International Association
for Cryptologic Research

XCB, a tweakable enciphering mode, is part of IEEE Std. 1619.2 for shared storage media. We show that all versions of XCB are not secure through three plaintext recovery attacks. A key observation is that XCB behaves like an LRW1-type tweakable block cipher for single-block messages, which lacks CCA security. The first attack targets one-block XCB, using three queries to recover the plaintext. The second one requires four queries to recover the plaintext that excludes one block. The last one requires seven queries to recover the full plaintext. The first attack applies to any scheme that follows the XCB structure, whereas the latter two attacks work on all versions of XCB, exploiting the separable property of the underlying universal hash function. To address these flaws, we propose the XCB* structure, an improved version of XCB that adds only two XOR operations. We prove that XCB* is STPRP-secure when using AXU hash functions, SPRPs, and a secure random-IV-based stream cipher.

DCT is a beyond-birthday-bound (BBB) deterministic authenticated encryption (DAE) mode proposed by Forler et al. in ACISP 2016, ensuring integrity by redundancy. The instantiation of DCT employs the BRW polynomial, which is more efficient than the usual polynomial in GCM by reducing half of the multiplication operations. However, we show that DCT suffers from a small stretch problem similar to GCM. When the stretch length τ is small, choosing a special m-block message, we can reduce the number of queries required by a successful forgery to O(2τ/m). We emphasize that this attack efficiently balances space and time complexity but does not contradict the security bounds of DCT. Finally, we propose an improved scheme named Robust DCT (RDCT) with a minor change to DCT, which improves the security when τ is small and makes it resist the above attack.