Evaluating Resilience of Electricity Distribution Networks via A Modification of Generalized Benders Decomposition Method

This paper presents a computational approach to evaluate the resilience of electricity Distribution Networks (DNs) to cyber-physical failures. In our model, we consider an attacker who targets multiple DN components to maximize the loss of the DN operator. We consider two types of operator response: (i) Coordinated emergency response; (ii) Uncoordinated autonomous disconnects, which may lead to cascading failures. To evaluate resilience under response (i), we solve a Bilevel Mixed-Integer Second-Order Cone Program which is computationally challenging due to mixed-integer variables in the inner problem and non-convex constraints. Our solution approach is based on the Generalized Benders Decomposition method, which achieves a reasonable tradeoff between computational time and solution accuracy. Our approach involves modifying the Benders cut based on structural insights on power flow over radial DNs. We evaluate DN resilience under response (ii) by sequentially computing autonomous component disconnects due to operating bound violations resulting from the initial attack and the potential cascading failures. Our approach helps estimate the gain in resilience under response (i), relative to (ii)

Towards joint decoding of binary Tardos fingerprinting codes

The class of joint decoder of probabilistic fingerprinting codes is of utmost importance in theoretical papers to establish the concept of fingerprint capacity. However, no implementation supporting a large user base is known to date. This article presents an iterative decoder which is, as far as we are aware of, the first practical attempt towards joint decoding. The discriminative feature of the scores benefits on one hand from the side-information of previously accused users, and on the other hand, from recently introduced universal linear decoders for compound channels. Neither the code construction nor the decoder make precise assumptions about the collusion (size or strategy). The extension to incorporate soft outputs from the watermarking layer is straightforward. An extensive experimental work benchmarks the very good performance and offers a clear comparison with previous state-of-the-art decoders.Comment: submitted to IEEE Trans. on Information Forensics and Security. - typos corrected, one new plot, references added about ECC based fingerprinting code

A Bounded-Space Near-Optimal Key Enumeration Algorithm for Multi-Dimensional Side-Channel Attacks

Enumeration of cryptographic keys in order of likelihood based on side-channel leakages has a significant importance in cryptanalysis. Previous algorithms enumerate the keys in optimal order, however their space complexity is $\Omega(n^{d/2})$ when there are d subkeys and n candidate values per subkey. We propose a new key enumeration algorithm that has a space complexity bounded by $O(d^2 w+dn)$, when w is a design parameter, which allows the enumeration of many more keys without exceeding the available space. The trade-off is that the enumeration order is only near-optimal, with a bounded ratio between optimal and near-optimal ranks. Before presenting our algorithm we provide bounds on the guessing entropy of the full key in terms of the easy-to-compute guessing entropies of the individual subkeys. We use these results to quantify the near-optimality of our algorithm\u27s ranking, and to bound its guessing entropy. We evaluated our algorithm through extensive simulations. We show that our algorithm continues its near-optimal-order enumeration far beyond the rank at which the optimal algorithm fails due to insufficient memory, on realistic SCA scenarios. Our simulations utilize a new model of the true rank distribution, based on long tail Pareto distributions, that is validated by empirical data and may be of independent interest

Poly-Logarithmic Side Channel Rank Estimation via Exponential Sampling

Rank estimation is an important tool for a side-channel evaluations laboratories. It allows estimating the remaining security after an attack has been performed, quantified as the time complexity and the memory consumption required to brute force the key given the leakages as probability distributions over $d$ subkeys (usually key bytes). These estimations are particularly useful where the key is not reachable with exhaustive search. We propose ESrank, the first rank estimation algorithm that enjoys provable poly-logarithmic time- and space-complexity, which also achieves excellent practical performance. Our main idea is to use exponential sampling to drastically reduce the algorithm\u27s complexity. Importantly, ESrank is simple to build from scratch, and requires no algorithmic tools beyond a sorting function. After rigorously bounding the accuracy, time and space complexities, we evaluated the performance of ESrank on a real SCA data corpus, and compared it to the currently-best histogram-based algorithm. We show that ESrank gives excellent rank estimation (with roughly a 1-bit margin between lower and upper bounds), with a performance that is on-par with the Histogram algorithm: a run-time of under 1 second on a standard laptop using 6.5 MB RAM