## 1 Introduction  
Deoxyribonucleic acid (DNA) cryptography is the most recent advancement in cryptographic approaches. The natural process of DNA synthesis or production is exploited to encrypt data and later decrypt it [1, 2]. DNA cryptography explains how DNA can be used as an information carrier and how the current science of biotechnology can transform plaintext to ciphertext. In addition, the primary aim of DNA cryptography is to provide greater secrecy than traditional cryptography by combining biological and computational properties [3]. DNA cryptography uses DNA computing, while DNA computing has several benefits, such as high parallelism, lower power consumption, and massive data storage. Based on these characteristics, DNA cryptography has a unique advantage in massively parallel data encryption applications, with less real-time demand, secure data storage, authentication, digital signature, and information hiding [1]. DNA cryptography transmits a message between a sender and a receiver such that an eavesdropper cannot comprehend it. A strong algorithm and strong key generation are needed to accomplish this task [4]. Numerous studies have been conducted on data security, particularly in DNA cryptography, to make data safe by encrypting it during transmission and using a specific key generation algorithm [5]. For example, the authors of [6] propose a key generation algorithm based on DNA cryptography and Linear Congruential Generator (LCG) sequences. The proposed algorithm uses unique biological characteristics and a pseudorandom generator to build a novel key generator. It was concluded that this algorithm only passed seven of the NIST tests. The authors of [7] generated a 128-bit key by combining DNA cryptography and the Hill cipher algorithm. They claimed that the proposed technique could make the system unbreakable and ensure a better and more secure cloud-distributed environment. The authors of [8] proposed hybrid methods combining DNA computing and mathematical division. The encryption and decryption are based on DNA computing; the key generation is based on mathematical division. Firstly, the initial key is a word with any length of characters. These characters are transformed into ASCII codes. Next, a random prime integer is triggered, greater than 255. Thirdly, each character's ASCII code is divided by the random prime number. These calculations produce the remainders. The same random prime number is divided by each character's ASCII code to obtain quotients. The final, newly generated key contains the random prime number, remainders, and quotients. The authors of [9] proposed a cipher algorithm using biological processes and mathematical operations. The DNA sequence of nucleotides known as DNA-OTP represents the generated OTP key. Initially, the message is taken as input. The length of the message is computed, and a DNA nucleotide sequence is randomly assigned accordingly. The annealing process then produces a double helix DNA-OTP key. The transcription process converts the key to the mRNA sequence in the next step. Finally, the translation process creates a protein key from the mRNA sequence. The output is tested through the NIST test, which passes 13 out of 15 NIST tests. Analyzing the techniques mentioned above, one may conclude that the techniques mentioned [6; 9] partially fulfil the NIST random test. The research in [9] revealed a linear operation and neglected the NIST random tests. The authors of [8] used the mathematical division technique, not purely DNA-based key generation. In this context, most research work utilizes machine-learning techniques [4; 10; 11] and does not strictly follow DNA properties. Second, the generated keys are not random and thus fail to meet all of the NIST security properties. A researcher in DNA computing [12; 13; 14] has leveraged DNA's biological features in information security techniques [15]. However, it is well understood that the lack of randomness in key generator logical methods or mathematical functions leads to cryptanalytic breaches.