There will be a CIRCA lunchtime seminar on 22nd Feb at 1pm in Theatre D of Maths.

Chris Brown and Victoria Ironmonger will speak.

**Chris’s Title:** Semi-Automatic Ladderisation: Improving Code Security through Rewriting and Dependent Types

**Chris’s Abstract:** Cyber attacks become more and more prevalent every day. An arms race is thus engaged between cyber attacks and cyber defences. One type of cyber attack is known as a side channel attack, where attackers exploit information leakage from the physical execution of a program, e.g. timing or power leakage, to uncover secret information, such as encryption keys or other sensitive data. There have been various attempts at addressing the problem of side-channel attacks, often relying on various measures to decrease the discernibility of several code variants or code paths. Most techniques require a high-degree of expertise by the developer, who often employs ad hoc, hand-crafted code-patching in an attempt to make it more secure. In this talk, we take a different approach: building on the idea of ladderisation, inspired by Montgomery Ladders. We present a semi-automatic tool-supported technique, aimed at the non-specialised developer, which rewrites (a class of) C programs into functionally (and even algorithmically) equivalent counterparts with improved security properties. Our rewriting mechanism provides refactorings that transform the source code into its ladderised equivalent, driven by an underlying verified rewrite system, based on dependent types. Our rewrite system automatically finds rewritings of C programs producing their equivalent ladderised counterparts for a subset of C. We demonstrate our ladder rewriting technique on a number of representative examples from the cryptographic domain, showing increased security thanks to the process.

**Victoria’s Title:** The atomicity problem for equivalence relations and other structures

**Victoria’s Abstract:** An *atomic* poset is one which cannot be expressed as a union of two proper subsets. Atomic sets are sometimes called *ideals*, and atomicity is equivalent to the joint embedding property. We look at posets where two combinatorial structures are related when one is a substructure of the other. Given such a poset, *avoidance sets* are subsets defined by their forbidden substructures. The atomicity problem asks whether it is decidable, given a finite set, whether its avoidance set is atomic. We will discuss the atomicity problem for various structures, finishing by solving it for equivalence relations under the non-consecutive order. In this, we show that an avoidance set is atomic if and only if each forbidden element has only one class size.