Avoidability index for binary patterns with reversal

For every pattern $p$ over the alphabet $\{x,y,x^R,y^R\}$, we specify the least $k$ such that $p$ is $k$-avoidable.Comment: 15 pages, 1 figur

Some properties of a Rudin-Shapiro-like sequence

We introduce the sequence $(i_n)_{n \geq 0}$ defined by $i_n = (-1)^{inv_2(n)}$, where $inv_2(n)$ denotes the number of inversions (i.e., occurrences of 10 as a scattered subsequence) in the binary representation of n. We show that this sequence has many similarities to the classical Rudin-Shapiro sequence. In particular, if S(N) denotes the N-th partial sum of the sequence $(i_n)_{n \geq 0}$, we show that $S(N) = G(\log_4 N)\sqrt{N}$, where G is a certain function that oscillates periodically between $\sqrt{3}/3$ and $\sqrt{2}$.Comment: 21 pages, 6 figure

Digital Signature Schemes Based on Hash Functions

Cryptographers and security experts around the world have been awakened to the reality that one day (potentially soon) large-scale quantum computers may be available. Most of the public-key cryptosystems employed today on the Internet, in both software and in hardware, are based on number-theoretic problems which are thought to be intractable on a classical (non-quantum) computer and hence are considered secure. The most popular such examples are the RSA encryption and signature schemes, and the Elliptic Curve Diffie-Hellman (ECDH) key-exchange protocol employed widely in the SSL/TLS protocols. However, these schemes offer essentially zero security against an adversary in possession of a large-scale quantum computer. Thus, there is an urgent need to develop, analyze and implement cryptosystems and algorithms that are secure against such adversaries. It is widely believed that cryptographic hash functions are naturally resilient to attacks by a quantum adversary, and thus, signature schemes have been developed whose security relies on this belief. The goal of this thesis is to give an overview of hash-based cryptography. We describe the most important hash-based signature schemes as well as the schemes and protocols used as subroutines within them. We give a juxtaposition between stateful and stateless signature schemes, discussing the pros and cons of both while including detailed examples. Furthermore, we detail serious flaws in the security proof for the WOTS-PRF signature scheme. This scheme had the feature that its security proof was based on minimal security assumptions, namely the pseudorandomness of the underlying function family. We explore how this flawed security argument affects the other signature schemes that utilize WOTS-PRF

On the security of the WOTS-PRF signature scheme

We identify a flaw in the security proof and a flaw in the concrete security analysis of the WOTS-PRF variant of the Winternitz one-time signature scheme, and discuss the implications to its concrete security

Aggregative Adherence and Intestinal Colonization by Enteroaggregative Escherichia coli Are Produced by Interactions among Multiple Surface Factors

ABSTRACT Enteroaggregative Escherichia coli (EAEC) bacteria are exceptional colonizers that are associated with diarrhea. The genome of EAEC strain 042, a diarrheal pathogen validated in a human challenge study, encodes multiple colonization factors. Notable among them are aggregative adherence fimbriae (AAF/II) and a secreted antiaggregation protein (Aap). Deletion of aap is known to increase adherence, autoaggregation, and biofilm formation, so it was proposed that Aap counteracts AAF/II-mediated interactions. We hypothesized that Aap sterically masks heat-resistant agglutinin 1 (Hra1), an integral outer membrane protein recently identified as an accessory colonization factor. We propose that this masking accounts for reduced in vivo colonization upon hra1 deletion and yet no colonization-associated phenotypes when hra1 is deleted in vitro. Using single and double mutants of hra1, aap, and the AAF/II structural protein gene aafA, we demonstrated that increased adherence in aap mutants occurs even when AAF/II proteins are genetically or chemically removed. Deletion of hra1 together with aap abolishes the hyperadherence phenotype, demonstrating that Aap indeed masks Hra1. The presence of all three colonization factors, however, is necessary for optimal colonization and for rapidly building stacked-brick patterns on slides and cultured monolayers, the signature EAEC phenotype. Altogether, our data demonstrate that Aap serves to mask nonstructural adhesins such as Hra1 and that optimal colonization by EAEC is mediated through interactions among multiple surface factors. IMPORTANCE Enteroaggregative Escherichia coli (EAEC) bacteria are exceptional colonizers of the human intestine and can cause diarrhea. Compared to other E. coli pathogens, little is known about the genes and pathogenic mechanisms that differentiate EAEC from harmless commensal E. coli. EAEC bacteria attach via multiple proteins and structures, including long appendages produced by assembling molecules of AafA and a short surface protein called Hra1. EAEC also secretes an antiadherence protein (Aap; also known as dispersin) which remains loosely attached to the cell surface. This report shows that dispersin covers Hra1 such that the adhesive properties of EAEC seen in the laboratory are largely produced by AafA structures. When the bacteria colonize worms, dispersin is sloughed off, or otherwise removed, such that Hra1-mediated adherence occurs. All three factors are required for optimal colonization, as well as to produce the signature EAEC stacked-brick adherence pattern. Interplay among multiple colonization factors may be an essential feature of exceptional colonizers