This research began as an investigation into post-quantum cryptography, and considering what steps people could take now to mitigate the risks of quantum computing to their security.

We reviewed the current state of the art for attacking cryptographic solutions. Some notable attacks include:

• LogJam Attack: Primes the RFCs were not large enough, allowing pre-computation to make encrypted traffic vulnerable.
• Exploitation of probabilistic tests: Papers showing the that the majority of cryptographic libraries can be given careful constructed composite numbers which will test as prime. 
• CurveBall: attacking the software implementation of the cryptographic library.

We see good practices in this area as using primes and encouraging standards where:

• The primes are as large as practical;
• The primes should not be specified by the protocols or listed in RFCs;
• The primes used for these purposes should be proved prime (ideally on-the-fly); and
• The algorithms and software should be as simple as possible and open source.

This talk will sketch the work to be presented at ANTS 2020. I look at an interesting representation of primes, Quadratic Iterations Graphs (QIG). I cover the properties of primes reflected in QIGs and focus on the cyclic nature of QIGs primes, and I will state the relevant proof from the paper. This offers a unified understandign of fast primality tests such as Proth's test, Procklington's test, Pepin's test, Lucas' test and Miller-Rabin. I conclude by showing how this is useful research towards our goals related to good practices in this area.

Speaker Bio

Dr Jonathan Oliver has been at Trend Micro for 14 years. His research has focused on a range of machine learning applications including ML for malware detection, the identification of ransomware outbreaks, BlackHole Exploit kit spam runs, and creating the antispam pattern. On the theoretical side, he invented TLSH a locality sensitive hash which has been recently adopted as part of the STIX standard. Prior to joining Trend Micro, Dr Oliver served as Chief Span Fighter and Director of Research at Mailfrontier; and as a data mining consultant in the Silicon Valley for organisations such as NASA and the FAA. He holds a doctorate in information theoretic approaches  to machine learning from Monash University, Melbourne.