On Verifying Information Extractors

Ministerio de Economía y Competitividad TIN2013-40848-

Extracting the Kolmogorov Complexity of Strings and Sequences from Sources with Limited Independence

An infinite binary sequence has randomness rate at least $\sigma$ if, for almost every $n$, the Kolmogorov complexity of its prefix of length $n$ is at least $\sigma n$. It is known that for every rational $\sigma \in (0,1)$, on one hand, there exists sequences with randomness rate $\sigma$ that can not be effectively transformed into a sequence with randomness rate higher than $\sigma$ and, on the other hand, any two independent sequences with randomness rate $\sigma$ can be transformed into a sequence with randomness rate higher than $\sigma$. We show that the latter result holds even if the two input sequences have linear dependency (which, informally speaking, means that all prefixes of length $n$ of the two sequences have in common a constant fraction of their information). The similar problem is studied for finite strings. It is shown that from any two strings with sufficiently large Kolmogorov complexity and sufficiently small dependence, one can effectively construct a string that is random even conditioned by any one of the input strings

Formal Verification of Security Protocol Implementations: A Survey

Automated formal verification of security protocols has been mostly focused on analyzing high-level abstract models which, however, are significantly different from real protocol implementations written in programming languages. Recently, some researchers have started investigating techniques that bring automated formal proofs closer to real implementations. This paper surveys these attempts, focusing on approaches that target the application code that implements protocol logic, rather than the libraries that implement cryptography. According to these approaches, libraries are assumed to correctly implement some models. The aim is to derive formal proofs that, under this assumption, give assurance about the application code that implements the protocol logic. The two main approaches of model extraction and code generation are presented, along with the main techniques adopted for each approac

New constructions of WOM codes using the Wozencraft ensemble

In this paper we give several new constructions of WOM codes. The novelty in our constructions is the use of the so called Wozencraft ensemble of linear codes. Specifically, we obtain the following results. We give an explicit construction of a two-write Write-Once-Memory (WOM for short) code that approaches capacity, over the binary alphabet. More formally, for every \epsilon>0, 0<p<1 and n =(1/\epsilon)^{O(1/p\epsilon)} we give a construction of a two-write WOM code of length n and capacity H(p)+1-p-\epsilon. Since the capacity of a two-write WOM code is max_p (H(p)+1-p), we get a code that is \epsilon-close to capacity. Furthermore, encoding and decoding can be done in time O(n^2.poly(log n)) and time O(n.poly(log n)), respectively, and in logarithmic space. We obtain a new encoding scheme for 3-write WOM codes over the binary alphabet. Our scheme achieves rate 1.809-\epsilon, when the block length is exp(1/\epsilon). This gives a better rate than what could be achieved using previous techniques. We highlight a connection to linear seeded extractors for bit-fixing sources. In particular we show that obtaining such an extractor with seed length O(log n) can lead to improved parameters for 2-write WOM codes. We then give an application of existing constructions of extractors to the problem of designing encoding schemes for memory with defects.Comment: 19 page