Volume 7, Issue 3

Abstract. There has been considerable recent interest in “cloud storage” wherein a user asks a server to store a large file. One issue is whether the user can verify that the server is actually storing the file, and typically a challenge-response protocol is employed to convince the user that the file is indeed being stored correctly. The security of these schemes is phrased in terms of an extractor which will recover or retrieve the file given any “proving algorithm” that has a sufficiently high success probability. This paper treats proof-of-retrievability schemes in the model of unconditional security, where an adversary has unlimited computational power. In this case retrievability of the file can be modelled as error-correction in a certain code. We provide a general analytical framework for such schemes that yields exact (non-asymptotic) reductions that precisely quantify conditions for extraction to succeed as a function of the success probability of a proving algorithm, and we apply this analysis to several archetypal schemes. In addition, we provide a new methodology for the analysis of keyed POR schemes in an unconditionally secure setting, and use it to prove the security of a modified version of a scheme due to Shacham and Waters [Lecture Notes in Comput. Sci. 5350, Springer (2008), 90–107] under a slightly restricted attack model, thus providing the first example of a keyed POR scheme with unconditional security. We also show how classical statistical techniques can be used to evaluate whether the responses of the prover are accurate enough to permit successful extraction. Finally, we prove a new lower bound on storage and communication complexity of POR schemes.

Abstract. It is well known that a congruence ax ≡ b (mod n ) has a solution if and only if , and, if the condition is satisfied, the number of incongruent solutions equals . In 2010, Alomair, Clark and Poovendran proved that the congruence ax ≡ b (mod n ) has a solution coprime to n if and only if , as an auxiliary result playing a key role in a problem related to an electronic signature. In this paper we provide a concise proof of this result, together with a closed formula for the number of incongruent solutions coprime to n as well. Moreover, a bound is presented for the probability that, for randomly chosen , this congruence possesses at least one solution coprime to n .

Abstract. HMAC is the most widely-deployed cryptographic-hash-function-based message authentication code. First, we describe a security issue that arises because of inconsistencies in the standards and the published literature regarding keylength. We prove a separation result between two versions of HMAC, which we denote and , the former being the real-world version standardized by Bellare et al. in 1997 and the latter being the version described in Bellare's proof of security in his Crypto 2006 paper. Second, we describe how (the FIPS version standardized by NIST), while provably secure (in the single-user setting), succumbs to a practical attack in the multi-user setting. Third, we describe a fundamental defect from a practice-oriented standpoint in Bellare's 2006 security result for HMAC, and show that because of this defect his proof gives a security guarantee that is of little value in practice. We give a new proof of NMAC security that gives a stronger result for NMAC and HMAC and we discuss why even this stronger result by itself fails to give convincing assurance of HMAC security.

Abstract. This paper presents a model for the generation of a MAC tag using a stream cipher. The input message is used indirectly to control segments of the keystream that form the MAC tag. Several recent proposals can be considered as instances of this general model, as they all perform message accumulation in this way. However, they use slightly different processes in the message preparation and finalisation phases. We examine the security of this model for different options and against different types of attack, and conclude that the indirect injection model can be used to generate MAC tags securely for certain combinations of options. Careful consideration is required at the design stage to avoid combinations of options that result in susceptibility to forgery attacks. Additionally, some implementations may be vulnerable to side-channel attacks if used in Authenticated Encryption (AE) algorithms. We give design recommendations to provide resistance to these attacks for proposals following this model.