The original version of this article unfortunately contained some mistakes in Table 5.The results in Table 5 have been revised due to a miscalculation resulting from a technical issue in the software.The data generated in binary format was tested using a.bin file; however, the characters interpreted through ASCII codes were not in true binary form but rather treated as if they were generated in 8-bit format for entropy tests.As a result, it was determined that the obtained results were incorrect.The data was retested in the correct binary format.The updated table now reflects the correct values.The changes in Table 5 do not alter the main conclusion.In the Discussion of Table 5: The commentary related to Table 5 has been updated to reflect the corrected results to read: "The expected entropy value for Markov sequences is 0.5155.It is observed that Markov, t-Tuple, Lag Prediction, MultiMMC Prediction, and LZ78Y Prediction estimates give accurate results for Markov sequences.Table 5 reveals that other estimators tend to

Recently in Çeşmelioğlu, Meidl (Adv. Math. Commun.,18, 2024), the study of EA-equivalence and CCZ-equivalence for functions from {mathbb {V}}_n^{(p)} to the cyclic group {mathbb {Z}}_{p^k} has been initiated, where {mathbb {V}}_n^{(p)} denotes an n-dimensional vector space over {mathbb {F}}_p. Amongst others it has been shown that there exist functions from {mathbb {V}}_n^{(2)} to {mathbb {Z}}_4 which are CCZ-equivalent but not EA-equivalent. We extend these results to larger classes of functions from {mathbb {V}}_n^{(p)} to {mathbb {Z}}_{p^k}. We then discuss constructions of generalized bent functions from {mathbb {V}}_n^{(p)} to {mathbb {Z}}_{p^k}, p odd or p=2 and n is even, which correspond to large affine spaces of bent functions. In particular we employ versions of the direct sum, the semi-direct sum and of a recent secondary bent function construction in Wang et. al., (IEEE Trans. Inform. Theory69, 2023), to generate large affine spaces of bent functions. Finally we present a solution for constructing generalized bent functions from {mathbb {V}}_n^{(2)} to {mathbb {Z}}_{2^k}, n odd, from arbitrary generalized bent functions from {mathbb {V}}_{n-1}^{(2)} to {mathbb {Z}}_{2^{k-1}}.

We instantiate the hash-then-evaluate paradigm for pseudorandom functions (PRFs), textsf{PRF}(k,x):=textsf{wPRF}(k,textsf{RO}(x)), which builds a PRF textsf{PRF} from a weak PRF textsf{wPRF} via a public pre-processing random oracle textsf{RO}. In applications to secure multiparty computation (MPC), only the low-complexity textsf{wPRF} performs secret-depending operations. Our construction replaces textsf{RO} by f(k_textsf{H},textsf{elf}(x)), where f is a non-adaptive PRF and the key k_textsf{H} is public and thus known to the distinguishing adversary. We show that, perhaps surprisingly, several existing weak PRF candidates are plausibly also secure when their inputs are generated by f(k_textsf{H},textsf{elf}(.)). Firstly, analogous cryptanalysis applies (because pseudorandomness of f implies good statistical properties) and/or secondly an attack against the weak PRF with such pseudorandom inputs generated by f would imply surprising results such as key agreement from the hardness of the high-noise version of the Learning Parity with Noise (LPN) when implementing both textsf{wPRF} and f from this assumption. Our simple transformation of replacing textsf{RO}(cdot ) public pre-processing by f(k_textsf{H},textsf{elf}(x)) public pre-processing applies to the entire family of PRF-style functions. Specifically, we obtain results for oblivious PRFs, which are a core building block for password-based authenticated key exchange (PAKE) and private set intersection (PSI) protocols, and we also obtain results for pseudorandom correlation functions (PCF), which are a key tool for silent oblivious transfer (OT) extension.