Post-Quantum Attribute-Based Verifiable Data Storage and Retrieval for Cloud Computing Environments

Cloud data storage and retrieval systems use attribute-based cryptographic primitives to obtain fine-grained access control, data-owner anonymity, and search-result verifiability without a trusted online authority. The schemes that achieve these properties together, most notably the Attribute-Based verifiable Data Storage and data Retrieval Scheme (ABDSRS), are built on bilinear pairings, whose underlying discrete-logarithm assumptions are broken by Shor’s algorithm. We present PQ-ABDSRS, a lattice-based construction that provides the same functional interface using only Learning with Errors (LWE) and Short Integer Solution (SIS) assumptions. The construction is modular: fine-grained access control is obtained from a lattice ciphertext-policy attribute-based encryption scheme for monotone disjunctive policies, keyword-policy search from a lattice key-policy attribute-based encryption scheme, and data-owner authentication from a lattice attribute-based signature, each used through a stated interface with stated security requirements. The pairing-bilinearity masking identity that ABDSRS uses for non-interactive verifiability has no lattice analogue, and we show that an additively homomorphic SIS commitment does not by itself authenticate an outsourced computation. We replace it with a SIS-based binding digest over the ciphertext components, bound into the data owner’s signature, together with a random-oracle preimage check on the search predicate. We state the decryption-error condition the composition requires and fix the modulus from it, and we prove IND-CPA confidentiality, EUF-CMA unforgeability, verifiability of the transformation step, signer privacy, and search-tag privacy in the classical random oracle model, collected in a single composition theorem that records every assumption and reduction loss. Two guarantees are deliberately narrow: verification of the search predicate holds per record only until that record’s first successful search, and the scheme provides no semantic keyword privacy, only the leakage profile we state explicitly. Parameters are derived subject to the worst-case LWE reduction condition as well as to concrete attack estimates from the lattice estimator. The resulting public parameters exceed ABDSRS’s by seven orders of magnitude and ciphertexts by three, and these figures are model-based lower bounds rather than complete serializations. We report the cost as the principal result: it is the measure of how far unstructured lattices are from reproducing this functionality. A structured-lattice variant is discussed as future work and is not claimed as an instantiated scheme.