of system parameters to be examined. Furthermore, a novel application of PSpice VECTOR1 parts allowed multiple digital signals to be recorded and exported from PSpice to a text file. This allowed the four chaos digital binary streams to form a single OTP which was encoded using modulo-two arithmetic with the data using a JavaScript application.
Data from thirty chaos systems was exported from PSpice and processed in software downloaded from the Internet to calculate the Lyapunov dimension. This metric was used as an indicator of the source entropy to select two novel modified delay Chua and Lorenz chaos oscillator for the alpha prototype constructed on a double-sided PCB using a cloud-based facility in China. The major benefit of build- ing a prototype was that extensive testing could be carried out on all fifteen tests of the internationally-accepted NIST tests for randomness. The encoder passed all the tests and produced excellent random OTP sequences, as is evidenced by the unifor- mity of the p-values histograms given in Chapter 9.