Sequencing Chess

We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude that the state space consists of several pockets between which transitions are rare. Skilled players explore an even smaller subset of positions that populate some of these pockets only very sparsely. These results suggest that the usual measures to estimate both, the size of the state space and the size of the tree of legal moves, are not unique indicators of the complexity of the game, but that topological considerations are equally important

A Proof of Entropy Minimization for Outputs in Deletion Channels via Hidden Word Statistics

From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that of the uniform prior measures the amount of information about the channel input which is conveyed by the output of length $m$, and it is natural to ask for which outputs this is extremized. This question was posed in a previous work, where it was conjectured on the basis of experimental data that the entropy of the posterior is minimized and maximized by the constant strings $\texttt{000}\ldots$ and $\texttt{111}\ldots$ and the alternating strings $\texttt{0101}\ldots$ and $\texttt{1010}\ldots$ respectively. In the present work we confirm the minimization conjecture in the asymptotic limit using results from hidden word statistics. We show how the analytic-combinatorial methods of Flajolet, Szpankowski and Vall\'ee for dealing with the hidden pattern matching problem can be applied to resolve the case of fixed output length and $n\rightarrow\infty$, by obtaining estimates for the entropy in terms of the moments of the posterior distribution and establishing its minimization via a measure of autocorrelation.Comment: 11 pages, 2 figure

PakeMail: Authentication and Key Management in Decentralized Secure Email and Messaging via PAKE

We propose the use of password-authenticated key exchange (PAKE) for achieving and enhancing entity authentication (EA) and key management (KM) in the context of decentralized end-to-end encrypted email and secure messaging, i.e., without a public key infrastructure or a trusted third party. This not only simplifies the EA process by requiring users to share only a low-entropy secret such as a memorable word, but it also allows us to establish a high-entropy secret key. This approach enables a series of cryptographic enhancements and security properties, which are hard to achieve using out-of-band (OOB) authentication. We first study a few vulnerabilities in voice-based OOB authentication, in particular a combinatorial attack against lazy users, which we analyze in the context of a secure email solution. We then propose tackling public key authentication by solving the problem of secure equality test using PAKE and discuss various protocols and their properties. This method enables the automation of important KM tasks such as key renewal and future key pair authentications, reduces the impact of human errors and lends itself to the asynchronous nature of email and modern messaging. It also provides cryptographic enhancements including multi-device synchronization, and secure secret storage/retrieval, and paves the path for forward secrecy, deniability and post-quantum security.We also discuss the use of auditable PAKEs for mitigating a class of online guess and abort attacks in authentication protocols. We present an implementation of our proposal, called PakeMail, to demonstrate the feasibility of the core idea and discuss some of its cryptographic details, implemented features and efficiency aspects. We conclude with some design and security considerations, followed by future lines of work