Volume 12, Issue 4

We provide a new heuristic polynomial time algorithm that computes short paths between arbitrary pairs of vertices in Lubotzky–Philipps–Sarnak’s Ramanujan graphs. The paths returned by our algorithm are shorter by a factor approximately 16/7 compared to previous work, and they are close to optimal for vertices corresponding to diagonal matrices. Our results also lead to an improved cryptanalysis of the Charles–Goren–Lauter hash function.

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 the file given any “proving algorithm” that has a sufficiently high success probability. This forms the basis of proof-of-retrievability (PoR) systems. In this paper, we study multiple server PoR systems. We formalize security definitions for two possible scenarios: (i) A threshold of servers succeeds with high enough probability (worst case), and (ii) the average of the success probability of all the servers is above a threshold (average case). We also motivate the study of confidentiality of the outsourced message. We give MPoR schemes which are secure under both these security definitions and provide reasonable confidentiality guarantees even when there is no restriction on the computational power of the servers. We also show how classical statistical techniques previously used by us can be extended to evaluate whether the responses of the provers are accurate enough to permit successful extraction. We also look at one specific instantiation of our construction when instantiated with the unconditionally secure version of the Shacham–Waters scheme. This scheme gives reasonable security and privacy guarantee. We show that, in the multi-server setting with computationally unbounded provers, one can overcome the limitation that the verifier needs to store as much secret information as the provers.

Code-based cryptography is one of the main areas of interest for NIST’s Post-Quantum Cryptography Standardization call. In this paper, we introduce DAGS, a Key Encapsulation Mechanism (KEM) based on quasi-dyadic generalized Srivastava codes. The scheme is proved to be IND-CCA secure in both random oracle model and quantum random oracle model. We believe that DAGS will offer competitive performance, especially when compared with other existing code-based schemes, and represent a valid candidate for post-quantum standardization.

A block is an n -bit string, and a (possibly keyed) block-function is a non-linear mapping that maps one block to another, e.g., a block-cipher. In this paper, we consider various symmetric key primitives with ℓ{\ell} block inputs and raise the following question: what is the minimum number of block-function invocations required for a mode to be secure? We begin with encryption modes that generate ℓ′{\ell^{\prime}} block outputs and show that at least (ℓ+ℓ′-1){(\ell+\ell^{\prime}-1)} block-function invocations are necessary to achieve the PRF security. In presence of a nonce, the requirement of block-functions reduces to ℓ′{\ell^{\prime}} blocks only. If ℓ=ℓ′{\ell=\ell^{\prime}}, in order to achieve SPRP security, the mode requires at least 2⁢ℓ{2\ell} many block-function invocations. We next consider length preserving r -block (called chunk ) online encryption modes and show that, to achieve online PRP security, each chunk should have at least 2⁢r-1{2r-1} many and overall at least 2⁢r⁢ℓ-1{2r\ell-1} many block-functions for ℓ{\ell} many chunks. Moreover, we show that it can achieve online SPRP security if each chunk contains at least 2⁢r{2r} non-linear block-functions. We next analyze affine MAC modes and show that an integrity-secure affine MAC mode requires at least ℓ{\ell} many block-function invocations to process an ℓ{\ell} block message. Finally, we consider affine mode authenticated encryption and show that in order to achieve INT-RUP security or integrity security under a nonce-misuse scenario, either (i) the number of non-linear block-functions required to generate the ciphertext is more than ℓ{\ell} or (ii) the number of extra non-linear block-functions required to generate the tag depends on ℓ{\ell}.