Lower bounds for polynomials using geometric programming

We make use of a result of Hurwitz and Reznick, and a consequence of this result due to Fidalgo and Kovacec, to determine a new sufficient condition for a polynomial $f\in\mathbb{R}[X_1,...,X_n]$ of even degree to be a sum of squares. This result generalizes a result of Lasserre and a result of Fidalgo and Kovacec, and it also generalizes the improvements of these results given in [6]. We apply this result to obtain a new lower bound $f_{gp}$ for $f$, and we explain how $f_{gp}$ can be computed using geometric programming. The lower bound $f_{gp}$ is generally not as good as the lower bound $f_{sos}$ introduced by Lasserre and Parrilo and Sturmfels, which is computed using semidefinite programming, but a run time comparison shows that, in practice, the computation of $f_{gp}$ is much faster. The computation is simplest when the highest degree term of $f$ has the form $\sum_{i=1}^n a_iX_i^{2d}$, $a_i>0$, $i=1,...,n$. The lower bounds for $f$ established in [6] are obtained by evaluating the objective function of the geometric program at the appropriate feasible points

Security analysis of standard authentication and key agreement protocols utilising timestamps

We propose a generic modelling technique that can be used to extend existing frameworks for theoretical security analysis in order to capture the use of timestamps. We apply this technique to two of the most popular models adopted in literature (Bellare-Rogaway and Canetti-Krawczyk). We analyse previous results obtained using these models in light of the proposed extensions, and demonstrate their application to a new class of protocols. In the timed CK model we concentrate on modular design and analysis of protocols, and propose a more efficient timed authenticator relying on timestamps. The structure of this new authenticator implies that an authentication mechanism standardised in ISO-9798 is secure. Finally, we use our timed extension to the BR model to establish the security of an efficient ISO protocol for key transport and unilateral entity authentication

Forward-Security in Private-Key Cryptography

This paper provides a comprehensive treatment of forward-security in the context of sharedkey based cryptographic primitives, as a practical means to mitigate the damage caused by key-exposure. We provide definitions of security, practical proven-secure constructions, and applications for the main primitives in this area. We identify forward-secure pseudorandom bit generators as the central primitive, providing several constructions and then showing how forward-secure message authentication schemes and symmetric encryption schemes can be built based on standard schemes for these problems coupled with forward-secure pseudorandom bit generators. We then apply forward-secure message authentication schemes to the problem of maintaining secure access logs in the presence of break-ins

Algorithmic and Hardness Results for the Colorful Components Problems

In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph $G$ such that in the resulting graph $G'$ all the connected components are colorful (i.e., any two vertices of the same color belong to different connected components). We want $G'$ to optimize an objective function, the selection of this function being specific to each problem in the framework. We analyze three objective functions, and thus, three different problems, which are believed to be relevant for the biological applications: minimizing the number of singleton vertices, maximizing the number of edges in the transitive closure, and minimizing the number of connected components. Our main result is a polynomial time algorithm for the first problem. This result disproves the conjecture of Zheng et al. that the problem is $NP$-hard (assuming $P \neq NP$). Then, we show that the second problem is $APX$-hard, thus proving and strengthening the conjecture of Zheng et al. that the problem is $NP$-hard. Finally, we show that the third problem does not admit polynomial time approximation within a factor of $|V|^{1/14 - \epsilon}$ for any $\epsilon > 0$, assuming $P \neq NP$ (or within a factor of $|V|^{1/2 - \epsilon}$, assuming $ZPP \neq NP$).Comment: 18 pages, 3 figure

Efficient public-key cryptography with bounded leakage and tamper resilience

We revisit the question of constructing public-key encryption and signature schemes with security in the presence of bounded leakage and tampering memory attacks. For signatures we obtain the first construction in the standard model; for public-key encryption we obtain the first construction free of pairing (avoiding non-interactive zero-knowledge proofs). Our constructions are based on generic building blocks, and, as we show, also admit efficient instantiations under fairly standard number-theoretic assumptions. The model of bounded tamper resistance was recently put forward by Damgård et al. (Asiacrypt 2013) as an attractive path to achieve security against arbitrary memory tampering attacks without making hardware assumptions (such as the existence of a protected self-destruct or key-update mechanism), the only restriction being on the number of allowed tampering attempts (which is a parameter of the scheme). This allows to circumvent known impossibility results for unrestricted tampering (Gennaro et al., TCC 2010), while still being able to capture realistic tampering attack

A PCP Characterization of AM

We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP Theorem for NP. Similar characterizations have been given for higher levels of the Polynomial Hierarchy, and for PSPACE; however, we suggest that the result for AM might be of particular significance for attempts to derandomize this class. To test this notion, we pose some `Randomized Optimization Hypotheses' related to our stochastic CSPs that (in light of our result) would imply collapse results for AM. Unfortunately, the hypotheses appear over-strong, and we present evidence against them. In the process we show that, if some language in NP is hard-on-average against circuits of size 2^{Omega(n)}, then there exist hard-on-average optimization problems of a particularly elegant form. All our proofs use a powerful form of PCPs known as Probabilistically Checkable Proofs of Proximity, and demonstrate their versatility. We also use known results on randomness-efficient soundness- and hardness-amplification. In particular, we make essential use of the Impagliazzo-Wigderson generator; our analysis relies on a recent Chernoff-type theorem for expander walks.Comment: 18 page

Subverting Decryption in AEAD

This work introduces a new class of Algorithm Substitution Attack (ASA) on Symmetric Encryption Schemes. ASAs were introduced by Bellare, Paterson and Rogaway in light of revelations concerning mass surveillance. An ASA replaces an encryption scheme with a subverted version that aims to reveal information to an adversary engaged in mass surveillance, while remaining undetected by users. Previous work posited that a particular class of AEAD scheme (satisfying certain correctness and uniqueness properties) is resilient against subversion. Many if not all real-world constructions – such as GCM, CCM and OCB – are members of this class. Our results stand in opposition to those prior results. We present a potent ASA that generically applies to any AEAD scheme, is undetectable in all previous frameworks and which achieves successful exfiltration of user keys. We give even more efficient non-generic attacks against a selection of AEAD implementations that are most used in practice. In contrast to prior work, our new class of attack targets the decryption algorithm rather than encryption. We argue that this attack represents an attractive opportunity for a mass surveillance adversary. Our work serves to refine the ASA model and contributes to a series of papers that raises awareness and understanding about what is possible with ASAs

Cryptographic Randomized Response Techniques

We develop cryptographically secure techniques to guarantee unconditional privacy for respondents to polls. Our constructions are efficient and practical, and are shown not to allow cheating respondents to affect the ``tally'' by more than their own vote -- which will be given the exact same weight as that of other respondents. We demonstrate solutions to this problem based on both traditional cryptographic techniques and quantum cryptography.Comment: 21 page

Securing Remote Access Inside Wireless Mesh Networks

Wireless mesh networks (WMNs) that are being increasingly deployed in communities and public places provide a relatively stable routing infrastructure and can be used for diverse carrier-managed services. As a particular example we consider the scenario where a mobile device initially registered for the use with one wireless network (its home network) moves to the area covered by another network inside the same mesh. The goal is to establish a secure access to the home network using the infrastructure of the mesh. Classical mechanisms such as VPNs can protect end-to-end communication between the mobile device and its home network while remaining transparent to the routing infrastructure. In WMNs this transparency can be misused for packet injection leading to the unnecessary consumption of the communication bandwidth. This may have negative impact on the cooperation of mesh routers which is essential for the connection establishment. In this paper we describe how to establish remote connections inside WMNs while guaranteeing secure end-to-end communication between the mobile device and its home network and secure transmission of the corresponding packets along the underlying multi-hop path. Our solution is a provably secure, yet lightweight and round-optimal remote network access protocol in which intermediate mesh routers are considered to be part of the security architecture. We also sketch some ideas on the practical realization of the protocol using known standards and mention extensions with regard to forward secrecy, anonymity and accounting

Non-interactive classical verification of quantum computation

In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. In this work, we show that this same task can in fact be performed non-interactively and in zero-knowledge. Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We begin by making the first message instance-independent and moving it to an offline setup phase. We then establish a parallel repetition theorem for the resulting three-message protocol, with an asymptotically optimal rate. This, in turn, enables an application of the Fiat-Shamir heuristic, eliminating the second message and giving a non-interactive protocol. Finally, we employ classical non-interactive zero-knowledge (NIZK) arguments and classical fully homomorphic encryption (FHE) to give a zero-knowledge variant of this construction. This yields the first purely classical NIZK argument system for QMA, a quantum analogue of NP. We establish the security of our protocols under standard assumptions in quantum-secure cryptography. Specifically, our protocols are secure in the Quantum Random Oracle Model, under the assumption that Learning with Errors is quantumly hard. The NIZK construction also requires circuit-private FHE.Comment: 37 page