The key derivation function (KDF) is crucial in cryptographic systems, aiming to derive an initial key source, which may lack even randomness or be partially known to attackers, and generate secure secret keys. The HMAC-based key derivation function (HKDF), built on HMAC, is claimed to have Pseudo-Random Bit Generator (PRBG) properties, though no formal proof exists in current literature. This paper conducts a comprehensive analysis and evaluation of the pseudo-randomness within the HKDF key derivation scheme, as specified in RFC 5869. We demonstrate that the HKDF scheme attains PRBG properties under the assumption that either the input salt or the Initial Keying Material (IKM) is random, and we further assume the underlying HMAC function is a Pseudo-Random Function (PRF). Additionally, we present results showcasing the pseudo-randomness in an extended scenario where HKDF is required to generate a large number of keys. Specifically, we perform various experimental evaluations of the randomness of the HKDF scheme based on statistical standards outlined in NIST SP 800-22. Finally, a sensitivity evaluation of HKDF is conducted, revealing that a change of 1 bit in the IKM input results in an approximate 50% change in the number of bits in the derived key (OKM). This outcome signifies the robust randomness and high sensitivity of the HKDF. Our findings not only offer novel proof confirming the pseudo-randomness of HKDF but also enhance the overall security of the algorithm.

Although block ciphers are widely used and are quite secure, there are still many types of attacks against components of block ciphers, and the Advanced Encryption Standard (AES) block cipher is no exception. To improve the security of AES, there have been many studies in the literature on methods of making this block cipher dynamic. There have been many works focused on the methods of making dynamic at the S-box and the MixColumn transformation of AES. In this paper, we propose a method to make dynamic at the Addroundkey transformation of AES using new key dependent XOR tables. We also propose a procedure to evaluate the randomness of the output of a block cipher and apply this procedure to evaluate the randomness of the modified AES block cipher using new XOR tables. The proposed dynamic method based on new XOR tables can help improve the security of the AES block cipher against many of today's strong attacks on block ciphers.

Block ciphers are a crucial type of cryptographic algorithm being used to ensure information security for many applications today. However, there are numerous potential active attacks on block ciphers, so the research and design of dynamic block ciphers to advance the security of block ciphers is a matter of concern today. Maximum distance separable (MDS) matrices are a crucial component of many block ciphers. Involutory MDS matrices are primarily selected because using an involutory matrix allows for both encryption and decryption operations to be performed using the identical circuitry, resulting in an equal implementation cost for both processes. In this article, we propose algorithms to generate 4 × 4 and 8 × 8 Hadamard involutory MDS matrices based on column and row permutations. Next, we propose an algorithm to create key-dependent involutory MDS matrices based on column and row permutation, scalar multiplication, and direct exponentiation. Then, we experimentally strengthen the dynamic AES block cipher based on the proposed algorithm, conduct security analysis, and evaluate the NIST statistical criteria for AES and the dynamic AES algorithm. The outcomes of our research could potentially enhance the robustness of the AES block cipher against numerous contemporary powerful attacks.