81 research outputs found
Towards Verifying Nonlinear Integer Arithmetic
We eliminate a key roadblock to efficient verification of nonlinear integer
arithmetic using CDCL SAT solvers, by showing how to construct short resolution
proofs for many properties of the most widely used multiplier circuits. Such
short proofs were conjectured not to exist. More precisely, we give n^{O(1)}
size regular resolution proofs for arbitrary degree 2 identities on array,
diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs
for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result
Processing Succinct Matrices and Vectors
We study the complexity of algorithmic problems for matrices that are
represented by multi-terminal decision diagrams (MTDD). These are a variant of
ordered decision diagrams, where the terminal nodes are labeled with arbitrary
elements of a semiring (instead of 0 and 1). A simple example shows that the
product of two MTDD-represented matrices cannot be represented by an MTDD of
polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by
allowing componentwise symbolic addition of variables (of the same dimension)
in rules. It is shown that accessing an entry, equality checking, matrix
multiplication, and other basic matrix operations can be solved in polynomial
time for MTDD_+-represented matrices. On the other hand, testing whether the
determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the
same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing
a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of
CSR 201
Restricted branching programs and hardware verification
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 71-77).by Stephen John Ponzio.Ph.D
From Dust to Dawn: Practically Efficient Two-Party Secure Function Evaluation Protocols and their Modular Design
General two-party Secure Function Evaluation (SFE) allows mutually distrusting parties to (jointly) correctly compute \emph{any} 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. Two-party SFE can benefit almost any client-server interaction where privacy is required, such as privacy-preserving credit checking, medical classification, or face recognition. Today, SFE is subject of an immense amount of research in a variety of directions, and is not easy to navigate.
In this paper, we systematize the most \emph{practically important} work of the vast research knowledge on \emph{general} SFE. It turns out that the most efficient SFE protocols today are obtained by combining several basic techniques, such as garbled circuits and homomorphic encryption. We limit our detailed discussion to efficient general techniques. In particular, we do not discuss the details of currently \emph{practically inefficient} techniques, such as fully homomorphic encryption (although we elaborate on its practical relevance), nor do we cover \emph{specialized} techniques applicable only to small classes of functions.
As an important practical contribution, we present a framework in which today\u27s practically most efficient techniques for general SFE can be viewed as building blocks with well-defined interfaces that can be easily combined to establish a complete efficient solution. Further, our approach naturally lends itself to automated protocol generation (compilation). This is evidenced by the implementation of (parts of) our framework in the TASTY SFE compiler (introduced at ACM CCS 2010).
In sum, our work is positioned as a comprehensive guide in state-of-the-art SFE, with the additional goal of extracting, systematizing and unifying the most relevant and promising general techniques from among the mass of SFE knowledge. We hope this guide would help developers of SFE libraries and privacy-preserving protocols in selecting the most efficient SFE components available today
Formal verification: further complexity issues and applications
Prof. Giacomo Cioffi (Università di Roma "La Sapienza"), Prof. Fabio Panzieri (Università di Bologna), Dott.ssa Carla Limongelli (Università di Roma Tre)
Probabilistic representation and manipulation of Boolean functions using free Boolean diagrams
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (p. 145-149).by Amelia Huimin Shen.Ph.D
Efficiently representing the integer factorization problem using binary decision diagrams
Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log2(α)3 + 16.5log2(α)2 + 6log2(α) whereas previous work on the subject has only produced systems in which at least one of the polynomials has an ordered binary decision diagram representation with size exponential in log2(α). Using a different approach based on the Chinese remainder theorem we prove that for α ≥ 4 there is an alternative system of boolean equations whose solutions correspond to nontrivial factorizations of α such that there exists a C \u3e 0, independent of α, such that for any order σ on the variables in the system every function in the system can be represented by a σ-OBDD with size less than C log2(log2(α))2log2(α)4
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