Home Technology Improvements in the randomness and security of digital currency using the photon sponge hash function through Maiorana–McFarland S-box replacement
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Improvements in the randomness and security of digital currency using the photon sponge hash function through Maiorana–McFarland S-box replacement

  • Asmaa A. Mohammed EMAIL logo , Abdul Monem S. Rahma and Hala Bahjat AbdulWahab
Published/Copyright: October 18, 2024
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Open Engineering
From the journal Open Engineering Volume 14 Issue 1

Abstract

There is a demand for a digital currency that facilitates remote trading over the Internet and strives to reduce external control, ensuring that transactions are conducted only between authorized persons or parties involved in the transfer. The financial sector has been significantly impacted by cryptocurrency, or digital currency, which brings new potential and challenges. The concept of digital currency is thoroughly examined, as are its complicated implications on various aspects of the economy. Trading digital currencies via the Internet may be vulnerable to theft and forgery due to the development of hacker programs. Therefore, we proposed to design a new digital currency and then built a 16 × 16 structure and filled the matrix with random numbers within GF(251). We used the random algorithm (Chun–Hui He’s iteration), then generated four directions, and used polynomial equations for the purpose of distributing powers between the parties in our future complete system. The original matrix was encoded with the photon sponge hash function after updating the S box by integrating the algorithms (Chun–Hui He’s iteration, Mariorana–McFarland method), and the results were good security measures (correlation coefficient, bijective property, balanced criteria, completeness criteria, and strict avalanche criteria) as well as the encryption and decryption time became faster (0.0005202). The major objective is to design a new digital currency system toward achieving security, scalability, and comprehensive adoption, looking into how it might improve security, promote financial inclusion, and change the present payment systems.

Keywords: electronic currency; types of digital currency; Chun–Hui He’s iteration; sponge hash function; Mariorana–McFarland method

1 Introduction

The main introduction of digital currency design refers to the foundational principles and concepts behind creating digital currencies. Digital currencies are virtual or electronic forms of money that use cryptography for secure transactions, decentralization for control, and rely on blockchain technology or other distributed ledger technologies for operation [1,2]. The development of currencies has witnessed significant changes. After the exchange or barter was the first commercial process between individuals and societies, it developed to include bronze in the mining of the first monetary coins. Then, it was followed by the entry of both silver and gold in transactions, which are currently known as currencies. By the end of the second millennium, there was a significant surge in development. This led to the transformation of commercial exchange tools into a digital form, including the emergence of credit cards and specialized applications designed for electronic payments, along with their corresponding digital payment methods. The financial sector experienced significant growth, leading to the emergence of encrypted digital or digital currencies. The trade volume of digital currencies had a significant surge toward the end of the first decade of the twenty-first century, reaching billions of US dollars. This increase in value has made them a destination for electronic hacks and piracy. For instance, the amount of one million US dollars in digital currencies raises concerns about the feasibility of protecting traders involved in this kind of currency [3,4]. It is important to note that designing a new digital currency requires careful consideration of various technical, economic, regulatory, and societal factors [5]. The strengths of our proposed system are as follows: 1. We used Chun–Hui He’s iteration and the photon sponge hash function to encrypt digital currency. 2. Direct interaction between users without the need for financial intermediaries, which increases the speed and efficiency of the exchange process between them. 3. Encryption and decryption time is faster. 4. Increased security ratio in our system due to the use of highly complex. The weaknesses facing our proposed system are as follows: 1. Adoption and acceptance: The new digital currency may face challenges in adoption and acceptance by users, institutions, or companies, which may affect its value and use. 2. Security and fraud: The new digital currency may face challenges in terms of security and fraud, especially in its early stages, which can affect customer’s trust. Algorithm Research problems: Because of the different aspects of life (commercial, industrial, agricultural, and others) need to exchange wages between people, and the exchange of wages (material) sometimes requires that it be between the two sides only without a third party, such as the bank or a specific supervisory authority, i.e., the exchange is independent, i.e., the currencies are free to exchange through the Internet and that they enjoy the same advantages as paper currencies and coins. That is, they have self-immunity against theft and forgery. Because of these problems, therefore, we proposed designing a digital currency that is electronically unrestricted and independent between people without the need for a third party and, at the same time, has immunity against theft and forgery. In our proposed system, a matrix of size 16 × 16 was designed and filled with numbers within GF(251) and randomly scattered with an algorithm (Chun–Hui He’s iteration) to increase randomness and security. Then, we generated from the original matrix four matrices (top, bottom, right, and left) for the purpose of distributing powers in our complete future system. Next, we encoded the random matrix with an algorithm (photon sponge hash function) by updating the S box by merging two algorithms (Chun–Hui He’s iteration and Mariorana–McFarland method) for the purpose of increasing randomness and complexity and the proposed method gave higher randomness, as well as the time of encoding and decoding became faster.

The remainder of this article is structured as follows: Related works are explained in Section 2. Section 3 deals with digital currencies with advantages, challenges, and design types of digital currencies. The random algorithm for Chun–Hui He’s iteration is highlighted in Section 4. The topic of hash function is explained in Section 5. The Mariorana–McFarland method is explained in Section 6. Finally, the proposal system of digital currency design is discussed in Section 7.

2 Related studies

Technology and finance practitioners, as well as researchers, are interested in the design of digital currencies. Research Gate, Google Scholar, and Google as a large library were searched.

Nakamoto [6] initially created Bitcoin to address the problem of double spending associated with e-accounts since digital currencies could be transferred between users without enabling the user to copy, transfer, and spend electronic currency twice.

Hineman and Blaum [7] presented an approach for accelerating and simplifying the encoding in Shamir’s secret-sharing approach by eliminating the need for symbols to be distinguishable at most a predetermined distance apart. Furthermore, this process is accelerated by using array codes based on XOR operations instead of Reed–Solomon codes.

A cryptocurrency wallet (Bitcoin wallet) for Android OS was developed and carried out by Khan et al. [8] with the use of a secure private key storage method (“Cold Wallet”) and an Android application based on QR codes. Because of its benefits in integrating Blockchain with IoT, Ghalwesh et al. [9] depended on the hyperledger project to maximize security in the two monitoring and storage operations. In order to reduce such time complexity, Mbaye et al. [10] devised two parallel approaches that rely on distributed systems and GPUs. We were able to reduce time complexity and enhance the algorithms with the aid of the distributed approach.

Garratt et al. [11] examined the consequences of utilizing commercial banks of different sizes in the introduction of a central bank digital currency (CBDC). They focused on two aspects of CBDC design: payment simplicity and interest rate. These traits reflect currencies’ qualities as a store of value and medium of trade. Payment simplicity is an overlooked aspect of CBDC design that interacts with the financial benefits of interest payments. A sufficiently high convenience value of a CBDC could enhance the transmission of monetary policy.

Kakebayashi [12] concluded that CBDC could address problems with the value-added tax (VAT) system while preserving its efficacy, simplicity, and fairness. According to the report, CBDCs have the potential to significantly alter public financing overall, but their design and acceptance should not be determined solely by how they could impact the tax system, as shown in Table 1.

Table 1

Compression between the related works

Reference and Years Type of digital currency Central authority Technique Strengths and weaknesses
[6] (2008) Bitcoin No Peer-to-peer principle, digital signatures, and the blockchain Strengths: Digital currency, like Bitcoin, introduced in 2009, offered decentralized transactions and borderless payments, fostering financial inclusion and reducing reliance on traditional banking systems. Weaknesses: digital currency faced limited adoption and regulatory uncertainty, raising concerns about security, stability, and potential use for illicit activities due to its pseudonymous nature
[7] (2022) Bitcoin No Multi-signature technique based on Shamir’s secret sharing Strengths: digital currencies demonstrated faster and more efficient cross-border transactions, highlighting their potential for reducing fees and transaction times in international remittances. Weaknesses: During this period, digital currencies faced high price volatility and scalability issues, posing challenges to their use as stable stores of value and mainstream payment methods
[8] (2019) Bitcoin No QR code and hot wallet Strengths: investors searching for alternative assets were more interested in digital currencies for guarding against economic dangers
Weaknesses: in various jurisdictions, unclear frameworks, as well as regulatory concerns, have hindered the implementation and broad acceptance of digital currencies in established financial systems
[9] (2020) Bitcoin No Depending on the Hyperledger project Strengths: digital currencies opened up novel channels to lend, borrow, and yield farming, showcasing their potential for decentralized finance (DeFi) applications. Weakness: the year has shown how easy it is for such currencies to get manipulated in the market, suffer a cyber-attack, or get penalized by governmental rules, resulting in clearer regulations and more robust security measures being demanded
[10] (2021) Altcoin Yes Altcoins can be adopted as a digital currency as they are mainly designed as a means of exchange between two counterparties directly Strengths: the main historically established financial institutions and multinational corporations showed intention to integrate digital currencies already into their activities alongside quickly rising institutional acceptability. Weaknesses: like a revelation, the year showed that these concerns over environmental and energy implications remain even with respect to proof-of-work-based cryptocurrencies, which brought about the question of whether renewable energies could be the future for this currency
[11] (2022) Bitcoin, CBDC No, yes Blockchain, unified payment interface Strengths: more state-of-the-art energy-efficient algorithms that are less likely to generate negative environmental effects for digital currencies have been introduced, subsequently ensuring the reliability and sustainability of the network. Weaknesses: however, this period saw regulators worldwide striving to create guidelines for the use of cryptocurrencies, an act that created uncertainty and even business disruptions in the ongoing financial landscape of the emerging world
[12] (2023) CBDC Yes VAT system Strengths: digital currencies continued to drive innovation in decentralized applications, smart contracts, and NFTs, expanding their utility beyond traditional financial transactions. Weaknesses: concerns about user privacy and data security remained, prompting discussions around implementing robust privacy solutions in digital currencies

3 Digital currency

Digital currency is issued through private parties and exclusively flows through the Internet instead of government-issued money circulating through traditional banks and financial organizations. While it shares certain characteristics with bank transfers, digital currency transactions are not burdened by high fees, fraudulent chargebacks, or protracted wait times for cleared funds, whereas those involving bank accounts and credit cards [13]. A digital representation of value that could be transferred, stored, or traded electronically is called a digital currency. The public authority or central bank does not issue it. It is not a fiduciary currency-linked payment. The fact that individuals accept it as a form of payment strengthens it [14,15]. Digital currencies are described as a digital representation of a value by the European Banking Committee. It is a form of payment accepted via legal and ordinary persons, not issued through a central bank or public authorities, is not always associated with a particular currency, and may be transferred, stored, and traded electronically. Virtual fake currencies made up of digital codes that could be kept on a network or hard drives are called digital currencies. It is challenging to keep track of the selling and buying activities on the Internet or even identify the owners of such currencies because their value depends on demand and supply [16,17].

3.1 Characteristics of electronic currency systems

  1. Digital: Electronic currency exists only in digital form and is stored, transferred, and verified electronically.

  2. Decentralized: Most electronic currency systems do not have a central authority or intermediary, such as a bank, that controls the system.

  3. Cryptographic: Electronic currencies use complex cryptographic algorithms to secure transactions and prevent fraud.

  4. Limited supply: Many electronic currencies have a limited supply, meaning that a finite number of units could be created.

  5. Peer-to-peer: Users of E-currency systems can frequently and directly interact with one another, bypassing the requirement for a central intermediary [18,19].

3.2 Challenges encountered by electronic currency systems

It is important to consider in relation to some factors before sharing confidential or personal information with the customer. Similarly, different types of businesses face the same cultural challenges when both cultural adaptation and assimilation are done [20,21].

  1. Security: E-currency systems are just as vulnerable to cyberattacks as any other financial system.

  2. Scalability: E-currency systems will face inconvenience when they get overwhelmed by the high volume of transactions due to the problems that they encounter while they are growing in popularity.

  3. Volatility: the challenges that user experience to determine the value of their digital assets are a result of the magnitude and the rate at which E-currencies value fluctuates.

  4. Regulation: Things can be complicated for the authorities as this type of financial system can be difficult to monitor, resulting in profit profiteering by illegal operators who launder and carry out their illegal activities.

  5. Integration with traditional financial systems: To collaborate electronic money systems with the standard financial systems may be tedious, as in the exercising of the traditional bank networks and the credit card systems [22].

3.3 Types of digital currency

Many types of digital currencies are available today, and some of the most common variants are listed as follows:

  1. Cryptocurrencies: Cryptocurrencies are virtual money systems that primarily use blockchain networks and cryptography technologies as their foundation: Bitcoin, Litecoin, and Ethereum.

  2. Stablecoins: Stablecoins are a sort of digital money that ties the price of each coin to one particular item or a basket of related assets, thereby ensuring that the value of each coin remains stable. Ones anchored to a fiat currency, like the United States Dollar or Euro.

  3. CBDCs: Digital currencies known as CBDCs are produced and controlled by central banks. CBDCs are centralized and administered by the issuing central bank, in contrast to decentralized cryptocurrencies. The goal of CBDCs is to provide the advantages of digital currencies without sacrificing control over monetary policy and financial stability [23].

  4. Utility tokens: Utility tokens are digital assets generated by projects or companies that are used to grant access to their products or services. Such tokens are mainly employed within a given ecosystem to allow for payments, utilization of features, and participation in the system’s governance. Here, we have BNB (Binance Coin) and LINK (Chain-link) to cite.

  5. Security tokens: Security tokens are used to represent ownership in underlying assets like real estate, stocks, or commodities. These tokens are subject to security regulations and provide investors with rights and benefits, such as dividends or voting rights. Security tokens aim to digitize traditional financial assets, enabling more efficient trading and ownership transfer [24].

  6. These are some of the main types of digital currencies available today. Each type serves different purposes and offers distinct features within the digital currency landscape [25,26].

4 Chun–Hui He’s iteration

The variant method of He Chun–Hui based on iteration belongs to the class of iterative computing algorithms for solving nonlinear equations and optimization problems. The main purpose of this technique is to solve nonlinear functions and obtain their roots or mains. The method involves an iterative algorithm, which allows the original solution to be updated by small adjustments and consequently leads to a desired precision level.

The main definition of Chun–Hui He’s iteration method can be summarized as follows:

Given a nonlinear equation f(x) = 0, where x is the variable to be solved for, the iterative update rule for Chun–Hui He’s method is as follows:

(1) x n + 1 = x n − f ( x n ) f ′ ( x n ) ,

where x n is the current estimate of the root or minimum, F(x n ) is the value of the function at (x n ), and F(x n ) is the derivative of the function with respect to (x) evaluated at (x n ).

The main algorithm of Chun–Hui He’s iteration method can be summarized as follows:

  1. Start with an initial guess (x 0) for the root or minimum.

  2. Implement a loop with the update rule x n + 1 = x n – f ( x n ) f ′ ( x n ) until reaching the minimum (convergence) or maximum number of iterations.

  3. To make sure how convergence is attained, one has to check whether the convergence criteria are met (for example, the absolute or relative difference between consecutive iterates is less than some specified threshold value or the function value is close to zero).

  4. In the case of convergence, the current iterate (x n ) is taken as the approximate root for the included function. This method operates on the basis of Newton’s method and it is particularly eloquent for functions with smooth and well-behaved derivatives. However, it may exhibit convergence issues for functions with complex behavior or near singularities. Proper initialization and convergence criteria are important aspects to consider when applying Chun–Hui He’s iteration method [27,28,29].

5 Sponge hash function

Megha Mukundan et al. created the cryptographic construction known as a sponge [30]. It uses an iterated model, processing r bits regarding a message block to produce n bits of output from a state S of b bits. The width of the permutation, or b = r + c ≥ n, represents the sponge state’s size. In the sponge state, the b bits undergo a permutation αb. The message block size or rate is denoted by the Algorithm 1.

Algorithm 1: Photon sponge structure

Input: data input or message

Output: hash blocks

parameter r, whereas the capacity is denoted by the value c [30,31].

Begin

Step 1: In order to make the input length an integral multiple of r, the data input, or message, is padded by adding a 1 bit and as many zeros as necessary.

Step 2: An internal t-bit state made up of an r-bit rate and a c-bit capacity.

Step 3: The permutation P is applied to the t-bit state after mi is XORed with the rate component of the internal state for each of the i iterations.

Step 4: For the squeezing phase, the internal state is divided into r′ and c′ sections, which may differ in length from r and c. This phase produces a sequence of I r′-bit hash blocks z0,., zj-1, zi ← P(zi-1)

There are 12 rounds of four stages in the permutation:

1-AddConstants: The first column of the matrix is XORed with round constants.

2-SubCells: An S-box performs the step of mapping each entry in the matrix by a new value.

3-ShiftRows: Each row’s cell positions are flipped.

4-MixColumnsSerial: Using this function, each column is individually mixed linearly [32,33,34].

End.

6 Maiorana–McFarland algorithm

S-boxes can be created using the Maiorana–McFarland algorithm, which is mostly applied to symmetric-key cryptography methods like block ciphers [35]. The algorithm’s goal is to produce S-boxes that have advantageous crypto-graphic characteristics, like strong non-linearity and resilience to cryptanalysis methods [36,37,38].

Let n be an even positive integer, “f: Z p n → * Z p m ” a function and denote the m output coordinate functions of f by “f = (f1,…, fm).” Assume that every “fi, i = 1, 2, …, m,” is a Maiorana function, i.e., has the form “fi(x) = fi(x1, x2) = πi(x1). xz + gi(xl), P” where πi is a permutation of the space Z,! and g, is a function from Z p n to Z p m . Then, f = (f1, f2, …, fm) is perfect nonlinear if every nonzero linear combination of the permutations “xi, i = 1, 2, …, m” is again a permutation of “Z p n 2 ” [39,40].

7 The proposal system for the digital currency design

Algorithm 2: Proposal system for the digital currency design

Input: Array of numbers, size 16 × 16

Output: SHA-256 hash for each cell in the array

Begin

Step 1: Create a 16 × 16 array of numbers.

Step 2: Fill the array with random numbers in the range of GF(251) using the logistic map random algorithm.

Step 3: Determine the interconnections for each cell by specifying the 1-Top, 2-Down, 3-Left, and 4-Right connections.

Step 4: Determine the value of the top (↑) neighbor for the first cell [0, 0] and assign it to the finite set (X 2) as the top value.

Step 5: Determine the value of the down (↓) neighbor for the first cell [0, 0] and assign it to the finite set (X 2 + 1) as the down value.

Step 6: Determine the value of the left (←) neighbor for the first cell [0, 0] and assign it to the finite set (x + 2) as the left value.

Step 7: Determine the value of the right (→) neighbor for the first cell [0, 0] and assign it to the finite set (x + 1) as the right value.

Step 8: Apply the SHA-256 hash algorithm to each cell in all four directions (Top, Down, Left, and Right).

Step 9: Return the hash value after replacing the S box of the photon sponge with the coupled Chun–Hui He’s iteration and Maiorana–McFarland S box for each cell.

End

1-Build structure size 16 × 16.

2-Fill the structure with random numbers within the Galois field (GF) 251 using the Chun–Hui He’s iteration random algorithm, which can be seen in the next array.

14 10 3 2 11 100 200 209 88 99 12 8 7 0 0 1
2 244 233 230 44 23 97 49 66 65 21 233 23 54 67 78
34 76 89 09 12 56 23 32 45 54 67 90 10 2 9 4
5 4 88 77 45 23 19 200 80 33 67 59 34 76 49 90
41 31 44 51 81 3 2 10 68 99 87 4 3 66 33 12
22 32 24 36 48 5 9 12 22 47 88 98 56 34 23 53
23 97 49 89 09 12 23 97 49 66 12 8 7 0 0 1
56 23 32 88 77 43 56 23 32 45 21 233 23 54 67 78
23 19 200 44 51 66 23 19 200 80 67 90 10 2 9 4
3 2 10 24 36 76 3 2 10 68 67 59 34 76 49 90
12 8 7 0 0 1 23 97 49 66 87 4 3 66 33 12
21 233 23 54 67 78 23 97 89 09 89 98 56 34 23 53
67 90 10 2 9 4 56 23 88 77 88 97 67 90 89 09
67 59 34 76 49 90 23 19 44 51 44 23 67 59 88 77
87 4 3 66 33 12 3 2 24 36 24 19 87 4 44 51
88 98 56 34 23 53 23 97 89 09 89 2 67 90 24 36

3-For each cell, we specify four directions: top, down, right, and left. Then, apply the finite set operations for each direction.

1. top (the top of row 0 is row 15) Top in index 0.0 is 88, then apply finite set operation x2

We select five cells to check:

Top [0, 0] = (88*88) mode 251 = 214

Top [0, 15] = (36*36) mode 251 = 41

Top [0, 3] = (34*34) mode 251 = 152

Top [0, 6] = (23*23) mode 251 = 27

Top [0, 8] = (89*89) mode 251 = 140

Then, this operation is applied to all cells.

The resulting array is as follows:

214 66 124 152 27 48 27 122 140 81 140 4 222 68 74 41
196 100 9 4 121 211 91 7 214 12 144 72 49 0 0 1
4 49 73 190 179 27 122 142 89 209 190 73 27 155 222 60
152 3 66 81 144 124 27 27 17 155 222 68 100 4 81 16
25 16 214 156 17 27 110 91 341 85 222 218 152 3 142 68
175 208 179 91 35 9 4 100 106 12 39 16 9 89 85 144
233 20 74 41 45 25 81 144 233 201 214 66 124 152 27 48
27 122 142 140 81 144 27 122 142 89 144 64 49 0 0 1
124 27 20 214 156 92 124 27 27 17 190 73 27 155 222 60
27 110 91 179 91 89 27 110 91 125 222 68 100 4 81 16
9 4 100 74 41 3 9 4 100 106 222 218 152 3 142 68
144 64 49 0 0 1 27 122 142 89 39 16 9 89 85 144
190 73 27 155 222 60 27 122 140 81 140 66 124 152 27 48
222 68 100 4 81 16 124 27 214 156 214 122 222 68 140 81
222 218 152 3 142 68 27 110 179 91 179 27 222 218 214 156
39 16 9 89 85 144 9 4 74 41 74 110 39 16 179 91

2-Down (the down of row 15 is row 0)

Down 14 is 2, then apply finite set operation x2 + 1

We select five cells randomly to check:

Down [15, 0] = (14*14) + 1 mode 251 = 197

Down [15, 15] = (1*1) + 1 mode 251 = 2

Down [0, 2] = (233*233) + 1 mode 251 = 74

Down [10, 3] = (0*0) + 1 mode 251 = 1

Down [0, 5] = (23*23) + 1 mode 251 = 28

The resulting array is as follows:

5 50 74 191 180 28 123 143 90 210 191 74 28 156 223 61
153 4 141 82 145 125 28 21 18 156 223 69 101 5 82 17
26 17 215 157 18 28 111 92 126 86 223 219 153 4 143 69
176 209 180 92 36 10 5 101 109 13 40 17 10 90 86 145
234 21 75 42 46 26 82 145 234 202 215 67 125 153 28 49
28 123 143 141 82 145 28 123 143 90 145 65 50 1 1 2
125 28 21 215 157 93 125 28 21 90 191 74 28 156 223 61
28 111 92 180 92 90 28 111 92 126 223 69 101 5 82 17
10 5 101 75 42 4 10 5 101 107 223 219 153 4 143 69
145 65 50 1 1 2 28 123 143 90 40 17 10 90 86 145
191 74 28 156 223 61 28 123 141 82 141 67 125 153 28 49
223 69 101 5 52 17 125 28 215 157 215 123 223 69 141 82
223 219 153 4 143 69 28 111 180 92 180 28 223 69 215 157
40 17 10 90 86 145 10 5 75 42 75 111 40 17 180 92
215 67 125 153 28 49 28 123 143 82 143 5 123 69 75 42
197 101 10 5 122 212 92 8 215 13 145 65 50 1 1 2

3-Left (the left of column 0 is column 15)

Left 14 is 1, then apply finite set operation x + 2

Left [0, 0] = (1 + 2) mode 251 = 3

Left [0, 1] = (14 + 2) mode 251 = 16

Left [15, 0] = (36 + 2) mode 251 = 38

Left [6, 0] = (1 + 2) mode 251 = 3

The resulting array is as follows:

3 16 12 5 4 13 102 202 211 90 101 14 10 9 2 2
80 4 246 235 232 46 25 99 51 68 67 23 235 25 56 69
6 36 78 91 11 14 58 25 34 47 56 69 92 12 4 11
92 7 6 90 79 47 25 21 202 82 35 69 61 36 78 51
14 43 33 46 53 83 5 4 12 70 101 89 6 5 68 35
55 24 34 26 38 50 7 11 14 24 49 90 100 58 36 25
3 25 99 51 91 11 14 25 99 51 68 14 10 9 2 2
80 58 25 34 90 79 45 58 25 34 47 23 235 25 56 69
6 25 21 202 46 53 68 25 21 202 82 69 92 12 4 11
11 5 4 12 26 38 78 5 4 12 70 69 61 36 78 51
14 14 10 9 2 2 3 25 99 51 68 89 6 5 68 35
55 23 235 25 56 69 80 25 99 91 11 91 100 58 36 25
11 69 92 12 4 11 6 58 25 90 79 90 99 69 92 91
79 69 61 36 78 51 92 25 21 46 53 46 25 69 61 90
53 89 6 5 68 35 14 5 4 26 38 26 21 89 6 46
38 90 100 58 36 25 55 25 99 91 11 91 4 69 92 26

4-Right (the right of column 15 is column 0)

Right [0, 0] is 10, then apply finite site x + 1

Select cells randomly to check:

Right [0, 0] = (10 + 1) mode 251 = 11

Right [0, 1] = (3 + 1) mode 251 = 4

Right [1, 0] = (244 + 1) mode 251 = 245

Right [0, 14] = (1 + 1) mode 251 = 2

Right [0, 15] = (14 + 1) mode 251 = 15

The resulting array is as follows:

11 4 3 12 101 201 210 89 100 13 9 8 1 1 2 15
245 234 231 45 24 98 50 67 66 22 234 24 55 68 79 3
77 90 10 13 57 24 33 46 55 68 91 11 3 10 5 35
5 89 78 46 24 20 201 81 34 68 60 35 77 50 91 6
32 45 52 82 4 3 11 69 100 89 5 4 67 34 13 42
33 25 37 49 6 10 13 23 48 89 99 57 35 24 54 23
98 50 90 10 13 24 98 50 67 13 9 8 1 1 2 24
24 33 89 78 44 57 24 33 46 22 234 24 55 68 79 57
20 201 45 52 67 24 20 201 81 68 91 11 3 10 5 24
3 11 25 37 77 4 3 11 69 68 60 35 77 50 91 4
9 8 1 1 2 24 98 50 67 88 5 4 67 34 13 13
234 24 54 68 79 4 98 90 10 90 99 57 35 24 54 22
91 11 3 10 5 57 24 89 78 89 98 68 91 90 10 68
60 35 477 50 91 24 20 45 52 45 24 68 60 89 78 68
5 4 67 34 13 4 3 25 37 25 20 88 5 45 52 88
99 57 35 24 54 24 98 90 10 90 3 68 91 25 37 89

4-Apply the hash function for each cell after replacing the S-box of the photon sponge hash function with the S-box constructed using the Maiorana–McFarland algorithm. We need to define a new S-box using the Chun–Hui He’s iteration and the Maiorana–McFarland method and integrate it into the photon sponge hash function, the result after replacing the S box of photon with the S box of MM.

Hash = f (top, down, left, right)

Cell [0, 15] = (41, 61, 2, 15)

SHA-256(41, 61, 2, 15) = 2ds43d61ccf89b7bb57e3d021b0da5a1a6e17a8a85b6ce890ae988af5205b940

Cell [15,15] = (91, 36, 26, 89)

SHA-256(91, 36, 26, 89) = 451a3e11a7a4c684758d1c065fdaf737e56b1a2bfc6bfa7c1b92561beeb67d9f

8 Results and discussion

The proposed system is compared with the traditional photon hash function n and photon hash function proposal algorithm according to several evaluation criteria mentioned. Tables 2 and 3 show this comparison.

Table 2

NIST Test Suite comparison between standard photon hash function and modified photon hash function

Test No. Statistical test name Standard photon Modified Photon
P-value Status P-value Status
1 Approximate entropy 0 Fail 0.421 Pass
2 Block frequency 0.050 Pass 0.556 Pass
3 Cumulative sum 0.876 Pass 0.786 Pass
4 Discrete Fourier transform 0.662 Pass 0.832 Pass
5 Frequency 0.433 Pass 0.671 Pass
6 Linear complexity 0.543 Pass 0.852 Pass
7 Longest run 1.000 Pass 1.000 Pass
8 Non-overlapping template 0.326 Pass 0.474 Pass
9 Overlapping template 0.025 Pass 0.222 Pass
10 Random excursions 0 Fail 0.659 Pass
11 Random excursion variant 0 Fail 0.399 Pass
12 Rank 0 Pass 0.228 Pass
13 Runs 0.132 Pass 0.723 Pass
14 Serial 0 Fail 0.743 Pass
15 Universal 0.044 Pass 0.322 Pass
Table 3

Compression between the standard photon sponge hash function and the modified Photon sponge hash function

Security metrics Traditional present Present proposal
1 – correlation coefficient −0.122251573 −0.30287
2 – entropy of plain text 0.395537806 0.20062288645
3 – entropy of cipher text 0.974489403 0.9936507
4 – bijective property False True
5 – balanced criteria False True
6 – completeness criteria False True
7 – avalanche criteria 60 64
8 – strict avalanche criteria (SAC) 64 64
9 – encryption time 0.000996828 0.000520229339
10 – decryption time 0.001009703 0.001325607299

As shown in Tables 2 and 3, the new method has produced more randomness and security than the standard photon sponge hash function. To enhance security and prevent forgery and replication attempts, the proposed digital currency employed a random (Chun–Hui He’s iteration) filling method to populate the matrix structure. We established interconnections from all directions (Top, Down, Left, and Right) and applied equations from the finite set to derive the values. Additionally, we utilized a hash function (SHA-256) that took the four directions as inputs. This approach strengthened the currency’s resistance against fraudulent activities and unauthorized duplication. The proposed system gave better results than the traditional photon sponge hash function, and the encryption and decryption time was less.

9 Conclusion and future work

Designing a new digital currency requires addressing various challenges, such as scalability, security, decentralization, user adoption, and regulatory compliance. We designed a structure size of 16 × 16 and distributed the numbers randomly using an algorithm (Chun–Hui He’s iteration) to increase randomness. Then, we generated four matrices, each matrix representing the direction (top, down, right, and left), and then encoded the arrays using the (photon sponge hash function) algorithm. Then, we updated the S-box by merging algorithms (Chun–Hui He’s iteration and Maiorana–McFarland) for the purpose of increasing randomness and security so that the theft and forgery process is difficult. A cipher’s cryptographic characteristics, especially its non-linearity, diffusion, and resistance to cryptanalysis, can be improved by combining the Maiorana–McFarland and Chun–Hei He’s iterations. While Chun–Hei He’s iteration can improve the confusion and diffusion qualities through its iterative procedure, the Maiorana–McFarland transformation increases non-linearity by altering the Boolean function representation. When these two methods are used together, the resulting cipher can function more efficiently and with greater security than when they are used separately. The cipher is also more appropriate for secure data transport and storage applications since the combination of these iterations can offer more resilient protection against different cryptanalytic attacks. Future studies could involve improving technical aspects of digital currency, enhancing privacy and security, investigating user experience and adoption as well as improving regulatory framework.

  1. Funding information: Authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and consented to its submission to the journal, reviewed all the results and approved the final version of the manuscript. AMSR and HBA presented the main problem, analyzed it, and developed a simple preliminary plan. AAM implemented the problem programmatically, analyzed the results, applied security and randomness measures.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: Most datasets generated and analyzed in this study are within the manuscript. The other datasets are available on reasonable request from the corresponding author with the attached information.

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Received: 2024-03-13
Revised: 2024-04-30
Accepted: 2024-05-01
Published Online: 2024-10-18

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/eng-2024-0050
Keywords for this article
electronic currency; types of digital currency; Chun–Hui He’s iteration; sponge hash function; Mariorana–McFarland method
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  16. Advanced vibrant controller results of an energetic framework structure
  17. Application of the Taguchi method and RSM for process parameter optimization in AWSJ machining of CFRP composite-based orthopedic implants
  18. Improved correlation of soil modulus with SPT N values
  19. Technologies for high-temperature batch annealing of grain-oriented electrical steel: An overview
  20. Assessing the need for the adoption of digitalization in Indian small and medium enterprises
  21. A non-ideal hybridization issue for vertical TFET-based dielectric-modulated biosensor
  22. Optimizing data retrieval for enhanced data integrity verification in cloud environments
  23. Performance analysis of nonlinear crosstalk of WDM systems using modulation schemes criteria
  24. Nonlinear finite-element analysis of RC beams with various opening near supports
  25. Thermal analysis of Fe3O4–Cu/water over a cone: a fractional Maxwell model
  26. Radial–axial runner blade design using the coordinate slice technique
  27. Theoretical and experimental comparison between straight and curved continuous box girders
  28. Effect of the reinforcement ratio on the mechanical behaviour of textile-reinforced concrete composite: Experiment and numerical modeling
  29. Experimental and numerical investigation on composite beam–column joint connection behavior using different types of connection schemes
  30. Enhanced performance and robustness in anti-lock brake systems using barrier function-based integral sliding mode control
  31. Evaluation of the creep strength of samples produced by fused deposition modeling
  32. A combined feedforward-feedback controller design for nonlinear systems
  33. Effect of adjacent structures on footing settlement for different multi-building arrangements
  34. Analyzing the impact of curved tracks on wheel flange thickness reduction in railway systems
  35. Review Articles
  36. Mechanical and smart properties of cement nanocomposites containing nanomaterials: A brief review
  37. Applications of nanotechnology and nanoproduction techniques
  38. Relationship between indoor environmental quality and guests’ comfort and satisfaction at green hotels: A comprehensive review
  39. Communication
  40. Techniques to mitigate the admission of radon inside buildings
  41. Erratum
  42. Erratum to “Effect of short heat treatment on mechanical properties and shape memory properties of Cu–Al–Ni shape memory alloy”
  43. Special Issue: AESMT-3 - Part II
  44. Integrated fuzzy logic and multicriteria decision model methods for selecting suitable sites for wastewater treatment plant: A case study in the center of Basrah, Iraq
  45. Physical and mechanical response of porous metals composites with nano-natural additives
  46. Special Issue: AESMT-4 - Part II
  47. New recycling method of lubricant oil and the effect on the viscosity and viscous shear as an environmentally friendly
  48. Identify the effect of Fe2O3 nanoparticles on mechanical and microstructural characteristics of aluminum matrix composite produced by powder metallurgy technique
  49. Static behavior of piled raft foundation in clay
  50. Ultra-low-power CMOS ring oscillator with minimum power consumption of 2.9 pW using low-voltage biasing technique
  51. Using ANN for well type identifying and increasing production from Sa’di formation of Halfaya oil field – Iraq
  52. Optimizing the performance of concrete tiles using nano-papyrus and carbon fibers
  53. Special Issue: AESMT-5 - Part II
  54. Comparative the effect of distribution transformer coil shape on electromagnetic forces and their distribution using the FEM
  55. The complex of Weyl module in free characteristic in the event of a partition (7,5,3)
  56. Restrained captive domination number
  57. Experimental study of improving hot mix asphalt reinforced with carbon fibers
  58. Asphalt binder modified with recycled tyre rubber
  59. Thermal performance of radiant floor cooling with phase change material for energy-efficient buildings
  60. Surveying the prediction of risks in cryptocurrency investments using recurrent neural networks
  61. A deep reinforcement learning framework to modify LQR for an active vibration control applied to 2D building models
  62. Evaluation of mechanically stabilized earth retaining walls for different soil–structure interaction methods: A review
  63. Assessment of heat transfer in a triangular duct with different configurations of ribs using computational fluid dynamics
  64. Sulfate removal from wastewater by using waste material as an adsorbent
  65. Experimental investigation on strengthening lap joints subjected to bending in glulam timber beams using CFRP sheets
  66. A study of the vibrations of a rotor bearing suspended by a hybrid spring system of shape memory alloys
  67. Stability analysis of Hub dam under rapid drawdown
  68. Developing ANFIS-FMEA model for assessment and prioritization of potential trouble factors in Iraqi building projects
  69. Numerical and experimental comparison study of piled raft foundation
  70. Effect of asphalt modified with waste engine oil on the durability properties of hot asphalt mixtures with reclaimed asphalt pavement
  71. Hydraulic model for flood inundation in Diyala River Basin using HEC-RAS, PMP, and neural network
  72. Numerical study on discharge capacity of piano key side weir with various ratios of the crest length to the width
  73. The optimal allocation of thyristor-controlled series compensators for enhancement HVAC transmission lines Iraqi super grid by using seeker optimization algorithm
  74. Numerical and experimental study of the impact on aerodynamic characteristics of the NACA0012 airfoil
  75. Effect of nano-TiO2 on physical and rheological properties of asphalt cement
  76. Performance evolution of novel palm leaf powder used for enhancing hot mix asphalt
  77. Performance analysis, evaluation, and improvement of selected unsignalized intersection using SIDRA software – Case study
  78. Flexural behavior of RC beams externally reinforced with CFRP composites using various strategies
  79. Influence of fiber types on the properties of the artificial cold-bonded lightweight aggregates
  80. Experimental investigation of RC beams strengthened with externally bonded BFRP composites
  81. Generalized RKM methods for solving fifth-order quasi-linear fractional partial differential equation
  82. An experimental and numerical study investigating sediment transport position in the bed of sewer pipes in Karbala
  83. Role of individual component failure in the performance of a 1-out-of-3 cold standby system: A Markov model approach
  84. Implementation for the cases (5, 4) and (5, 4)/(2, 0)
  85. Center group actions and related concepts
  86. Experimental investigation of the effect of horizontal construction joints on the behavior of deep beams
  87. Deletion of a vertex in even sum domination
  88. Deep learning techniques in concrete powder mix designing
  89. Effect of loading type in concrete deep beam with strut reinforcement
  90. Studying the effect of using CFRP warping on strength of husk rice concrete columns
  91. Parametric analysis of the influence of climatic factors on the formation of traditional buildings in the city of Al Najaf
  92. Suitability location for landfill using a fuzzy-GIS model: A case study in Hillah, Iraq
  93. Hybrid approach for cost estimation of sustainable building projects using artificial neural networks
  94. Assessment of indirect tensile stress and tensile–strength ratio and creep compliance in HMA mixes with micro-silica and PMB
  95. Density functional theory to study stopping power of proton in water, lung, bladder, and intestine
  96. A review of single flow, flow boiling, and coating microchannel studies
  97. Effect of GFRP bar length on the flexural behavior of hybrid concrete beams strengthened with NSM bars
  98. Exploring the impact of parameters on flow boiling heat transfer in microchannels and coated microtubes: A comprehensive review
  99. Crumb rubber modification for enhanced rutting resistance in asphalt mixtures
  100. Special Issue: AESMT-6
  101. Design of a new sorting colors system based on PLC, TIA portal, and factory I/O programs
  102. Forecasting empirical formula for suspended sediment load prediction at upstream of Al-Kufa barrage, Kufa City, Iraq
  103. Optimization and characterization of sustainable geopolymer mortars based on palygorskite clay, water glass, and sodium hydroxide
  104. Sediment transport modelling upstream of Al Kufa Barrage
  105. Study of energy loss, range, and stopping time for proton in germanium and copper materials
  106. Effect of internal and external recycle ratios on the nutrient removal efficiency of anaerobic/anoxic/oxic (VIP) wastewater treatment plant
  107. Enhancing structural behaviour of polypropylene fibre concrete columns longitudinally reinforced with fibreglass bars
  108. Sustainable road paving: Enhancing concrete paver blocks with zeolite-enhanced cement
  109. Evaluation of the operational performance of Karbala waste water treatment plant under variable flow using GPS-X model
  110. Design and simulation of photonic crystal fiber for highly sensitive chemical sensing applications
  111. Optimization and design of a new column sequencing for crude oil distillation at Basrah refinery
  112. Inductive 3D numerical modelling of the tibia bone using MRI to examine von Mises stress and overall deformation
  113. An image encryption method based on modified elliptic curve Diffie-Hellman key exchange protocol and Hill Cipher
  114. Experimental investigation of generating superheated steam using a parabolic dish with a cylindrical cavity receiver: A case study
  115. Effect of surface roughness on the interface behavior of clayey soils
  116. Investigated of the optical properties for SiO2 by using Lorentz model
  117. Measurements of induced vibrations due to steel pipe pile driving in Al-Fao soil: Effect of partial end closure
  118. Experimental and numerical studies of ballistic resistance of hybrid sandwich composite body armor
  119. Evaluation of clay layer presence on shallow foundation settlement in dry sand under an earthquake
  120. Optimal design of mechanical performances of asphalt mixtures comprising nano-clay additives
  121. Advancing seismic performance: Isolators, TMDs, and multi-level strategies in reinforced concrete buildings
  122. Predicted evaporation in Basrah using artificial neural networks
  123. Energy management system for a small town to enhance quality of life
  124. Numerical study on entropy minimization in pipes with helical airfoil and CuO nanoparticle integration
  125. Equations and methodologies of inlet drainage system discharge coefficients: A review
  126. Thermal buckling analysis for hybrid and composite laminated plate by using new displacement function
  127. Investigation into the mechanical and thermal properties of lightweight mortar using commercial beads or recycled expanded polystyrene
  128. Experimental and theoretical analysis of single-jet column and concrete column using double-jet grouting technique applied at Al-Rashdia site
  129. The impact of incorporating waste materials on the mechanical and physical characteristics of tile adhesive materials
  130. Seismic resilience: Innovations in structural engineering for earthquake-prone areas
  131. Automatic human identification using fingerprint images based on Gabor filter and SIFT features fusion
  132. Performance of GRKM-method for solving classes of ordinary and partial differential equations of sixth-orders
  133. Visible light-boosted photodegradation activity of Ag–AgVO3/Zn0.5Mn0.5Fe2O4 supported heterojunctions for effective degradation of organic contaminates
  134. Production of sustainable concrete with treated cement kiln dust and iron slag waste aggregate
  135. Key effects on the structural behavior of fiber-reinforced lightweight concrete-ribbed slabs: A review
  136. A comparative analysis of the energy dissipation efficiency of various piano key weir types
  137. Special Issue: Transport 2022 - Part II
  138. Variability in road surface temperature in urban road network – A case study making use of mobile measurements
  139. Special Issue: BCEE5-2023
  140. Evaluation of reclaimed asphalt mixtures rejuvenated with waste engine oil to resist rutting deformation
  141. Assessment of potential resistance to moisture damage and fatigue cracks of asphalt mixture modified with ground granulated blast furnace slag
  142. Investigating seismic response in adjacent structures: A study on the impact of buildings’ orientation and distance considering soil–structure interaction
  143. Improvement of porosity of mortar using polyethylene glycol pre-polymer-impregnated mortar
  144. Three-dimensional analysis of steel beam-column bolted connections
  145. Assessment of agricultural drought in Iraq employing Landsat and MODIS imagery
  146. Performance evaluation of grouted porous asphalt concrete
  147. Optimization of local modified metakaolin-based geopolymer concrete by Taguchi method
  148. Effect of waste tire products on some characteristics of roller-compacted concrete
  149. Studying the lateral displacement of retaining wall supporting sandy soil under dynamic loads
  150. Seismic performance evaluation of concrete buttress dram (Dynamic linear analysis)
  151. Behavior of soil reinforced with micropiles
  152. Possibility of production high strength lightweight concrete containing organic waste aggregate and recycled steel fibers
  153. An investigation of self-sensing and mechanical properties of smart engineered cementitious composites reinforced with functional materials
  154. Forecasting changes in precipitation and temperatures of a regional watershed in Northern Iraq using LARS-WG model
  155. Experimental investigation of dynamic soil properties for modeling energy-absorbing layers
  156. Numerical investigation of the effect of longitudinal steel reinforcement ratio on the ductility of concrete beams
  157. An experimental study on the tensile properties of reinforced asphalt pavement
  158. Self-sensing behavior of hot asphalt mixture with steel fiber-based additive
  159. Behavior of ultra-high-performance concrete deep beams reinforced by basalt fibers
  160. Optimizing asphalt binder performance with various PET types
  161. Investigation of the hydraulic characteristics and homogeneity of the microstructure of the air voids in the sustainable rigid pavement
  162. Enhanced biogas production from municipal solid waste via digestion with cow manure: A case study
  163. Special Issue: AESMT-7 - Part I
  164. Preparation and investigation of cobalt nanoparticles by laser ablation: Structure, linear, and nonlinear optical properties
  165. Seismic analysis of RC building with plan irregularity in Baghdad/Iraq to obtain the optimal behavior
  166. The effect of urban environment on large-scale path loss model’s main parameters for mmWave 5G mobile network in Iraq
  167. Formatting a questionnaire for the quality control of river bank roads
  168. Vibration suppression of smart composite beam using model predictive controller
  169. Machine learning-based compressive strength estimation in nanomaterial-modified lightweight concrete
  170. In-depth analysis of critical factors affecting Iraqi construction projects performance
  171. Behavior of container berth structure under the influence of environmental and operational loads
  172. Energy absorption and impact response of ballistic resistance laminate
  173. Effect of water-absorbent polymer balls in internal curing on punching shear behavior of bubble slabs
  174. Effect of surface roughness on interface shear strength parameters of sandy soils
  175. Evaluating the interaction for embedded H-steel section in normal concrete under monotonic and repeated loads
  176. Estimation of the settlement of pile head using ANN and multivariate linear regression based on the results of load transfer method
  177. Enhancing communication: Deep learning for Arabic sign language translation
  178. A review of recent studies of both heat pipe and evaporative cooling in passive heat recovery
  179. Effect of nano-silica on the mechanical properties of LWC
  180. An experimental study of some mechanical properties and absorption for polymer-modified cement mortar modified with superplasticizer
  181. Digital beamforming enhancement with LSTM-based deep learning for millimeter wave transmission
  182. Developing an efficient planning process for heritage buildings maintenance in Iraq
  183. Design and optimization of two-stage controller for three-phase multi-converter/multi-machine electric vehicle
  184. Evaluation of microstructure and mechanical properties of Al1050/Al2O3/Gr composite processed by forming operation ECAP
  185. Calculations of mass stopping power and range of protons in organic compounds (CH3OH, CH2O, and CO2) at energy range of 0.01–1,000 MeV
  186. Investigation of in vitro behavior of composite coating hydroxyapatite-nano silver on 316L stainless steel substrate by electrophoretic technic for biomedical tools
  187. A review: Enhancing tribological properties of journal bearings composite materials
  188. Improvements in the randomness and security of digital currency using the photon sponge hash function through Maiorana–McFarland S-box replacement
  189. Design a new scheme for image security using a deep learning technique of hierarchical parameters
  190. Special Issue: ICES 2023
  191. Comparative geotechnical analysis for ultimate bearing capacity of precast concrete piles using cone resistance measurements
  192. Visualizing sustainable rainwater harvesting: A case study of Karbala Province
  193. Geogrid reinforcement for improving bearing capacity and stability of square foundations
  194. Evaluation of the effluent concentrations of Karbala wastewater treatment plant using reliability analysis
  195. Adsorbent made with inexpensive, local resources
  196. Effect of drain pipes on seepage and slope stability through a zoned earth dam
  197. Sediment accumulation in an 8 inch sewer pipe for a sample of various particles obtained from the streets of Karbala city, Iraq
  198. Special Issue: IETAS 2024 - Part I
  199. Analyzing the impact of transfer learning on explanation accuracy in deep learning-based ECG recognition systems
  200. Effect of scale factor on the dynamic response of frame foundations
  201. Improving multi-object detection and tracking with deep learning, DeepSORT, and frame cancellation techniques
  202. The impact of using prestressed CFRP bars on the development of flexural strength
  203. Assessment of surface hardness and impact strength of denture base resins reinforced with silver–titanium dioxide and silver–zirconium dioxide nanoparticles: In vitro study
  204. A data augmentation approach to enhance breast cancer detection using generative adversarial and artificial neural networks
  205. Modification of the 5D Lorenz chaotic map with fuzzy numbers for video encryption in cloud computing
  206. Special Issue: 51st KKBN - Part I
  207. Evaluation of static bending caused damage of glass-fiber composite structure using terahertz inspection
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