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- Melissa Chase, Alexander Healy, Anna Lysyanskaya, Tal Malkin, Leonid Reyzin
- Journal of Cryptology
- 2005

We introduce a new flavor of commitment schemes, which we call mercurial commitments. Informally, mercurial commitments are standard commitments that have been extended to allow for soft decommitment. Soft decommitments, on the one hand, are not binding but, on the other hand, cannot be in conflict with true decommitments. We then demonstrate that a… (More)

A d-dimensional framework is a graph and a map from its vertices to Ed . Such a framework is globally rigid if it is the only framework in Ed with the same graph and edge lengths, up to rigid motions. For which underlying graphs is a generic framework globally rigid? We answer this question by proving a conjecture by Connelly, that his sufficient condition… (More)

- Alexander Healy, Salil P. Vadhan, Emanuele Viola
- STOC
- 2004

We revisit the problem of hardness amplification in NP, as recently studied by O'Donnell (STOC '02). We prove that if NP has a balanced function <i>f</i> such that any circuit of size <i>s</i>(<i>n</i>) fails to compute <i>f</i> on a 1/poly(<i>n</i>) fraction of inputs, then NP has a function <i>f</i>′ such that any circuit of size… (More)

- Alexander Healy, Emanuele Viola
- STACS
- 2005

We study the complexity of arithmetic in finite fields of characteristic two, F2n . We concentrate on the following two problems: • Iterated Multiplication: Given α1, α2, . . . , αt ∈ F2n , compute α1 · α2 · · ·αt ∈ F2n . • Exponentiation: Given α ∈ F2n and a t-bit integer k, compute α k ∈ F2n . First, we consider the explicit realization of the field F2n… (More)

Program checking, program self-correcting and program self-testing were pioneered by [Blum and Kannan] and [Blum, Luby and Rubinfeld] in the mid eighties as a new way to gain confidence in software, by considering program correctness on an input by input basis rather than full program verification. Work in the field of program checking focused on designing,… (More)

We develop a general approach for improving the efficiency of a computationally bounded receiver interacting with a powerful and possibly malicious sender. The key idea we use is that of delegating some of the receiver's computation to the (potentially malicious) sender. This idea was recently introduced by Goldwasser et al. [14] in the area of program… (More)

- Alexander Healy
- computational complexity
- 2006

We construct a randomness-efficient averaging sampler that is computable by uniform constant-depth circuits with parity gates (i.e., in uniform AC 0[⊕]). Our sampler matches the parameters achieved by random walks on constant-degree expander graphs, allowing us to apply a variety expander-based techniques within NC 1. For example, we obtain the following… (More)

- Alexander Healy
- 2006

We construct a randomness-efficient averaging sampler that is computable by uniform constantdepth circuits with parity gates (i.e., in uniform AC0[⊕]). Our sampler matches the parameters achieved by random walks on constant-degree expander graphs, allowing us to apply a variety expander-based techniques within NC. For example, we obtain the following… (More)

We will develop the machinery of resultants and resolvent polynomials with the ultimate goal of understanding the so-called “resolvent method” for computing Galois groups over Q. Along the way, we will encounter tangential applications of these tools, such as the determination of the minimal polynomial of, say, the sum of two algebraic numbers using… (More)

- C Masson, D Biss, +11 authors Jonathan Simon
- 2006

this possibility (Fig. 1, A to C, and movie S4). This central feature of Western counterpoint is made possible by composers_ interest in the harmonic property of acoustic consonance. A chord with duplicate pitch classes is permutationally symmetrical (P-symmetrical) because there is some nontrivial permutation of its notes that is a trivial voice leading.… (More)