# Special Issue on Cryptography and Its Applications in Information Security
###### Abstract  
The security of the security of  
In the field of security, four papers are presented. The first one suggests employing a homomorphic encryption (HE) scheme that can directly perform arithmetic operations on ciphertexts without decryption to protect the model parameters. Using the HE scheme, the proposed privacy-preserving federated learning (PPFL) algorithm enables a centralized server to aggregate encrypted local model parameters without decryption. Furthermore, the proposed algorithm allows each node to use a different HE private key in the same FL-based system using a distributed cryptosystem [1]. A second paper in this field proposes a new anomaly detection algorithm for the Intrusion Detection System (IDS), where a machine learning algorithm is applied to detect deviations from legitimate traffic, which may indicate an intrusion. It involves a novel approach based on the transformation of the network flow statistics to gray images on which the Gray-Level Co-occurrence Matrix (GLCM) is applied together with an entropy measure recently proposed in the literature--2D Dispersion Entropy. This approach is assessed using the recently public IDS data set CIC-IDS2017. The results show that it is competitive in comparison to other approaches proposed in the literature on the same data set [2]. The main objective of the third paper is the classification of the Strongly Asymmetric Public Key Agreement (SAPKA) algorithms. SAPKA is a class of key exchanges between [PERSON] and [PERSON] that was introduced in 2011. The greatest difference from the standard PKA algorithms is that [PERSON] constructs multiple public keys and [PERSON] uses one of these to calculate her public key and her secret shared key. Therefore, the number of public keys and calculation rules for each key differ for each user. Although algorithms with high security and computational efficiency exist in this class, the relation between the parameters of SAPKA and its security and computational efficiency has not yet been fully clarified. By attempting algorithm attacks, the authors found that certain parameters are more strongly related to security. On this basis, they construct concrete algorithms and a new subclass of SAPKA, in which the responsibility of maintaining security is significantly more associated with the secret parameters of [PERSON] than those of [PERSON] [3]. The last paper in security designs a secure chaos-based stream cipher (SCbSC) and evaluates its hardware implementation performance in terms of computational complexity and its security. The fundamental element of this system is the proposed secure pseudo-chaotic number generator (SPCNG). The architecture of the proposed SPCNG includes three first-order recursive filters, each containing a discrete chaotic map and a mixing technique using an internal pseudo-random number (PRN). The three discrete chaotic maps, namely, the 3D Chebyshev map (3D Ch), the 1D logistic map (L), and the 1D skew-tent map (S), are weakly coupled by a predefined coupling matrix M. The mixing technique combined with the weak coupling technique of the three chaotic maps allows the system to be protected against side-channel attacks (SCAs) [4]. Linked to the topic of this paper, two other papers analyze the performances of stream ciphers. In [5], the bit independence criterion, which was proposed to evaluate the security of the S-boxes used in block ciphers, is assessed and improved. This paper proposes an algorithm that extends this criterion to evaluate the degree of independence between the bits of inputs and outputs of the stream ciphers. The effectiveness of the algorithm is experimentally confirmed in two scenarios: random outputs independent of the input, in which it does not detect dependence; and in the RC4 ciphers, where it detects significant dependencies related to some known weaknesses. The complexity of the algorithm is estimated based on the number of inputs l, and the dimensions, n and m, of the inputs and outputs, respectively.