Conditional Disclosure of Secrets: Amplification, Closure, Amortization, Lower-bounds, and Separations

In the \emph{conditional disclosure of secrets} problem (Gertner et al., J. Comput. Syst. Sci., 2000) Alice and Bob, who hold inputs $x$ and $y$ respectively, wish to release a common secret $s$ to Carol (who knows both $x$ and $y$) if only if the input $(x,y)$ satisfies some predefined predicate $f$. Alice and Bob are allowed to send a single message to Carol which may depend on their inputs and some joint randomness and the goal is to minimize the communication complexity while providing information-theoretic security. Following Gay, Kerenidis, and Wee (Crypto 2015), we study the communication complexity of CDS protocols and derive the following positive and negative results. 1. *Closure* A CDS for $f$ can be turned into a CDS for its complement $\bar{f}$ with only a minor blow-up in complexity. More generally, for a (possibly non-monotone) predicate $h$, we obtain a CDS for $h(f_1,\ldots,f_m)$ whose cost is essentially linear in the formula size of $h$ and polynomial in the CDS complexity of $f_i$. 2. *Amplification* It is possible to reduce the privacy and correctness error of a CDS from constant to $2^{-k}$ with a multiplicative overhead of $O(k)$. Moreover, this overhead can be amortized over $k$-bit secrets. 3. *Amortization* Every predicate $f$ over $n$-bit inputs admits a CDS for multi-bit secrets whose amortized communication complexity per secret bit grows linearly with the input length $n$ for sufficiently long secrets. In contrast, the best known upper-bound for single-bit secrets is exponential in $n$. 4. *Lower-bounds* There exists a (non-explicit) predicate $f$ over $n$-bit inputs for which any perfect (single-bit) CDS requires communication of at least $\Omega(n)$. This is an exponential improvement over the previously known $\Omega(\log n)$ lower-bound. 5. *Separations* There exists an (explicit) predicate whose CDS complexity is exponentially smaller than its randomized communication complexity. This matches a lower-bound of Gay et. al., and, combined with another result of theirs, yields an exponential separation between the communication complexity of linear CDS and non-linear CDS. This is the first provable gap between the communication complexity of linear CDS (which captures most known protocols) and non-linear CDS

Measuring Risk Attitudes Controlling for Personality Traits*

Abstract: This study measures risk attitudes using two paid experiments: the Holt and Laury (2002) procedure and a variation of the game show Deal or No Deal. The participants also completed a series of personality questionnaires developed in the psychology literature including the risk domains of Weber, Blais, and Betz (2002). As in previous studies risk attitudes vary within subjects across elicitation methods. However, this variation can be explained by individual personality traits. Specifically, subjects behave as though the Holt and Laury task is an investment decision while the Deal or No Deal task is a gambling decision

Justice: Greater Access, Lower Costs

Litigation imposes large costs on society; this justifies settlement considerations. In any case, access to justice is critical to socioeconomic development; as such, it needs to be balanced with litigation minimization. This study examines the tradeoff between litigation and access to justice and explicitly elucidates their relationship. In considering access issues, this study finds that the outcomes of policies that affect parties’ litigation decisions partially depart from those in the standard literature. For instance, increasing parties’ litigation costs does not necessarily promote settlement in the shadow of the court. Rather, effects depend on the elasticity of the demand for legal remedies. Furthermore, even while pushing litigation, enhancing access to justice is efficient as long as the claimant’s marginal propensity to litigate is smaller than the social opportunity-cost of access to justice. This finding offers further insight into the suitability of litigation subsidization through legal aid