Biblio

This paper analyzes the formalizations of information-theoretic security for the fundamental primitives in cryptography: symmetric-key encryption and key agreement. Revisiting the previous results, we can formalize information-theoretic security using different methods, by extending Shannon's perfect secrecy, by information-theoretic analogues of indistinguishability and semantic security, and by the frameworks for composability of protocols. We show the relationships among the security formalizations and obtain the following results. First, in the case of encryption, there are significant gaps among the formalizations, and a certain type of relaxed perfect secrecy or a variant of information-theoretic indistinguishability is the strongest notion. Second, in the case of key agreement, there are significant gaps among the formalizations, and a certain type of relaxed perfect secrecy is the strongest notion. In particular, in both encryption and key agreement, the formalization of composable security is not stronger than any other formalizations. Furthermore, as an application of the relationships in encryption and key agreement, we simultaneously derive a family of lower bounds on the size of secret keys and security quantities required under the above formalizations, which also implies the importance and usefulness of the relationships.

We determine the semantic security capacity for quantum wiretap channels. We extend methods for classical channels to quantum channels to demonstrate that a strongly secure code guarantees a semantically secure code with the same secrecy rate. Furthermore, we show how to transform a non-secure code into a semantically secure code by means of biregular irreducible functions (BRI functions). We analyze semantic security for classical-quantum channels and for quantum channels.

A distinguisher is employed by an adversary to explore the privacy property of a cryptographic primitive. If a cryptographic primitive is said to be private, there is no distinguisher algorithm that can be used by an adversary to distinguish the encodings generated by this primitive with non-negligible advantage. Recently, two privacy-preserving matrix transformations first proposed by Salinas et al. have been widely used to achieve the matrix-related verifiable (outsourced) computation in data protection. Salinas et al. proved that these transformations are private (in terms of indistinguishability). In this paper, we first propose the concept of a linear distinguisher and two constructions of the linear distinguisher algorithms. Then, we take those two matrix transformations (including Salinas et al.\$'\$s original work and Yu et al.\$'\$s modification) as example targets and analyze their privacy property when our linear distinguisher algorithms are employed by the adversaries. The results show that those transformations are not private even against passive eavesdropping.

We consider the problem of verifying the security of finitely many sessions of a protocol that tosses coins in addition to standard cryptographic primitives against a Dolev-Yao adversary. Two properties are investigated here - secrecy, which asks if no adversary interacting with a protocol P can determine a secret sec with probability textgreater 1 - p; and indistinguishability, which asks if the probability observing any sequence 0$øverline$ in P1 is the same as that of observing 0$øverline$ in P2, under the same adversary. Both secrecy and indistinguishability are known to be coNP-complete for non-randomized protocols. In contrast, we show that, for randomized protocols, secrecy and indistinguishability are both decidable in coNEXPTIME. We also prove a matching lower bound for the secrecy problem by reducing the non-satisfiability problem of monadic first order logic without equality.