Jason Teutsch

On the minimal pseudo-codewords of codes from finite geometries

In order to understand the performance of a code under maximum-likelihood (ML) decoding, it is crucial to know the minimal codewords. In the context of linear programming (LP) decoding, it turns out to be necessary to know the minimal pseudo-codewords. This paper studies the minimal codewords and minimal pseudo-codewords of some families of codes derived from projective and Euclidean planes. Although our numerical results are only for codes of very modest length, they suggest that these code families exhibit an interesting property. Namely, all minimal pseudo-codewords that are not multiples of a minimal codeword have an AWGNC pseudo-weight that is strictly larger than the minimum Hamming weight of the code. This observation has positive consequences not only for LP decoding but also for iterative decoding

Short lists for shortest descriptions in short time

Is it possible to find a shortest description for a binary string? The well-known answer is “no, Kolmogorov complexity is not computable.” Faced with this barrier, one might instead seek a short list of candidates which includes a laconic description. Remarkably such approximations exist. This paper presents an efficient algorithm which generates a polynomial-size list containing an optimal description for a given input string. Along the way, we employ expander graphs and randomness dispersers to obtain an Explicit Online Matching Theorem for bipartite graphs and a refinement of Muchnik’s Conditional Complexity Theorem. Our main result extends recent work by Bauwens, Mahklin, Vereshchagin, and Zimand.

When Cryptocurrencies Mine Their Own Business.

Bitcoin and hundreds of other cryptocurrencies employ a consensus protocol called Nakamoto consensus which rewards miners for maintaining a public blockchain. In this paper, we study the security of this protocol with respect to rational miners and show how a minority of the computation power can incentivize the rest of the network to accept a blockchain of the minority’s choice. By deviating from the mining protocol, a mining pool which controls at least 38.2% of the network’s total computational power can, with modest financial capacity, gain mining advantage over honest mining. Such an attack creates a longer valid blockchain by forking the honest blockchain, and the attacker’s blockchain need not disrupt any “legitimate” non-mining transactions present on the honest blockchain. By subverting the consensus protocol, the attacking pool can double-spend money or simply create a blockchain that pays mining rewards to the attacker’s pool. We show that our attacks are easy to encode in any Nakamoto-consensus-based cryptocurrency which supports a scripting language that is sufficiently expressive to encode its own mining puzzles.

Translating the Cantor set by a random real

We determine the constructive dimension of points in random translates of the Cantor set. The Cantor set “cancels randomness” in the sense that some of its members, when added to Martin-Lof random reals, identify a point with lower constructive dimension than the random itself. In particular, we find the Hausdorff dimension of the set of points in a Cantor set translate with a given constructive dimension. 1. Fractals and random reals We explore an essential interaction between algorithmic randomness, classical fractal geometry, and additive number theory. In this paper, we consider the dimension of the intersection of a given set with a translate of another given set. We shall concern ourselves not only with classical Hausdorff measures and dimension but also the effective analogs of these concepts. More specifically, let C denote the standard middle third Cantor set [7, 18], and for each number α let (1.1) E=α = {x : cdimH{x} = α} consist of all real numbers with constructive dimension α. We answer a question posed to us by Doug Hardin by proving the following theorem: Theorem 1.1. If 1− log 2/ log 3 ≤ α ≤ 1 and r is a Martin-Lof random real, then the Hausdorff dimension of (1.2) (C + r) ∩ E=α is α−(1− log 2/ log 3). Moreover the Hausdorff measure of this set in its dimension is positive. From this result we obtain a simple relation between the effective and classical Hausdorff dimensions of (1.2); the difference is exactly 1 minus the dimension of the Cantor set. We conclude that many points in the Cantor set additively cancel randomness. We discuss some of the notions involved in this paper. Intuitively, a real is “random” if it does not inherit any special properties by belonging to an effective null class. We say a number is Martin-Lof random [3, 13] if it “passes” all MartinLof tests. A Martin-Lof test is a uniformly computably enumerable (c.e.) sequence 2000 Mathematics Subject Classification. Primary 68Q30; Secondary 11K55, 28A78.

Index sets and universal numberings

This paper studies the Turing degrees of various properties defined for universal numberings, that is, for numberings which list all partial-recursive functions. In particular properties relating to the domain of the corresponding functions are investigated like the set DEQ of all pairs of indices of functions with the same domain, the set DMIN of all minimal indices of sets and DMIN^@? of all indices which are minimal with respect to equality of the domain modulo finitely many differences. A partial solution to a question of Schaefer is obtained by showing that for every universal numbering with the Kolmogorov property, the set DMIN^@? is Turing equivalent to the double jump of the halting problem. Furthermore, it is shown that the join of DEQ and the halting problem is Turing equivalent to the jump of the halting problem and that there are numberings for which DEQ itself has 1-generic Turing degree.

Transforming commodity security policies to enforce Clark-Wilson integrity

Modern distributed systems are composed from several off-the-shelf components, including operating systems, virtualization infrastructure, and application packages, upon which some custom application software (e.g., web application) is often deployed. While several commodity systems now include mandatory access control (MAC) enforcement to protect the individual components, the complexity of such MAC policies and the myriad of possible interactions among individual hosts in distributed systems makes it difficult to identify the attack paths available to adversaries. As a result, security practitioners react to vulnerabilities as adversaries uncover them, rather than proactively protecting the systems data integrity. In this paper, we develop a mostly-automated method to transform a set of commodity MAC policies into a system-wide policy that proactively protects system integrity, approximating the Clark-Wilson integrity model. The method uses the insights from the Clark-Wilson model, which requires integrity verification of security-critical data and mediation at program entrypoints, to extend existing MAC policies with the proactive mediation necessary to protect system integrity. We demonstrate the practicality of producing Clark-Wilson policies for distributed systems on a web application running on virtualized Ubuntu SELinux hosts, where our method finds: (1) that only 27 additional entrypoint mediators are sufficient to mediate the threats of remote adversaries over the entire distributed system and (2) and only 20 additional local threats require mediation to approximate Clark-Wilson integrity comprehensively. As a result, available security policies can be used as a foundation for proactive integrity protection from both local and remote threats.

Smart Contracts Make Bitcoin Mining Pools Vulnerable

Despite their incentive structure flaws, mining pools account for more than 95% of Bitcoin’s computation power. This paper introduces an attack against mining pools in which a malicious party pays pool members to withhold their solutions from their pool operator. We show that an adversary with a tiny amount of computing power and capital can execute this attack. Smart contracts enforce the malicious party’s payments, and therefore miners need neither trust the attacker’s intentions nor his ability to pay. Assuming pool members are rational, an adversary with a single mining ASIC can, in theory, destroy all big mining pools without losing any money (and even make some profit).

On Approximate Decidability of Minimal Programs

An index e in a numbering of partial-recursive functions is called minimal if every lesser index computes a different function from e. Since the 1960s, it has been known that, in any reasonable programming language, no effective procedure determines whether or not a given index is minimal. We investigate whether the task of determining minimal indices can be solved in an approximate sense. Our first question, regarding the set of minimal indices, is whether there exists an algorithm that can correctly label 1 out of k indices as either minimal or nonminimal. Our second question, regarding the function that computes minimal indices, is whether one can compute a short list of candidate indices that includes a minimal index for a given program. We give negative answers to both questions for the important case of numberings with linearly bounded translators.

Using security policies to automate placement of network intrusion prevention

System administrators frequently use Intrusion Detection and Prevention Systems (IDPS) and host security mechanisms, such as firewalls and mandatory access control, to protect their hosts from remote adversaries. The usual techniques for placing network monitoring and intrusion prevention apparatuses in the network do not account for host flows and fail to defend against vulnerabilities resulting from minor modifications to host configurations. Therefore, despite widespread use of these methods, the task of security remains largely reactive. In this paper, we propose an approach to automate a minimal mediation placement for network and host flows. We use Intrusion Prevention System (IPS) as a replacement for certain host mediations. Due to the large number of flows at the host level, we summarize information flows at the composite network level, using a conservative estimate of the host mediation. Our summary technique reduces the number of relevant network nodes in our example network by 80% and improves mediation placement speed by 87.5%. In this way, we effectively and efficiently compute network-wide defense placement for comprehensive security enforcement.

A Brief on Short Descriptions

We discuss research developments on the complexity of shortest programs since the turn of the millennium. In particular, we will delve into the phenomenon of list approximation: while its impossible to compute the shortest description for a given string, we can efficiently generate a short list of candidates which includes a (nearly) shortest description.