First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in timeO(n3) fornqubits, which improves upon the previously known timeO(n6). Finally, the related problem of finite blocklength bounds for stabilizer codes and Pauli noise is studied. A finite blocklength refinement of the hashing bound is derived, and it is shown that no argument that uses guessing the error as a substitute for guessing the coset can lead to a significantly better achievability bound.

This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the syndrome measurements. In a certain subfamily of the general construction, the resulting codes are related to a natural generalization of classical Reed-Muller codes, and this leads to formulas for the distance of the quantum code as well as for the distance of the associated classical code that protects against errors in the syndrome. The paper gives a number of examples of codes with block size$2^{m}, m=3, {\dots },9$, and with syndrome measurements involving 2, 4 or 8 qubits. These include codes for which the distance exceeds the syndrome measurement weight, as well as codes which provide asymmetric protection against bit flip and phase flip errors.

We consider a setup in which the channel from Alice to Bob is less noisy than the channel from Eve to Bob. We show that there exist encoding and decoding which accomplish error correction and authentication simultaneously; that is, Bob is able to correctly decode a message coming from Alice and reject a message coming from Eve with high probability. The system does not require any secret key shared between Alice and Bob, provides information theoretic security, and can safely be composed with other protocols in an arbitrary context.

Security models for PAKE protocols aim to capture the desired security properties that such protocols must satisfy when executed in the presence of an active adversary. They are usually classified into i) indistinguishability-based (IND-based) or ii) simulation-based (SIM-based). The relation between these two security notions is unclear and mentioned as a gap in the literature. In this work, we prove that the SIM-based model of Boyko, Mackenzie and Patel [EUROCRYPT00] and the IND-based model of Abdalla, Fouque and Pointcheval are equivalent, in the sense that a protocol proven secure in one model is also secure in the other model.