This lecture presents Euclidean algorithm, and then introduces Vigenère, Hill, permutation and stream ciphers. We define attack models for performing cryptanalysis on different ciphers, and show how statistical analysis of the English language can be used to cryptanalyze cryptosystems with large key spaces. Readings from Chapter 1 of D. Stinson. 1 The Euclidean Algorithm(s) Many of the crypto s...

Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, and ${rm Z}(£)$ its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by ${rm T}(G (£))$. It is the graph with all elements of £ as vertices, and for distinct $x, y in £$, the vertices $x$ and $y$ are adjacent if and only if $x vee y in {rm Z}(£)$. The basic properties of the ...

The density of NAND flash grows at the price of significantly reduced reliability. To enable the continued scaling of flash memory more fundamental changes are needed. In this paper, we show that existing flash is much more reliable by adopting the rank modulation (RM) scheme [2]. RM encodes data using the relative orders of memory cell voltages, which is inherently resilient to asymmetric erro...

In the optimization of canonical Reed-Muller (RM) circuits, RM polynomials with different polarities are usually derived directly from Boolean expressions. Time efficiency is thus not fully achieved because the information in finding RM expansion of one polarity is not utilized by others. We show in this paper that two fixed-polarity RM expansions that have the same number of variables and whos...

We have reported some type II restriction-modification (RM) gene complexes on plasmids resist displacement by an incompatible plasmid through postsegregational host killing. Such selfish behavior may have contributed to the spread and maintenance of RM systems. Here we analyze the role of regulatory genes (C), often found linked to RM gene complexes, in their interaction with the host and the o...