Abstract. Goldreich (ECCC 2000) proposed a candidate one-way function construction which is parameterized by the choice of a small predicate (over d = O(1) variables) and of a bipartite expanding graph of right-degree d. The function is computed by labeling the n vertices on the left with the bits of the input, labeling each of the n vertices on the right with the value of the predicate applied to the neighbors, and outputting the n-bit string of labels of the vertices on the right.Inverting Goldreich's one-way function is equivalent to finding solutions to a certain constraint satisfaction problem (which easily reduces to SAT) having a "planted solution," and so the use of SAT solvers constitutes a natural class of attacks.We perform an experimental analysis using MiniSat, which is one of the best publicly available algorithms for SAT. Our experiment shows that the running time required to invert the function grows exponentially with the length of the input, and that such an attack becomes infeasible already with small input length (a few hundred bits).Motivated by these encouraging experiments, we initiate a rigorous study of the limitations of back-tracking based SAT solvers as attacks against Goldreich's function. Results by Alekhnovich, Hirsch and Itsykson imply that Goldreich's function is secure against "myopic" backtracking algorithms (an interesting subclass) if the 3-ary parity predicate P (x1, x2, x3) = x1 ⊕ x2 ⊕ x3 is used. One must, however, use non-linear predicates in the construction, which otherwise succumbs to a trivial attack via Gaussian elimination.We generalized the work of Alekhnovich et al. to handle a more general class of predicates, and we present a lower bound for the construction that uses the predicate P d (x1, . . . , x d ) := x1 ⊕x2 ⊕· · ·⊕x d−2 ⊕(x d−1 ∧x d ) and a random graph.

Did celebrity last longer in 1929, 1992 or 2009? We investigate the phenomenon of fame by mining a collection of news articles that spans the twentieth century, and also perform a side study on a collection of blog posts from the last 10 years. By analyzing mentions of personal names, we measure each person's time in the spotlight, using two simple metrics that evaluate, roughly, the duration of a single news story about a person, and the overall duration of public interest in a person. We watched the distribution evolve from 1895 to 2010, expecting to find significantly shortening fame durations, per the much popularly bemoaned shortening of society's attention spans and quickening of media's news cycles. Instead, we conclusively demonstrate that, through many decades of rapid technological and societal change, through the appearance of Twitter, communication satellites, and the Internet, fame durations did not decrease, neither for the typical case nor for the extremely famous, with the last statistically significant fame duration decreases coming in the early 20th century, perhaps from the spread of telegraphy and telephony. Furthermore, while median fame durations stayed persistently constant, for the most famous of the famous, as measured by either volume or duration of media attention, fame durations have actually trended gently upward since the 1940s, with statistically significant increases on 40-year timescales. Similar studies have been done with * This version supercedes the short version of this paper published in the proceedings of WWW 2012.† Work done while interning at Google. ‡ Work done while at Google Research much shorter timescales specifically in the context of information spreading on Twitter and similar social networking sites. To the best of our knowledge, this is the first massive scale study of this nature that spans over a century of archived data, thereby allowing us to track changes across decades.

No abstract