We show that the Rényi entropy implies artificial biases not warranted by the data and incorrect updating information due to the finite size of the data despite being additive. It is demonstrated that this is so because it does not conform to the system and subset independence axioms of Shore and Johnson [J. IEEE Trans. Inf. Theory 26, 26 (1980)]. We finally show that the escort averaged constraints do not remedy the situation.

The existence and exact form of the continuum expression of the discrete nonlogarithmic $q$-entropy is an important open problem in generalized thermostatistics, since its possible lack implies that nonlogarithmic $q$-entropy is irrelevant for the continuous classical systems. In this work, we show how the discrete nonlogarithmic $q$-entropy in fact converges in the continuous limit and the negative of the $q$-entropy with continuous variables is demonstrated to lead to the (Csiszár type) $q$-relative entropy just as the relation between the continuous Boltzmann-Gibbs expression and the Kullback-Leibler relative entropy. As a result, we conclude that there is no obstacle for the applicability of the $q$-entropy to the continuous classical physical systems.

We reply to the preceding Comment by Jizba and Korbel [Jizba and Korbel, Phys. Rev. E 100, 026101 (2019)] by first pointing out that the Schur concavity proposed by them falls short of identifying the correct intervals of normalization for the optimum probability distribution even though normalization is a necessary ingredient in the entropy maximization procedure. Second, their treatment of the subset independence axiom requires a modification of the Lagrange multipliers one begins with, thereby rendering the optimization less trustworthy. We also explicitly demonstrate that the Rényi entropy violates the subset independence axiom and compare it with the Shannon entropy. Third, the composition rule offered by Jizba and Korbel is shown to yield probability distributions even without a need for the entropy maximization procedure at the expense of creating artificial bias in the data.

It has been known for some time that the usual $q$-entropy $S_q^{\left(n\right)}$ cannot be shown to converge to the continuous case. In Phys. Rev. E 97, 012104 (2018), we have shown that the discrete $q$-entropy ${\tilde{S}}_q^{\left(n\right)}$ converges to the continuous case when the total number of states are properly taken into account in terms of a convergence factor. Ou and Abe [previous Comment, Phys. Rev. E 97, 066101 (2018)] noted that this form of the discrete $q$-entropy does not conform to the Shannon-Khinchin expandability axiom. As a reply, we note that the fulfillment or not of the expandability property by the discrete $q$-entropy strongly depends on the origin of the convergence factor, presenting an example in which ${\tilde{S}}_q^{\left(n\right)}$ is expandable.

Private integer comparison has been an essential computation function for many applications, including online auction, credential identification, data mining, and joint bidding. In the setting of two-party computation, two parties with private inputs (x and y) want to jointly compare them without revealing the value of those inputs to others (also known as the Millionaires’ problem) while the output should ensure correctness and preserve data privacy. The private inputs only can be revealed if they are equal, i.e., x = y. Many related works have been proposed to solve the integer comparison problem in various settings, focusing on different properties such as round and computation complexity. Most solutions decompose integers into bitwise representation and then securely evaluate the function in a Boolean circuit on encrypted bits. However, this type of solution is costly (especially for large integers) as each bit requires encryption and decryption. In this paper, we transform the private integer comparison into a block comparison problem. In particular, we employ a block vectorization mechanism to encode the private inputs into blocks. We show the security of our two-party protocol in the semi-honest model. Also, we implement the protocol to demonstrate its efficiency using block vectorization mechanism and homomorphic encryption. The experimental result proves that our proposed solution achieves high efficiency, particularly for large integer comparisons.