Searching for authors named "Alexander Russell" – sorted by Relevance.
34 documents found, showing 1 through 10.
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Necessary and Sufficient Conditions for Collision-Free Hashing
- …This paper determines an exact relationship between collision-free hash functions and other cryptographic primitives. Namely, it introduces a new concept, the pseudopermutation, and shows that the existence of collision-free hash functions is equivalent to the existence of claw-free pairs of pseudo-…
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Random cayley graphs are expanders: a simple proof of the alon-roichman theorem
- …We give a simple proof of the Alon–Roichman theorem, which asserts that the Cayley graph obtained by selecting�ÐÓ����elements, independently and uniformly at random, from a finite group�has expected second eigenvalue no more than�; here�is a constant that depends only on�. In particular, such a grap…
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A Note on the Asymptotics and Computational Complexity of Graph Distinguishability
- …A graph G is said to be d-distinguishable if there is a d-coloring of G which no non-trivial automorphism preserves. That is, ## : G#{1,...,d}, ## # Aut(G)\{id},#v,#(v) #= #(#(v)). It was conjectured that if |G| > |Aut(G)| and the Aut(G)actiononG has no singleton orbits, then G is 2-disti…
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Spectral Bounds on General Hard Core Predicates (Extended Abstract)
- …. A Boolean function b is a hard core predicate for a one-way function f if b is polynomial time computable but b(x) is dicult to predict from f(x). A general family of hard core predicates is a family of functions containing a hard core predicate for any one-way function. A seminal result of Goldre…
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The Complexity of Solving Equations over Finite Groups
- …We study the computational complexity of solving systems of equations over a finite group. An equation over a group G is an expression of the form w1 w2 wk = id where each w i is either a variable, an inverted variable, or group constant and id is the identity element of G. A solution …
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Quantum Walks on the Hypercube
- …Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the n-dimensional hypercube, one in discrete time and one in cont…
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Tight Results on Multiregister Fourier Sampling: Quantum Measurements for Graph Isomorphism Require
- …We establish a general method for proving bounds on the information that can be extracted via arbitrary entangled measurements on tensor products of hidden subgroup coset states. When applied to the symmetric group, the method yields an Ω(n log n) lower bound on the number of coset states over which…
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Quantum Computing and the Hunt for Hidden Symmetry
- …In 1994, Peter Shor gave e cient quantum algorithms for factoring integers and extracting discrete logarithms [20]. If we believe that nature will permit us to faithfully implement our current model of quantum computation, then these algorithms dramatically contradict the Strong Church-Turing thesis…
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A Note on Embedding Complete Graphs into Hypercubes
- …An embedding of K n into a hypercube is a mapping of the n vertices of K n to distinct vertices of the hypercube, and the associated cost is the sum over all pairs of (mapped) vertices of the Hamming distance between the vertices. Let f(n) denote the minimum cost over all embeddings of K n into a hy…
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Faster Algorithms for Optical Switch Configuration
- …All-optical networks using wavelength division multiplexing are increasingly coming to be regarded as the technology of choice for the next generation of wide-area backbone networks. These networks incorporate optical switches that employ the concept of Latin Routers [BH93] for assigning wavelengths…
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