Chapter
New Bounds on the OBDDSize of Integer Multiplication via Universal Hashing
Electronic Colloquium on Computational Complexity  ECCC 12/2000; 7(46):563574. DOI:10.1007/3540446931_49

Conference Proceeding: A Larger Lower Bound on the OBDD Complexity of the Most Significant Bit of Multiplication.
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ABSTRACT: Ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. The reachability problem, i.e., computing the set of nodes reachable from a predefined vertex s ∈ V in a digraph G = (V,E), is an important problem in computeraided design, hardware verification, and model checking. Sawitzki (2006) has presented exponential lower bounds on the space complexity of a restricted class of symbolic OBDDbased algorithms for the reachability problem. Here, these lower bounds are improved by presenting a larger lower bound on the OBDD complexity of the most significant bit of integer multiplication.LATIN 2010: Theoretical Informatics, 9th Latin American Symposium, Oaxaca, Mexico, April 1923, 2010. Proceedings; 01/2010  [show abstract] [hide abstract]
ABSTRACT: Integer multiplication as one of the basic arithmetic functions has been in the focus of several complexity theoretical investigations and ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. Only in 2008 the question whether the deterministic OBDD complexity of the most significant bit of integer multiplication is exponential has been answered affirmatively. Since probabilistic methods have turned out to be useful in almost all areas of computer science, one may ask whether randomization can help to represent the most significant bit of integer multiplication in smaller size. Here, it is proved that the randomized OBDD complexity is also exponential.Inf. Process. Lett. 01/2011; 111:151155.  [show abstract] [hide abstract]
ABSTRACT: Twoparty Secure Function Evaluation (SFE) al lows mutually distrusting parties to (jointly) correctly compute a function on their private input data, without revealing the inputs. SFE, properly designed, guarantees to satisfy the most stringent security requirements, even for interactive computation. Twoparty SFE can benefit almost any client server interaction where privacy is required, such as banking, TV, targeted advertisements, etc. Today, SFE is a subject of immense amount of research in a variety of directions, and is not easy to navigate. In this work, we systematize some of the vast SFE research knowledge. It turns out that the most efficient SFE protocols are obtained by combining several basic techniques, such as Garbled Circuit (GC) and computation under Homomorphic Encryption (HE). We show how these techniques can be viewed as building blocks with clean interfaces, which can be easily combined for a complete efficient solution. Further, our approach naturally lends itself to automated protocol generation (compilation). We believe, today, this approach is the best candidate for implementation and deployment. We consider passive and active cheating, and give exact computation and communication costs of the building blocks.IACR Cryptology ePrint Archive. 01/2010; 2010:79.
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