Directed Multicut with linearly ordered terminals

Motivated by an application in network security, we investigate the following "linear" case of Directed Mutlicut. Let $G$ be a directed graph which includes some distinguished vertices $t_1, \ldots, t_k$. What is the size of the smallest edge cut which eliminates all paths from $t_i$ to $t_j$ for all $i < j$? We show that this problem is fixed-parameter tractable when parametrized in the cutset size $p$ via an algorithm running in $O(4^p p n^4)$ time.Comment: 12 pages, 1 figur

Implementing a Unification Algorithm for Protocol Analysis with XOR

In this paper, we propose a unification algorithm for the theory $E$ which combines unification algorithms for E\_{\std} and E\_{\ACUN} (ACUN properties, like XOR) but compared to the more general combination methods uses specific properties of the equational theories for further optimizations. Our optimizations drastically reduce the number of non-deterministic choices, in particular those for variable identification and linear orderings. This is important for reducing both the runtime of the unification algorithm and the number of unifiers in the complete set of unifiers. We emphasize that obtaining a ``small'' set of unifiers is essential for the efficiency of the constraint solving procedure within which the unification algorithm is used. The method is implemented in the CL-Atse tool for security protocol analysis

Worst case QC-MDPC decoder for McEliece cryptosystem

McEliece encryption scheme which enjoys relatively small key sizes as well as a security reduction to hard problems of coding theory. Furthermore, it remains secure against a quantum adversary and is very well suited to low cost implementations on embedded devices. Decoding MDPC codes is achieved with the (iterative) bit flipping algorithm, as for LDPC codes. Variable time decoders might leak some information on the code structure (that is on the sparse parity check equations) and must be avoided. A constant time decoder is easy to emulate, but its running time depends on the worst case rather than on the average case. So far implementations were focused on minimizing the average cost. We show that the tuning of the algorithm is not the same to reduce the maximal number of iterations as for reducing the average cost. This provides some indications on how to engineer the QC-MDPC-McEliece scheme to resist a timing side-channel attack.Comment: 5 pages, conference ISIT 201

Optimizing Utility-Energy Efficiency for the Metaverse over Wireless Networks under Physical Layer Security

The Metaverse, an emerging digital space, is expected to offer various services mirroring the real world. Wireless communications for mobile Metaverse users should be tailored to meet the following user characteristics: 1) emphasizing application-specific perceptual utility instead of simply the transmission rate, 2) concerned with energy efficiency due to the limited device battery and energy intensiveness of some applications, and 3) caring about security as the applications may involve sensitive personal data. To this end, this paper incorporates application-specific utility, energy efficiency, and physical-layer security (PLS) into the studied optimization in a wireless network for the Metaverse. Specifically, after introducing utility-energy efficiency (UEE) to represent each Metaverse user's application-specific objective under PLS, we formulate an optimization to maximize the network's weighted sum-UEE by deciding users' transmission powers and communication bandwidths. The formulated problem belongs to the sum-of-ratios optimization, for which prior studies have demonstrated its difficulty. Nevertheless, our proposed algorithm 1) obtains the global optimum for the weighted sum-UEE optimization, via a transform to parametric convex optimization problems, 2) applies to any utility function which is concave, increasing, and twice differentiable, and 3) achieves a linear time complexity in the number of users (the optimal complexity in the order sense). Simulations confirm the superiority of our algorithm over other approaches. We explain that our technique for solving the sum-of-ratios optimization is applicable to other optimization problems in wireless networks and mobile computing

Compiling and securing cryptographic protocols

Protocol narrations are widely used in security as semi-formal notations to specify conversations between roles. We define a translation from a protocol narration to the sequences of operations to be performed by each role. Unlike previous works, we reduce this compilation process to well-known decision problems in formal protocol analysis. This allows one to define a natural notion of prudent translation and to reuse many known results from the literature in order to cover more crypto-primitives. In particular this work is the first one to show how to compile protocols parameterised by the properties of the available operations.Comment: A short version was submitted to IP

Flow Logic

Flow networks have attracted a lot of research in computer science. Indeed, many questions in numerous application areas can be reduced to questions about flow networks. Many of these applications would benefit from a framework in which one can formally reason about properties of flow networks that go beyond their maximal flow. We introduce Flow Logics: modal logics that treat flow functions as explicit first-order objects and enable the specification of rich properties of flow networks. The syntax of our logic BFL* (Branching Flow Logic) is similar to the syntax of the temporal logic CTL*, except that atomic assertions may be flow propositions, like $> \gamma$ or $\geq \gamma$, for $\gamma \in \mathbb{N}$, which refer to the value of the flow in a vertex, and that first-order quantification can be applied both to paths and to flow functions. We present an exhaustive study of the theoretical and practical aspects of BFL*, as well as extensions and fragments of it. Our extensions include flow quantifications that range over non-integral flow functions or over maximal flow functions, path quantification that ranges over paths along which non-zero flow travels, past operators, and first-order quantification of flow values. We focus on the model-checking problem and show that it is PSPACE-complete, as it is for CTL*. Handling of flow quantifiers, however, increases the complexity in terms of the network to ${\rm P}^{\rm NP}$, even for the LFL and BFL fragments, which are the flow-counterparts of LTL and CTL. We are still able to point to a useful fragment of BFL* for which the model-checking problem can be solved in polynomial time. Finally, we introduce and study the query-checking problem for BFL*, where under-specified BFL* formulas are used for network exploration

The problem with the SURF scheme

There is a serious problem with one of the assumptions made in the security proof of the SURF scheme. This problem turns out to be easy in the regime of parameters needed for the SURF scheme to work. We give afterwards the old version of the paper for the reader's convenience.Comment: Warning : we found a serious problem in the security proof of the SURF scheme. We explain this problem here and give the old version of the paper afterward

A decidable policy language for history-based transaction monitoring

Online trading invariably involves dealings between strangers, so it is important for one party to be able to judge objectively the trustworthiness of the other. In such a setting, the decision to trust a user may sensibly be based on that user's past behaviour. We introduce a specification language based on linear temporal logic for expressing a policy for categorising the behaviour patterns of a user depending on its transaction history. We also present an algorithm for checking whether the transaction history obeys the stated policy. To be useful in a real setting, such a language should allow one to express realistic policies which may involve parameter quantification and quantitative or statistical patterns. We introduce several extensions of linear temporal logic to cater for such needs: a restricted form of universal and existential quantification; arbitrary computable functions and relations in the term language; and a "counting" quantifier for counting how many times a formula holds in the past. We then show that model checking a transaction history against a policy, which we call the history-based transaction monitoring problem, is PSPACE-complete in the size of the policy formula and the length of the history. The problem becomes decidable in polynomial time when the policies are fixed. We also consider the problem of transaction monitoring in the case where not all the parameters of actions are observable. We formulate two such "partial observability" monitoring problems, and show their decidability under certain restrictions