The main problem in designing effective code obfuscation is to guarantee security. State of the art obfuscation techniques rely on an unproven concept of security, and therefore are not regarded as provably secure. In this paper, we undertake a theoretical investigation of code obfuscation security based on Kolmogorov complexity and algorithmic mutual information. We introduce a new definition of code obfuscation that requires the algorithmic mutual information between a code and its obfuscated version to be minimal, allowing for controlled amount of information to be leaked to an adversary. We argue that our definition avoids the impossibility results of Barak et al. and is more advantageous then obfuscation indistinguishability definition in the sense it is more intuitive, and is algorithmic rather than probabilistic.

A variant of public key encryption that promises efficiency gains due to batch processing is multi-recipient public key encryption (MR-PKE). Precisely, in MR-PKE, a dedicated encryption routine takes a vector of messages and a vector of public keys and outputs a vector of ciphertexts, where the latter can be decrypted individually, as in regular PKE. In this paper we revisit the established security notions of MR-PKE and the related primitive MR-KEM. We identify a subtle flaw in a security model by Bellare, Boldyreva, and Staddon, that also appears in later publications by different authors. We further observe that these security models rely on the knowledge-of-secret-key (KOSK) assumption---a requirement that is rarely met in practice. We resolve this situation by proposing strengthened security notions for MR-PKE and MR-KEMs, together with correspondingly secure yet highly efficient schemes. Importantly, our models abstain from restricting the set of considered adversaries in the way prior models did, and in particular do not require the KOSK setting. We prove our constructions secure assuming hardness of the static Diffie-Hellman problem, in the random oracle model.

Attribute-based encryption (ABE) has attracted considerable attention in the research community in recent years. It has a number of applications such as broadcast encryption and the cryptographic enforcement of access control policies. Existing instantiations of ABE make use of access structures encoded either as trees of Shamir threshold secret-sharing schemes or monotone span programs. In both cases, the appropriate computations for these schemes are interleaved with the standard operations for cryptographic pairings. Moreover, the resulting schemes are not particularly appropriate for access control policies. In this paper, therefore, we start by examining the representation of access control policies and investigate alternative secret-sharing schemes that could be used to enforce them. We develop new ABE schemes based on the Benaloh-Leichter scheme, which employs only elementary arithmetic operations, and then extend this to arbitrary linear secret-sharing schemes. We then compare the complexity of existing schemes with our scheme based on Benaloh-Leichter.

This paper addresses the scenario of multi-release anonymization of datasets. We consider dynamic datasets where data can be inserted and deleted, and view this scenario as a case where each release is a small subset of the dataset corresponding, for example, to the results of a query. Compared to multiple releases of the full database, this has the obvious advantage of faster anonymization. We present an algorithm for post-processing anonymized queries that prevents anonymity attacks using multiple released queries. This algorithm can be used with several distinct protection principles and anonymization algorithms, which makes it generic and flexible. We give an experimental evaluation of the algorithm and compare it to $m$-invariance both in terms of efficiency and data quality. To this end, we propose two data quality metrics based on Shannon's entropy, and show that they can be seen as a refinement of existing metrics.

Antunes, Fortnow, van Melkebeek and Vinodchandran captured the notion of non-random information by computational depth, the difference between the polynomial-time- bounded Kolmogorov complexity and traditional Kolmogorov complexity. We show unconditionally how to probabilistically find satisfying assignments for formulas that have at least one assignment of logarithmic depth. The converse holds under a standard hardness assumption though fails if BPP = FewP = EXP. We also show that assuming good pseudorandom generators one cannot increase the depth of a string efficiently.