1 - 8 of 8 articles
Abstract. We extend results of (Proc. Lond. Math. Soc. 104 (2012), 486–512) and prove shortlex automaticity and regularity of geodesics in a family of Artin groups that includes all groups of large type but also allows some commuting pairs of generators.
Abstract. The generic-case approach to algorithmic problems was suggested by Myasnikov, Kapovich, Schupp and Shpilrain in 2003. This approach studies the behavior of an algorithm on “most” or “typical” inputs. The remaining inputs form the so-called black hole of the algorithm. In the present...
Abstract. We show that some problems in information security can be solved without using one-way functions. The latter are usually regarded as a central concept of cryptography, but the very existence of one-way functions depends on difficult conjectures in complexity theory, most notably on the...
Abstract. We construct a provably pseudo-free family of finite computational groups under the general integer factoring intractability assumption. This family has exponential size. But each element of a group in our pseudo-free family is represented by infinitely many bit strings.
Abstract. We present a new algorithm to find apartments in coset geometries. It permits to obtain some missing results in a paper by Buekenhout and Leemans. We compare the performance of our algorithm to the one given by Buekenhout and Leemans.
Abstract. In (Groups Complex. Cryptol. 3 (2011), 349–355) we showed that any hyperbolic limit group can be faithfully represented in . The proof was constructive in that given a fixed JSJ decomposition for the given limit group the representation can be constructed. The proof depended on showing...
Abstract. We offer a public key exchange protocol in the spirit of Diffie–Hellman, but we use (small) matrices over a group ring of a (small) symmetric group as the platform. This “nested structure” of the platform makes computation very efficient for legitimate parties. We discuss security of...
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