Next-Generation Block Ciphers: Achieving Superior Memory Efficiency and Cryptographic Robustness for IoT Devices

Abstract

Traditional cryptographic methods often need complex designs that require substantial memory and battery power, rendering them unsuitable for small handheld devices. As the prevalence of these devices continues to rise, there is a pressing need to develop smart, memory-efficient cryptographic protocols that provide both high speed and robust security. Current solutions, primarily dependent on dynamic permutations, fall short in terms of encryption and decryption speeds, the cryptographic strength, and the memory efficiency. Consequently, the evolution of lightweight cryptographic algorithms incorporating randomised substitution properties is imperative to meet the stringent security demands of handheld devices effectively. In this paper, we present an advanced design of lightweight block ciphers that enhances traditional dynamic permutations with innovative randomised substitutions. This design utilises straightforward randomized encryption methods such as XOR, nibble swap, count ones, and left shift. The cryptographic robustness of our proposed block cipher has been rigorously tested through several standardised statistical tests, as recommended by the National Institute of Standards and Technology (NIST). These evaluations confirm that our algorithm maintains strong cryptographic properties with randomised substitutions and outperforms existing models in several key aspects. Moreover, comparative assessments reveal that our algorithm achieves a throughput of 853.31 Kbps while consuming only 1510 bytes of memory and demonstrating over 60% avalanche properties, significantly outperforming other solutions in terms of CPU utilisation and memory consumption. These results underscore the efficacy of our approach in fulfilling the advanced security requirements of modern handheld devices.

1. Introduction

Lightweight cryptography has swiftly become the “matter of the moment”. The main reason behind this upsurge in interest is that it offers enhanced security for handheld devices. These small computing devices are increasing rapidly, and traditional cryptography techniques for Internet of Things (IoT) devices cannot fulfil their emerging security needs [1,2]. Therefore, lightweight cryptography has the potential to overcome such problems. In the related articles, the maximum number of block ciphers is primarily based on a light weight. However, they are deficient as a number of the algorithms are not dynamic in nature, like PRESENT [3], Piccolo [4], KATAN and KATANTAN [5], mCrypton [6], HIGHT [7], ITUbee [8], BORON [9], TEA [10], SIMON and SPECK [11], RECTANGLE [12] and TWINE [13]. Normally, those ciphers are characterised by either a Feistel-type shape or a Substitution Permutation Network (SPN) [14]. Comparative analysis of existing lightweight cryptosystems is demonstrated in Table 1.

The maximum of the lightweight block ciphers is organised on a SPN community structure [6,24,25,26]. Lightweight cryptography gives the solution for small computing devices like RFID, chip cards, tablets, and smartphones. The forthcoming challenge for lightweight devices is the time of execution. A set of rules is green if it needs less time for execution and makes use of much less space. By focusing on all the above-mentioned points, the algorithm of a lightweight block cipher is efficient and simple because it occupies a smaller area of memory [27]. Lightweight gadgets, including cards, RFIDs, and lots of smaller gadgets, are included now in lots of programs to make communication secure [14,28,29].

The IoT needs very small devices because its host comprises lightweight devices [28,30]. Many distinct kinds of algorithms are used for the safety of lightweight gadgets with three main functions: confidentiality, data integrity, and authentication. Lightweight cryptography is an extensive area of study that focuses on the length of data, CPU utilisation and memory space [4,15,31,32].

The main target of lightweight gadgets is to maintain a cryptographic set of rules that secures the tool in limited surroundings and focuses on the strength intake and memory space to focus on security [16,27,31]. The proposed method is designed to achieve the ideal security and effective speed of encryption and decryption. To make it efficient, it uses simpler functions such as XOR, Count Ones, Left Shift Operation, and Bit Swap.

The remainder of this paper is organised as follows: Section 2 presents a literature review and delineates the contributions of this study, providing a critical examination of previous works and highlighting the novel aspects of our research. Section 3 details the methodology employed in our research, along with a comprehensive description of the proposed block cipher. Section 4 presents and discusses the results of the proposed methodology, including a comparative analysis of prior efforts in the field. Section 5 is the discussion section. Finally, Section 6 concludes the study, summarizing the key findings and proposing directions for future research.

2. Literature Review and Contribution of the Study

2.1. Related Work

Multiple studies linked to lightweight encryption have been published in recent years and used different methods, but the key shortcomings are the speed of encryption decryption, the dynamicity of permutation and substitution operations, as well as the security [33,34]. This section discusses some of the end results of such studies. The encryption algorithm based on ADD, XOR, and ROTL (R-bit Left Rotation) presented by Alina [35,36] has a three-times higher performance than AES (Advanced Encryption Standard). The algorithm presented in [37] is based on ten rounds of encryption, but it consumes much time and resources, and it attains the avalanche criteria after the 4th round. This set of rules works with static substitution but with dynamic permutation. In statistics, the safety block symmetric cipher performs a critical function for security [37,38]. The lightweight crypto cipher has been used to curb energy consumption, and it also uses less memory in the device, although the algorithm’s speed is increased. But the threats of an algorithm are key to consider [34]. In both algorithms, Cypress-512 [17] takes 14 rounds to complete the encryption process, whilst in the case of Cypress-256, it takes ten rounds. However, after the 4th round of iteration, the avalanche effect is satisfied for encryption. The author concluded that Cypress’s set of rules perform better than the Kalyna and AES Block cipher [17,39].

Sehrawat presented a brand-new generation of block cipher; it is lightweight and has the label of “ultra-BRIGHT: A tiny and fast ultra-lightweight block cipher for IoT” [40,41]. The author additionally proposed resilience to one-of-a-kind key attacks. A few operations have been used, such as pre-key whitening, spherical diversifications, and Addition Rotation XOR (ARX) round operations. A Feistel network structure is commonly employed to design cryptographic algorithms. This architecture involves dividing a plaintext message into two equal parts. The initial layer of the function is designed to enhance the key’s strength against the algorithm, which is crucial for resisting brute force attacks. Additionally, key whitening operations using XOR have been implemented to secure cryptographic integrity further. ARX operations are strategically utilised to safeguard the structural integrity of the algorithm. XOR gate operations are used for the last stage in the method. The key distribution algorithm is taken from the Chaskey and RoadRunner lightweight algorithms [19]. Eighty bits of key are specified, and these are further broken into five sub-sections. Diffusion and confusion assets are used simultaneously while designing the algorithm technique. The avalanche criteria are also fulfilled in the algorithm. The speed of the proposed algorithm is maintained at 52.52 Megabytes per second. The randomness of the algorithm is also tested and proven by a number of zeros and ones, which are evenly divided by the ciphertext. It takes up less memory space. The main drawback is that the test is not tested using the National Institute of Statistical Test (NIST) statistical test for randomness, considered a milestone in the evaluation criteria of ciphers [16,42,43].

A. Biswas developed the one-block cipher, which is based on the Substitution and Feistel Network [15]. The author designed the algorithm using a few basic operations such as XOR, Ex-NOR, and concatenation. In this paper [15], 16 bits of block length were used as plaintext. Four identical keys, which are 16 bits, are used in the algorithm. It consists of 24 iterations. A round transposition function is used to make the algorithm structure strong. The inverse method is used for the decryption process [31,44,45]. The algorithm is also applied at the hardware level to check the throughput and complexity. The average avalanche turned out to be 58% with respect to plaintext, but 55.75% with reference to key. A major weakness of this algorithm is its quite small block size and key length, which opens the location of the attack [15,29,31].

Gaurav Bansod designed an ultra-lightweight cipher [9,46,47] with a block nature based on static permutation and static substitution. It is based on 25 rounds. It uses complex mathematics in which matrix functions are involved [48]. This was based on the Substitution Permutation network. This consists of 25 rounds, all based on confusion and diffusion. The key used for the Add round operation has 64-bit plaintext and 64-bit keys in its algorithm. The 64 bits are divided further into four blocks of sixteen bits each. The author uses the PRESENT key planning algorithm because it is so far safe from an attack. Stability is provided by the BORON software as well as the hardware architecture. This algorithm uses strong substitution boxes and permutation functions to provide inherent non-linearity and to protect the algorithm from attacks [9,25,49].

The concept of chaos-based non-linear components for block ciphers was introduced in [50]. This author claimed to access information easily through smartphones within no time [51]. He proposed a chaotic substitution box that defines the cryptographic characteristics. He designed it with randomness, which is mainly responsible for the randomness in the algorithm. The main drawback of this scheme is that the time factor is not calculated, which is the main factor in the case of lightweight devices. The second issue is that the rounds of iterations are not mentioned, which is also a main factor in lightweight ciphers. Chaos-based solutions are complex and therefore not suitable for lightweight devices, and this method is appropriate for image-based encryption. The proposed scheme sets the length of data to 128 bits, which is considered to be safe from cryptanalysis attacks [52]. Considering all the previous algorithms, the proposed algorithm is practically sound and strong compared to the previous lightweight block ciphers.

2.2. Motivation and Contribution

Lightweight block ciphers, as reviewed in Table 1, have been proposed, but all these block ciphers do not retain any substitution operation with dynamic tactics. However, a few solutions that utilise only the static substitution policy rather than dynamic substitution strategies exist [32,53,54]. Compared to the static substitution policy, the dynamic substitution strategy always triggers optimal confusion, more dynamicity, and greater randomness in symmetric block ciphers to save them from modern cryptanalysis attacks [44,46,47]. Existing static substitution-based cryptography methods are not optimally secure as these are vulnerable to attacks [39,44,45,55]. The cryptography algorithm is always as secure as it contains dynamicity and randomness. The lightweight cryptography algorithms, which are based on dynamic permutations [29,31,35,55,56], are not effective with regard to their cryptographic strength; they need to be evolved with dynamic substitution properties. Thus, there exists a great need for progressing the design of lightweight block ciphers using dynamic substitution to enhance dynamicity and randomness to achieve cryptographically strengthened ciphers [39,46,47,55]. As a contribution, the proposed method is designed with dynamic substitutions as well as dynamic permutations to provide less memory consumption, CPU utilisation, and encryption and decryption time compared to the other lightweight block ciphers [57,58,59]. The proposed algorithm has also been validated through NIST-based standard statistical tests to validate its randomness properties and security strength.

3. Method

This section comprises the working of the proposed algorithm. The proposed algorithm utilises 128-bit data blocks with 128-bit encryption keys. It provides a unique key generator function with the encryption keys of the same length for each iteration. The key generation functions further split the 128-bit key into sub-key blocks (32 bits each), denoted with (k[0], k[1], k[2], k[3]) in Figure 1. In each round, every key (128 bits) is identical in length but unique in bits. There is a slight change in the plaintext, which spreads completely as if it affects about 67% of the ciphertext changes. The time complexity is quite remarkable. The first part of the algorithm covers the function of permutation, and the second half covers the function of substitution. In the proposed algorithm, “⊕” is specified for the XOR function. The functions used by this algorithm include NAND, XOR and left shift operations. For encoding, a combination of confusion and spread transforms the data into ciphertext. The clarification of the proposed method is stated in the set of rules and is expressed in graphical form in Figure 1. The proposed methodology provides a solution in the lightweight cryptography field. Figure 1 depicts all modules of this proposed method.

There are two major modules of ciphers: permutations and substitutions. We will explain in detail the functions of each process.

Key Generation: As the initial step, a key with 128 bits is generated by the key generation in every round of the iteration; to make the algorithm strong and secure, a unique key is used for every round. A 128-bit key is generated from the master key for each iteration, which is a combination of mixed values.

Permutation: Each part of the 128-bit key is further divided into four parts, each containing 32 bits. To make it complex, part 1 of the key is ⊕ with part 2, and part 3 is ⊕ with part 4. The result of the first two parts is ⊕ the result of the remaining two parts. From the result of part 1 of the key, the number of ones from the results of all the parts of the key is counted. Then, the results of all parts are converted to decimal format. Then, the decimal values and count ones are summed. Afterwards, the first two values from decimal + count ones are selected; then, a left shift to the plaintext value is performed. The plaintext values are sorted based on decimal + number 1. Afterwards, permutation is performed with a bit swap with all the bit values.

In Table 2, the case of substitution is displayed, and the working scheme of the key generation of the proposed method is shown in Figure 2. To make the algorithm more robust, the sub-key values are explicitly replaced with other values in plaintext at different locations. For Sub1, the first eight bits of part 1 of the key are replaced with the first eight bits of plaintext. For Sub2, the second eight bits of part 2 of the first half key are replaced with 32-bit plaintext. In Sub3, the third eight bits of the key are replaced with the last eight bits of the second half of the 32-bit plaintext. In Sub4, the fourth eight bits of part 3 of the key are replaced with the third half of the 32 bits of plaintext. For Sub5, the fifth eight bits of the key are replaced by the last eight bits of the second half of the 32 bits.

After the substitution process, the NAND operation is applied, ⊕ and the key value is used to generate the ciphertext value for the first round of the algorithm. The ciphertext value in the first round will be the input in the second round for all three rounds of the proposed algorithm.

3.1. Proposed Algorithm: Encryption Routine

3.1.1. Step-by-Step Procedure

The proposed method consists of simple but cryptographically complex functions or operations. Permutation and substitution methods are performed dynamically with a 128-bit master key. The step-by-step working of the proposed method is outlined in Algorithm 1 and presented in Figure 1.

• Step 1: The 128-bit master key is divided into four equal parts, K1, K2, K3 and K4, containing 32 bits equally

• Step 2: K1 is XOR with K2 and K3 is XOR with K4

• Step 3: Count the number of ones from the result of the keys

• Step 4: The first part of the result is XOR with the second part of the key

• Step 5: Convert it into decimal format

• Step 6: Count the decimals and count ones

• Step 7: Left shift the values in plaintext on the result of the decimal and count ones

• Step 8: Bit swap all the values in the plaintext

• Step 9: Substitute the value in the plaintext based on the division of values of the key. In Sub1, the first eight bits of the key from the first half of the 32 bits are substituted in plaintext.

• Step 10: In Sub2, the first eight bits from the second half of the 32 bits are substituted in plaintext

• Step 11: The NAND operations are applied

• Step 12: The result of NAND and the key is XOR

• Step 13: The ciphertext is generated

Algorithm 1: Encryption Routine
	Input: Plaintext, Key
	Output: Ciphertext
1:	For i = 1 → 3 do
2:			R1 ← K1 ⊕ K2
3:			R2 ← K3 ⊕ K4
4:		Count 1’s ← R1 + R2
5:		R3 ← R1 ⊕ R2
6:		Decimal form ← Count 1’s
7:		Left shift on Decimal form + count 1’s
8:		PT ← Input random number
9:			perm ← permutate plaintext Decimal + Count 1’s
10:			sub ← sub1 + sub2 + sub3 + sub4 + sub5
11:			R4 ← sub-NAND-Key
12:			R5 ← R4 ⊕ Key
13:			Return R5 (Ciphertext)
14:
15:	End for

3.1.2. Decryption Step-by-Step Procedure

Decryption is the reverse of the encryption process.

• Step 1: Take Ciphertext of 128 bits

• Step 2: XOR operation is applied to the ciphertext and key to obtain the previous value

• Step 3: The NAND operation is applied

• Step 4: Sub1, Sub 2, Sub 3, Sub 4 and Sub 5 are substituted back their value in the plaintext

• Step 5: Bit Swap all the values in plaintext according to encryption

• Step 6: Left Shift Permutate back the values in plaintext based on Decimal Count ones

• Step 7: Convert the values of count ones to the decimal number system

• Step 8: The second part of the key is XOR, with the first part of the key

• Step 9: Count the number of ones from the result of the key values

• Step 10: K3 is XOR with K4

• Step 11: K2 is XOR with K1

• Step 12: K1, K2, K3 and K4 add altogether

• Step 13: plaintext is generated

3.2. Security and Resistance Against Side-Channel Attacks

The static or fixed permutation and substitution-based block ciphers are not significantly resistive against modern attacks [60]. The proposed lightweight block cipher retains dynamic operations (substitution and permutation) compared to existing solutions with similar static-natured operations. The effectiveness of these dynamic operations has been rigorously analysed using a NIST-based standard tool, validating the cipher’s probabilistic randomness and cryptographic robustness. Thus, instead of static operations (permutation and substitution), the proposed lightweight block cipher is based on dynamic permutation and dynamic substitution operations. The security strength of any block cipher is excessively dependent on dynamic behaviours [47,61]. The dynamic behaviours in substitution and permutation operations are crucial to resisting linear, differential, and side-channel attacks [47,60,62,63,64]. Moreover, specific tests for side-channel attack resistance were conducted. To comprehensively evaluate our cipher’s resistance to side-channel attacks, future research will include hardware-based experiments, providing a more practical assessment of its security against physical side-channel threats. This will include measuring how dynamic parameters change with each execution and between different keys, substantially limiting the effectiveness of side-channel attacks, which often rely on static properties to extract information [44,65,66,67]. This dynamic nature is supported by statistical evidence from NIST-based standard experiments, such as non-overlapping patterns and longest-run tests, further demonstrating the cipher’s robustness [27].

Furthermore, the proposed block cipher has shown higher avalanche properties, which have also been tested experimentally and compared with other solutions (Table 3 and Table 4). It is commonly known that higher avalanche properties are also a very good indicator of resistance to known plaintext attacks and known cipher attacks, including modern cryptanalysis. Conclusively, any block cipher that has dynamic permutation and dynamic substitution operations with good randomness and avalanche properties can significantly resist modern cryptanalysis.

The proposed method’s brute force attack calculation was conducted using its initial encryption key (128 bits) against 1 Tera Hz Processors, which take 10¹² instructions per second. Thus, approximately 3.6516 × 10⁸⁴ years will be required for exhaustive key searching against the proposed method’s initial 128-bit encryption key.

• 2¹²⁸/10¹² = 10³⁸/10¹² = 10²⁶ instruction/s

• Time in days = 10²⁶/(60 × 60 × 24)

• Time in days = 10²⁶/(3600 × 24) = 100,000 × 10¹⁹/36 × 24

• Time in years = (100,000 × 10¹⁹)/864 × 365 = 0.32 × 10¹⁹ years → 3 × 10¹⁷ Years (Approximately)

Thus, as shown in Figure 3, exhaustive key searching against the proposed method’s initial 128-bit encryption key will require approximately 3.6516 × 10⁸⁴ years.

3.2.1. Resistance of Proposed Method Against Modern Differential Cryptanalysis

In a Chosen-Plaintext attack, adversaries are granted the ability to select specific plaintexts to observe the corresponding ciphertexts produced by an encryption system, and differential cryptanalysis utilises the differential properties between plaintext/cipher–text pairs to deduce information about the secret key. It analyses how differences propagated through the rounds of a block cipher can reveal statistical imbalances that can be exploited to recover the secret key. This affords a degree of control over the data in the encryption process, potentially revealing vulnerabilities within the algorithm and leading to the retrieval of the secret key [47,63,64]. However, when operating within a framework featuring a fixed 128-bit key and implementing dynamic elements such as variable block sizes, dynamic padding, permutation, and substitution, the effectiveness of such an attack is notably resisted. These dynamic elements introduce a heightened level of complexity and unpredictability into the encryption process, making it significantly more challenging for attackers to predict or control the outcome of chosen plaintexts. Consequently, the security of the encryption algorithm is enhanced significantly against chosen attacks and other modern attacks [47,63,64]. However, the extent of these dynamic measures’ protection remains contingent on the specific implementation and the inherent robustness of the encryption algorithm. While the dynamic elements enhance security, it is essential to ensure that the encryption system is resilient against Chosen-Plaintext attacks and maintains its integrity under varying conditions, thus safeguarding sensitive data from potential threats [47,63,64].

3.2.2. Resistance of Proposed Method for Modern Algebraic Attacks

Algebraic attacks are extensively utilised in the analysis of block ciphers to evaluate their security. One common approach involves modelling ciphers as systems of explicit difference equations over a finite field, referred to as “difference ciphers”. By employing difference algebra, it is possible to define a few properties, such as inevitability and periodicity. These attacks have become a crucial focus in the field, aiming to describe the encryption operation of block ciphers through sets of multivariate polynomial equations. The solution to these equations can be used to recover the secret key, and the difficulty of solving them directly influences the cipher’s security [47,63,64]. Numerous research papers have concentrated on algebraic attacks in block ciphers, introducing innovative techniques and optimisations. Algebraic attacks function as puzzles to unlock encrypted data, leveraging mathematical principles to recover secret keys. Despite their formidable nature, breaking 128-bit encryption through these attacks remains highly challenging due to the vast number of possible keys. This process demands a significant amount of time and computing power. The proposed method is based on dynamic features such as dynamic permutations and dynamic substitutions. Dynamic features are built upon pseudo-randomness. An algorithm incorporating dynamicity and randomness can resist algebraic-type attacks well. When any symmetric encryption algorithm retains randomised and dynamic characteristics (e.g., dynamic substitution and dynamic permutation, etc.), it is considered significantly secure. Static-natured substitution supports the cracker in finding useful and secret information related to the encryption algorithm or secret key. Dynamic substitution is greatly beneficial to resisting differential and linear attacks compared to static substitution. Static substitution is significantly helps crackers to initiate side-channel attacks due to publicly known or static values [27,47]. Thus, the proposed method has good design properties that resist modern and side-channel attacks. Moreover, the proposed method has successfully passed all recommended statistical randomness tests, demonstrating that it possesses good randomness and dynamic features. This is confirmed by its passing of a linear complexity test.

4. Analysis of Results and Discussion

The proposed algorithm has been tested many times regarding its avalanche properties. It has been concluded that the plaintext avalanche results are far superior to those of existing work. All ciphers that provide a good avalanche effect are more likely to withstand various cryptanalysis attacks. The results obtained from Table 3 show the avalanche effect associated with plaintext. Figure 4 shows the graphical representation of Table 3. For these results, specific matrices have been tested on the avalanche characteristics; these include the memory consumption of the proposed algorithm compared to those in the existing literature, the CPU utilisation in the proposed algorithm, the throughput results of the proposed algorithm, and a comparison with related work; for the randomness, some tests mentioned in the NIST statistical proceedings are used. As a result of the results of the matrix, it can be inferred that this proposed algorithm is quite efficient when it comes to speed, also providing excellent security and requiring less memory. All the above results prove that this proposed algorithm meets the requirements of a lightweight cryptosystem.

Avalanche Effect: This is an important method of measuring the strength of cryptographic algorithms. In such a method, changing one bit in the plaintext results in a significant change in the ciphertext.

4.1. Results of Average Avalanche Effect for the PlainText

The average avalanche effect is shown in plaintext in Table 3, in comparison to the existing literature.

Table 3

Comparison of average avalanche effect for plaintext.

Algorithm’s	Average Avalanche Effect for Plaintext (%)
LRBC [15]	58.00
QTL [67]	52.56
SIMECK [11]	53.00
PRINCE [68]	51.18
PRINT [69]	49.08
TEA [10]	49.12
LED [70]	52.83
Proposed Algorithm	67.00

It is very clear that, on average, there is a 67% change in the ciphertext, as if there were some changes in the plaintext.

The proposed method is superior to those proposed in other existing literature, as displayed in Table 3. This is because it maintains a good average plaintext avalanche effect of 67%. This means that if the plaintext changes by 1 bit, the ciphertext will change by 67%. Many changes in the ciphertext are considered strong algorithms due to the lack of network cryptanalysis attacks.

The proposed method generates a higher curve than the prevailing methods in the literature, as shown in Figure 4. The higher the algorithm’s average avalanche, the stronger it is. Also, it is evident that the greater the change in the bit of the ciphertext when changing only 1 bit of plaintext, the stronger the algorithm. Intruders cannot infer the plaintext values and private keys to protect the algorithm against network attacks.

4.2. Results of Average Avalanche Effect for the Key

The results regarding the average avalanche effect, in correlation with the cryptographic key, are presented in Table 4. The analysis reveals that altering a single bit of the key induces an average ciphertext variation of 65.6%. The performance remains consistent, with average scores between 46.42% and 55.75%, even as other algorithms are introduced. To ensure the algorithm’s integrity against network attacks, such as man-in-the-middle and brute force attacks, it is imperative to allocate sufficient security measures to the secret key.

Table 4

Comparison of the average avalanche effect for the key.

Algorithm’s	Average Avalanche Effect for Key (%)
LRBC [15]	55.75
QTL [67]	50.31
SIMECK [11]	51.25
PRINCE [68]	49.06
PRINT [69]	46.42
TEA [10]	47.12
LED [70]	50.37
Proposed Algorithm	65.60

The following table shows the results of the average avalanche effect associated with the key, as shown in Figure 5. It claims that LRBC maintained a 55.75% average avalanche effect with respect to the key, whereas the proposed method achieved a 65.60% average avalanche effect, in comparison to the norm of 46.42–65.60.

The respective results for the average avalanche effect for the key are displayed in Figure 5. It is very clear from the results that by changing one bit of the key, the average change in the ciphertext is 65.6%. The average value maintained by the existing algorithm is between 46.42 and 55.75%. The value change in the ciphertext from a change in the value of the key depicts the strength of the algorithm. The secret key must be secure and robust to protect the algorithm against attacks on the network, such as man-in-the-middle and brute force attacks.

4.3. Memory Comparison with Proposed Algorithm (Bytes)

Table 5 presents a comparative analysis of the memory utilisation, measured in bytes, between the proposed algorithm and existing techniques. The proposed algorithm demonstrates superior efficiency in using memory for encryption, decryption, and key scheduling tasks. Specifically designed to minimise disk space usage, the proposed method requires only 1510 bytes to perform these operations effectively. This is a significant reduction compared to other algorithms’ memory requirements. The reduced memory footprint of the proposed algorithm surpasses the criteria for lightweight architecture, offering a compelling solution for applications where resource conservation is paramount, as shown in Figure 6.

4.4. Proposed Algorithm’s Utilization of CPU (1000 Samples/s)

Table 6 details the CPU utilisation metrics for the proposed algorithm, which processes data at a rate of 1000 samples per second, corresponding to 181 cycles. This represents a CPU usage of 8.17%, an efficiency level deemed highly favourable for lightweight algorithms.

4.5. Throughput Comparison with Proposed Algorithm (Kbps)

Table 7 compares the proposed algorithm’s throughput. Throughput is a parameter that indicates the results of processing a plaintext block with a combination of the key plans and values shown in the table. The proposed algorithm produces a throughput of 853.31 Kbps, which is good in terms of the software implementation of a lightweight block cipher as it provides effective security.

The throughput comparison with the proposed algorithm is displayed in Table 7. Throughput is calculated from the formula given in Equation (1), and the graphical representation of the results is shown in Figure 7.

(1)$\left(\right(Throughput=size of a data\ast max.clock speed)/(no.of clocks per cycle\ast no.of cycles\left)\right)$

4.6. Statistical Test for Randomness

Numerous tests have already been performed to assess the algorithm’s randomness. To validate the result, the proposed algorithm is tested many times. Multiple statistical tests and the resulting p-values are mentioned in Table 8, and a graphical representation of the statistical test of randomness is shown in Figure 8.

The randomness of statistical tests and their p-values are displayed in Table 8 and demonstrated in the same order in Figure 8 The algorithm passed all NIST statistical tests and proved that the algorithm is efficient in speed, security, and randomness. Statistical tests that reach probability values (p-values) in the range of 0.01 to 1.00 pass. This ensures that the tested series has a null hypothesis and 99% randomness (it means that H0 is true). If not, the hypothesis results in a non-randomness of 99% (which means that H1 is true). The statistical test in the case of the specified range of p-value is (0.01 ≤ θ ≤ 1.00) [72]. The tested method described above clearly shows this. It contains reasonable random characteristics and is ready for a robust and secure cryptanalysis method.

4.6.1. Frequency (Monobit) Test

This test is performed to verify that the sequence of the numbers 1 and 0 is equal, as it is used to test the random sequence. Its standard formula is given in Equation (2).

(2)$\mathit{\text{p-value}}=erfc Sobs/\surd 2$

4.6.2. Frequency Test within a Block

This test is used to determine whether the frequency of 1s and 0s is ½ in each block or not. Its formula is given below in Equation (3).

(3)$\mathit{\text{p-value}}=igamc (N/2,(x^2(obs\left)\right)/2)$

4.6.3. Runs Test

This test verifies the number of 1s and 0s that are of different lengths and acceptable according to the NIST for any random sequence. Its formula is given below in Equation (4).

(4)$\mathit{\text{p-value}}=erfc \left[\left(\left|Vn\left(obs\right)-2n\pi \left(1-\pi \right)\right|\right)\right]∕\surd (2\&2n\pi (1-\pi ))$

4.6.4. Test for Longest Run of Ones in a Block

This test is used to verify that the length of the longest run of ones is consistent in the tested sequence range with the range of any expected random sequence. Its formula is given in Equation (5).

(5)$\mathit{\text{p-value}}=igamc [K/2,\hspace{1em}(x^2 \left(obs\right))/2]$

4.6.5. Non-Overlapping Template Matching Test

This test is used to test the specific patterns of bits occurring throughout each testing sequence. Its formula is represented in Equation (6).

(6)$\mathit{\text{p-value}}=igamc [N/2,\hspace{1em}(x^2 \left(obs\right))/2]$

4.6.6. Overlapping Template Matching Test

This test is performed to test the occurrence of an m-bit pattern within a sequence. Its formula is represented in Equation (7).

(7)$\mathit{\text{p-value}}=igamc [n/2,\hspace{1em}(x^2 \left(obs\right))/2]$

The results based on the p-value indicate that the output obtained from the proposed algorithm passed the criteria set by NIST. Thus, the proposed method maintains good randomness, as any strong cryptographic algorithm requires.

5. Discussion

The use of dynamic substitution is good for achieving effective confusion in symmetric block ciphers to resist modern cryptanalysis [73]. A good and cryptographically strong cipher should also have higher nonlinearity [73]. The proposed method has an average nonlinearity (105.67), which is better than several existing ciphers. The proposed method shows good linear complexity (0.4562), which is quite significant in resisting linear and differential attacks. Moreover, the proposed method contains an average avalanche effect (67% for plaintext and 65.6% for key), which is better than existing algorithms. The proposed algorithm provides dynamic permutation as well as dynamic substitution to provide a fully dynamic and cryptographically strong cipher. The dynamic nature of the algorithm can resist linear, differential, and side-channel attacks. The proposed algorithm is capable of generating the balanced output mentioned in Table 8 to resist modern attacks. Moreover, the proposed method has passed several NIST-based statistical tests, in which all p-values lie under an acceptable range (0.01 < p-value ≤ 1.00) to satisfy randomness properties. The security strength of symmetric block ciphers is highly dependent on dynamicity and randomness properties. Thus, the proposed method includes good dynamicity and randomness.

6. Conclusions

In this research, we have developed an intelligent and memory-efficient data encryption algorithm that incorporates both dynamic permutation and substitution, distinguishing it from previous algorithms that relied on static methods. This dynamic approach significantly enhances the security of block ciphers. Several standard statistical tests recommended by NIST validated the randomness and dynamism of our proposed block cipher, confirming that it achieves significant probabilistic randomness within NIST’s defined ranges. Moreover, the algorithm excels in avalanche properties, exhibiting an average effect of 67% relative to plaintext and 65.6% relative to the secret key. Additionally, it is highly efficient in CPU utilisation and minimises memory usage to just 1510 bytes while achieving a superior throughput of 853.31 Kbps, markedly outperforming other lightweight block ciphers. Given the escalating security demands in IoT environments, as discussed in [74], the robustness of our cipher could prove crucial in safeguarding interconnected devices against sophisticated cyber threats. The need for advanced training solutions becomes apparent with the increasing complexity of IoT and security systems. In this regard, our proposed LLM-based method, as detailed in [75], can be effectively utilised to train employees in handling these complex systems, enhancing their ability to manage and secure modern technological environments. Our cipher exceeds existing solutions in dynamic design parameters, including substitution and permutation operations, and sets a new standard regarding avalanche properties, memory consumption, CPU utilisation, and enciphering throughput. The integration of the advanced key management systems explored in recent studies supports our findings, further confirming the efficacy of dynamic strategies in cryptographic security tailored explicitly for IoT applications [76]. Future enhancements will explore alternative bit-swap operations to save computational time, meet evolving security and speed requirements, and incorporate rigorous testing against physical side-channel attacks.

Author Contributions

Conceptualisation, S.A., I.A.S., M.I. and M.M.; methodology, S.A., I.A.S., M.I. and M.M; Validation, S.A., I.A.S., M.I., M.M., A.M.A., C.-C.L. and I.T.; formal analysis, S.A., I.A.S., M.I., M.M., A.M.A., C.-C.L. and I.T.; writing—original draft preparation, S.A., I.A.S., M.I. and M.M.; writing—review and editing, S.A., I.A.S., M.I., M.M., A.M.A., C.-C.L. and I.T.; visualisation, S.A. and I.A.S.; supervision, I.A.S., M.I. and M.M. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Working scheme of the proposed method.

Figure 2. Working scheme of key generation of proposed method.

Figure 3. Comparison of brute force attack with existing algorithms.

Figure 4. Comparison of the average avalanche for the plaintext [10,15,67,68,69,70].

Figure 5. Comparison of the average avalanche effect for the key [10,11,15,67,68,69,70].

Figure 6. Memory comparison with proposed algorithm.

Figure 7. Throughput comparison with proposed algorithm [3,4,68,70].

Figure 8. Statistical test for randomness.

Table 1

Comparative analysis of existing lightweight cryptosystems.

Existing Cryptosystems	Existing Cryptosystem Title	Based on Dynamic Permut.	Subst. Operation Used	Based on Dynamic Substi.	Effectiveness in Dynamicityand Randomisation
[1]	Design, analysis, and implementation of a new lightweight block cipher for protecting IoT smart devices	✓	✓	×	×
[15]	LRBC: a lightweight block cipher design for resource-constrained IoT devices	✓	×	×	×
[16]	A tiny and fast ultra-lightweight block cipher for IoT,” International Journal of Scientific and Technology Research	×	×	×	×
[17]	A Prospective Lightweight Block Cipher for Green IT Engineering	✓	×	×	×
[18]	ECC Based Encryption Algorithm for Lightweight Cryptography	×	×	×	×
[19]	An effective, lightweight cryptographic algorithm used to secure resource-constrained devices	×	×	×	×
[20]	Lightweight MDS serial-type matrices with a minimal fixed XOR count	×	×	×	×
[9]	BORON: an ultra-lightweight and low-power encryption design for pervasive computing	×	✓	×	×
[21]	Enhancement of a lightweight attribute-based encryption scheme for the Internet of Things	✓	×	×	×
[22]	A novel lightweight cryptography for mobile database with performance analysis	×	×	×	×
[12]	RECTANGLE: A bit-slice lightweight block cipher suitable for multiple platforms	✓	✓	×	×
[23]	A lightweight attribute-based encryption scheme for the Internet of things and future generation computer systems	×	×	×	×
[24]	Triathlon of lightweight block ciphers for the Internet of Things	×	✓	×	×
Our Work		✓	✓	✓	✓

Table 2

Scheme of substitution.

Key of 128 Bits
First Half of 64 Bits								Second Half of 64 Bits
First half of 32 bits				Second half of 32 bits				First half of 32 bits				Second half of 32 bits
16		16		16		16		16		16		16		16
8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8
Sub-1				Sub-2			Sub-3			Sub-4					Sub-5

Table 5

Memory consumption comparison with proposed algorithm.

Algorithm(Block Size/Key Size)	Rounds	Memory (Bytes)Encryption, Decryption, Key Schedule
BRIGHT (64/80) [16]	32	1084
RoadRunner (64/80) [9]	10	2334
BRIGHT (64/96) [16]	33	1806
SPECK (64/96) [15]	26	1802
BRIGHT (64/128) [16]	34	1807
SPECK (64/128) [15]	27	1820
HIGHT (64/128) [22]	32	4280
SPARK (64/128) [24]	8	3516
CHASKEY (128/128) [71]	8	1982
BRIGHT (128/128) [16]	35	1819
SPARK (128/128) [72]	8	5059
BRIGHT (128/192) [16]	36	1821
BRIGHT (128/256) [16]	37	1823
Proposed Algorithm	3	1510

Table 6

CPU utilisation of the proposed algorithm.

Block Size	Key Size	Rounds	CPU Utilization (1000 Samples/s)
128 bit	128 bit	3	181 (8.17%)

Table 7

Throughput comparison with proposed algorithm (Kbps).

Algorithm’s	Throughput (Kbps)
LBlock [70]	822.41
PRESENT [3]	104.36
HIGHT [68]	833.61
Piccolo64-128 [4]	571.84
Proposed Algorithm	853.31

Table 8

Statistical test for randomness.

Name of Test	Average p-Value	Test (Pass/Fail)
1. Test for The Frequency (Monobit)	0.3214	Passed
2. Test for The Non-overlapping Template Matching (m = 128)	0.4674	Passed
3. Test for The Runs	0.5743	Passed
4. Test for the Longest-Run-of-Ones in a Block	0.5178	Passed
5.a Test for The Non-overlapping Template Matching (m = 3, B = 001)	0.4567	Passed
5.b Test for The Non-overlapping Template Matching (m = 3, B = 011)	0.5496	Passed
5.c Test for The Non-overlapping Template Matching (m = 3, B = 111)	0.4981	Passed
5.d Test for The Non-overlapping Template Matching (m = 3, B = 100)	0.5127	Passed
5.e Test for The Non-overlapping Template Matching (m = 3, B = 110)	0.4156	Passed
5.f Test for The Non-overlapping Template Matching (m = 3, B = 000)	0.4823	Passed
6. Test for Overlapping Template Matching	0.4762	Passed
7. Linear Complexity Test	0.4562	Passed

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