A Formalization of Polytime Functions

We present a deep embedding of Bellantoni and Cook's syntactic characterization of polytime functions. We prove formally that it is correct and complete with respect to the original characterization by Cobham that required a bound to be proved manually. Compared to the paper proof by Bellantoni and Cook, we have been careful in making our proof fully contructive so that we obtain more precise bounding polynomials and more efficient translations between the two characterizations. Another difference is that we consider functions on bitstrings instead of functions on positive integers. This latter change is motivated by the application of our formalization in the context of formal security proofs in cryptography. Based on our core formalization, we have started developing a library of polytime functions that can be reused to build more complex ones.Comment: 13 page

Order-Revealing Encryption and the Hardness of Private Learning

An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally efficient PAC learning from efficient $(\epsilon, \delta)$-differentially private PAC learning. That is, we construct a concept class that is efficiently PAC learnable, but for which every efficient learner fails to be differentially private. This answers a question of Kasiviswanathan et al. (FOCS '08, SIAM J. Comput. '11). To prove our result, we give a generic transformation from an order-revealing encryption scheme into one with strongly correct comparison, which enables the consistent comparison of ciphertexts that are not obtained as the valid encryption of any message. We believe this construction may be of independent interest.Comment: 28 page

Multi-dimensional key generation of ICMetrics for cloud computing

Despite the rapid expansion and uptake of cloud based services, lack of trust in the provenance of such services represents a significant inhibiting factor in the further expansion of such service. This paper explores an approach to assure trust and provenance in cloud based services via the generation of digital signatures using properties or features derived from their own construction and software behaviour. The resulting system removes the need for a server to store a private key in a typical Public/Private-Key Infrastructure for data sources. Rather, keys are generated at run-time by features obtained as service execution proceeds. In this paper we investigate several potential software features for suitability during the employment of a cloud service identification system. The generation of stable and unique digital identity from features in Cloud computing is challenging because of the unstable operation environments that implies the features employed are likely to vary under normal operating conditions. To address this, we introduce a multi-dimensional key generation technology which maps from multi-dimensional feature space directly to a key space. Subsequently, a smooth entropy algorithm is developed to evaluate the entropy of key space

Codes, Cryptography, and the McEliece Cryptosystem

Over the past several decades, technology has continued to develop at an incredible rate, and the importance of properly securing information has increased significantly. While a variety of encryption schemes currently exist for this purpose, a number of them rely on problems, such as integer factorization, that are not resistant to quantum algorithms. With the reality of quantum computers approaching, it is critical that a quantum-resistant method of protecting information is found. After developing the proper background, we evaluate the potential of the McEliece cryptosystem for use in the post-quantum era by examining families of algebraic geometry codes that allow for increased security. Finally, we develop a family of twisted Hermitian codes that meets the criteria set forth for security

The Random Oracle Methodology, Revisited

We take a critical look at the relationship between the security of cryptographic schemes in the Random Oracle Model, and the security of the schemes that result from implementing the random oracle by so called "cryptographic hash functions". The main result of this paper is a negative one: There exist signature and encryption schemes that are secure in the Random Oracle Model, but for which any implementation of the random oracle results in insecure schemes. In the process of devising the above schemes, we consider possible definitions for the notion of a "good implementation" of a random oracle, pointing out limitations and challenges.Comment: 31 page