arXiv subjects

Marten van Dijk

Publications and source records attributed to Marten van Dijk.

45 records · Page 3Linked to original sources

arXiv2018

SGD and Hogwild! Convergence Without the Bounded Gradients Assumption

Stochastic gradient descent (SGD) is the optimization algorithm of choice in many machine learning applications such as regularized empirical risk minimization and training deep neural networks. The classical convergence analysis of SGD is carried out under the assumption that the norm of the stochastic gradient is uniformly bounded. While this might hold for some loss functions, it is always violated for cases where the objective function is strongly convex. In (Bottou et al.,2016), a new analysis of convergence of SGD is performed under the assumption that stochastic gradients are bounded with respect to the true gradient norm. Here we show that for stochastic problems arising in machine learning such bound always holds; and we also propose an alternative convergence analysis of SGD with diminishing learning rate regime, which results in more relaxed conditions than those in (Bottou et al.,2016). We then move on the asynchronous parallel setting, and prove convergence of Hogwild! algorithm in the same regime, obtaining the first convergence results for this method in the case of diminished learning rate.

math.OC↗

arXiv2017

Revisiting Definitional Foundations of Oblivious RAM for Secure Processor Implementations

Oblivious RAM (ORAM) is a renowned technique to hide the access patterns of an application to an untrusted memory. According to the standard ORAM definition presented by Goldreich and Ostrovsky, two ORAM access sequences must be computationally indistinguishable if the lengths of these sequences are identically distributed. An artifact of this definition is that it does not apply to modern ORAM implementations adapted in current secure processors technology because of their arbitrary lengths of memory access sequences depending on programs' behaviors (their termination times). As a result, the ORAM definition does not directly apply; the theoretical foundations of ORAM do not clearly argue about the timing and termination channels. This paper conducts a first rigorous study of the standard Goldreich-Ostrovsky ORAM definition in view of modern practical ORAMs (e.g., Path ORAM) and demonstrates the gap between theoretical foundations and real implementations. A new ORAM formulation which clearly separates out termination channel leakage is proposed. It is shown how this definition implies the standard ORAM definition (for finite length input access sequences) and better fits the modern practical ORAM implementations. The proposed definition relaxes the constraints around the stash size and overflow probability for Path ORAM, and essentially transforms its security argument into a performance consideration problem. Finally, a `strong' ORAM formulation which clearly includes obfuscation of termination leakage is shown to imply our new ORAM formulation and applies to ORAM for outsourced disk storage. In this strong formulation constraints are not relaxed and the security argument for Path ORAM remains complex as one needs to prove that the stash overflows with negligible probability.

cs.CR↗

arXiv2017

Flat ORAM: A Simplified Write-Only Oblivious RAM Construction for Secure Processors

Oblivious RAM (ORAM) is a cryptographic primitive which obfuscates the access patterns to a storage thereby preventing privacy leakage. So far in the current literature, only `fully functional' ORAMs are widely studied which can protect, at a cost of considerable performance penalty, against the strong adversaries who can monitor all read and write operations. However, recent research has shown that information can still be leaked even if only the write access pattern (not reads) is visible to the adversary. For such weaker adversaries, a fully functional ORAM turns out to be an overkill causing unnecessary overheads. Instead, a simple `write-only' ORAM is sufficient, and, more interestingly, is preferred as it can offer far more performance and energy efficiency than a fully functional ORAM. In this work, we present Flat ORAM: an efficient write-only ORAM scheme which outperforms the closest existing write-only ORAM called HIVE. HIVE suffers from performance bottlenecks while managing the memory occupancy information vital for correctness of the protocol. Flat ORAM resolves these bottlenecks by introducing a simple idea of Occupancy Map (OccMap) which efficiently manages the memory occupancy information resulting in far better performance. Our simulation results show that, on average, Flat ORAM only incurs a moderate slowdown of $3\times$ over the insecure DRAM for memory intensive benchmarks among Splash2 and $1.6\times$ for SPEC06. Compared to HIVE, Flat ORAM offers $50\%$ performance gain on average and up to $80\%$ energy savings.

cs.AR↗

arXiv2017

Connecting the Dots: Privacy Leakage via Write-Access Patterns to the Main Memory

Data-dependent access patterns of an application to an untrusted storage system are notorious for leaking sensitive information about the user's data. Previous research has shown how an adversary capable of monitoring both read and write requests issued to the memory can correlate them with the application to learn its sensitive data. However, information leakage through only the write access patterns is less obvious and not well studied in the current literature. In this work, we demonstrate an actual attack on power-side-channel resistant Montgomery's ladder based modular exponentiation algorithm commonly used in public key cryptography. We infer the complete 512-bit secret exponent in $\sim3.5$ minutes by virtue of just the write access patterns of the algorithm to the main memory. In order to learn the victim algorithm's write access patterns under realistic settings, we exploit a compromised DMA device to take frequent snapshots of the application's address space, and then run a simple differential analysis on these snapshots to find the write access sequence. The attack has been shown on an Intel Core(TM) i7-4790 3.60GHz processor based system. We further discuss a possible attack on McEliece public-key cryptosystem that also exploits the write-access patterns to learn the secret key.

cs.CR↗

arXiv2017

Advancing the State-of-the-Art in Hardware Trojans Design

Electronic Design Automation (EDA) industry heavily reuses third party IP cores. These IP cores are vulnerable to insertion of Hardware Trojans (HTs) at design time by third party IP core providers or by malicious insiders in the design team. State of the art research has shown that existing HT detection techniques, which claim to detect all publicly available HT benchmarks, can still be defeated by carefully designing new sophisticated HTs. The reason being that these techniques consider the HT landscape to be limited only to the publicly known HT benchmarks, or other similar (simple) HTs. However the adversary is not limited to these HTs and may devise new HT design principles to bypass these countermeasures. In this paper, we discover certain crucial properties of HTs which lead to the definition of an exponentially large class of Deterministic Hardware Trojans $H_D$ that an adversary can (but is not limited to) design. The discovered properties serve as HT design principles, based on which we design a new HT called 'XOR-LFSR' and present it as a 'proof-of-concept' example from the class $H_D$. These design principles help us understand the tremendous ways an adversary has to design a HT, and show that the existing publicly known HT benchmarks are just the tip of the iceberg on this huge landscape. This work, therefore, stresses that instead of guaranteeing a certain (low) false negative rate for a small constant set of publicly known HTs, a rigorous HT detection tool should take into account these newly discovered HT design principles and hence guarantee the detection of an exponentially large class (exponential in number of wires in IP core) of HTs with negligible false negative rate.

cs.CR↗

arXiv2017

Intrinsically Reliable and Lightweight Physical Obfuscated Keys

Physical Obfuscated Keys (POKs) allow tamper-resistant storage of random keys based on physical disorder. The output bits of current POK designs need to be first corrected due to measurement noise and next de-correlated since the original output bits may not be i.i.d. (independent and identically distributed) and also public helper information for error correction necessarily correlates the corrected output bits.For this reason, current designs include an interface for error correction and/or output reinforcement, and privacy amplification for compressing the corrected output to a uniform random bit string. We propose two intrinsically reliable POK designs with only XOR circuitry for privacy amplification (without need for reliability enhancement) by exploiting variability of lithographic process and variability of granularity in phase change memory (PCM) materials. The two designs are demonstrated through experiments and simulations.

cs.CR↗

arXiv2014

Path ORAM: An Extremely Simple Oblivious RAM Protocol

We present Path ORAM, an extremely simple Oblivious RAM protocol with a small amount of client storage. Partly due to its simplicity, Path ORAM is the most practical ORAM scheme known to date with small client storage. We formally prove that Path ORAM has a O(log N) bandwidth cost for blocks of size B = Omega(log^2 N) bits. For such block sizes, Path ORAM is asymptotically better than the best known ORAM schemes with small client storage. Due to its practicality, Path ORAM has been adopted in the design of secure processors since its proposal.

cs.CR↗

arXiv2006

Knowledge Flow Analysis for Security Protocols

Knowledge flow analysis offers a simple and flexible way to find flaws in security protocols. A protocol is described by a collection of rules constraining the propagation of knowledge amongst principals. Because this characterization corresponds closely to informal descriptions of protocols, it allows a succinct and natural formalization; because it abstracts away message ordering, and handles communications between principals and applications of cryptographic primitives uniformly, it is readily represented in a standard logic. A generic framework in the Alloy modelling language is presented, and instantiated for two standard protocols, and a new key management scheme.

cs.CR↗

arXiv2006

A Generalized Two-Phase Analysis of Knowledge Flows in Security Protocols

We introduce knowledge flow analysis, a simple and flexible formalism for checking cryptographic protocols. Knowledge flows provide a uniform language for expressing the actions of principals, assump- tions about intruders, and the properties of cryptographic primitives. Our approach enables a generalized two-phase analysis: we extend the two-phase theory by identifying the necessary and sufficient proper- ties of a broad class of cryptographic primitives for which the theory holds. We also contribute a library of standard primitives and show that they satisfy our criteria.

cs.CR↗