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Error correction is an effective way to mitigate fault attacks in cryptographic hardware. It is also an effective solution to soft errors in deep sub-micron technologies. To this end, we present a systematic method for designing single error correcting (SEC) and double error detecting (DED) finite field (Galoisfield) multipliers over GF(2m). The detection and correction are done on-line. We use multiple...
We show how to prove (and disprove) theorems in the initial algebra of an equational variety by a simple extension of the Knuth-Bendix completion algorithm. This allows us to prove by purely equational reasoning theorems whose proof usually requires induction. We show applications of this method to proofs of programs computing over data structures, and to proofs of algebraic summation identities....
Trie structures are a convenient way of indexing files in which keys are specified by values of attributes. Records correspond to leaves in the trie. Retrieval proceeds by following a path from the root to a leaf, the choice of edges being determined by attribute values. The size of a trie for a file depends on the order in which attributes are tested. We show that determining minimal size tries is...
Let Σ be a finite alphabet, Σ* the free monoid generated by Σ and |x| the length of x ε Σ*. For any integer k ≥ 0, fk(x)(tk (x)) is x if |x| ≪ k+1, and it is the prefix (suffix) of x of length k, otherwise. Also let mk+1 (x) = {v|x = uvw and |v| = k+1}. For x,y ε Σ* define x ∼k+1y iff fk(x) = fk(y), tk(x) = tk(y) and mk+1(x) = mk+1 (y). The relation ∼k+1 is a congruence of finite index over Σ*. An...
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