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Investigations on Application of Probabilistic and Mathematical 

Computing in Design and Statistical Analysis of Lightweight 

Cryptography  
 

Bhawna Garg1, Raghavendra Patidar2 

1 Research Scholar, Department of Electronics and Communication Engineering, University of Technology, 

Jaipur, India   

2 Professor, Department of Electronics and Communication Engineering, Arya College of Engineering & IT, 

Jaipur, India 

Email: hibhawna21@gmail.com , raghavendrapatidar@gmail.com  

 

Article History: 

Received: 06-02-2024 

Revised: 24-04-2024 

Accepted: 08-05-2024 

Abstract:  

 This research provides in-depth investigation into the application and role of 

probability and mathematics in lightweight cryptography featuring IoT software. The 

IoT device fleet growth is continuously accompanied by its resources, often poor. It 

creates a critical need for cryptographic solutions that will be effective and a heavy 

burden. The research article underlines the use of latest probabilistic models and 

mathematical concepts to create cryptographic algorithms that are cryptographically 

powerful and IoT-embedded devices can process them. The study commences with its 

deep mathematics investigation and focuses on consequently essential permutations, 

combinations, modular arithmetic and prime number theory, all of which represents the 

cornerstone of strong cryptographic algorithms development. The article then proceeds 

to demonstrate the use of probabilistic tools for scrutinizing the security and the 

effectiveness of these algorithms. A novel approach to grasping the vulnerabilities that 

may occur in the course of cryptographic implementations is also brought to light. A 

remarkable part of the investigation is toward designing small-sized cryptographic 

algorithms by using methods of mathematics computations to decrease the size of key, 

complexity and implementations of increased safety margin. The research process 

involves a thorough statistical demonstration of the algorithmic performance in several 

agendas of IoT exposing the resistance of the algorithms against cryptographic issues 

and the intensity of their resource consumption on ordinary IoT devices. By conducting 

these investigations, the paper contributes a lot of useful information on the harmonious 

relationship between probability methods, mathematical computing, and cryptographic 

development as well as providing the solid foundation for creating a lightweight 

cryptography which can be used in the Internet of Things (IoT) and other similar 

environments that have their unique needs and constraints. However, it not only 

advances the field of cryptography itself, but also outlines a practical roadmap on how 

to design secure, efficient cryptosystems, that can be used in its subsequent applications 

in the small but fast growing IoT technology landscape. 

Keywords: Lightweight Encryption, Iot Security, Histogram Analysis, Correlation 

Analysis, Entropy Analysis, NPCR, UACI, Execution Time, Memory Usage, 

Reversible Data Hiding, Digital Images, Cryptographic Algorithm, Differential 

Attacks, Resource Efficiency, Digital Media Security. 

 

 



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1. INTRODUCTION 

The Internet of Things (IoT) has gained popularity in recent decades. It is imperative that the 

internet ensures the security, reliability, and stability of its applications. Internet users should 

also possess a significant amount of confidence in the programs they are employing. The stage 

provides a vast perspective on utilizing the internet for many purposes, and the Internet of 

Things (IoT) presents the opportunity to remotely control and manage any object or system 

over the internet. However, if we rely on technology for all our needs, we must also consider 

whether we can trust the internet for everything, especially for security reasons. The 

applications we use should be reliable, and the data we exchange should be protected from any 

form of hacking or attacks. Any device connected to the internet should include adequate 

security measures to ensure its safe usage. If the customers lack faith in the system they are 

connected to, it would lead to their reluctance to use the internet and undermine the entire 

concept. Currently, the Internet of Things (IoT) is being used extensively in many industries 

and for a wide range of applications. Therefore, ensuring the security of IoT is of utmost 

importance and significance. With the increasing use of the internet, the network is becoming 

more susceptible to threats. Insufficiently validated online platforms or inadequately validated 

devices might pose a threat to an individual's privacy. Verification of the internet is necessary 

to provide security for clients. In addition to inadequate security measures, the proliferation of 

Internet of Things (IoT) devices further amplifies the risk of a cyber-attack. When poorly 

secured devices connected to the internet are paired with the concept of IoT devices, it 

negatively impacts the security of the global internet. For example, if an unsecured television 

in India becomes infected with a virus, it may transmit a significant number of harmful 

messages to users using the owner's home Wi-Fi connection. When discussing the economy, 

the lack of security in the Internet of Things (IoT) has a detrimental impact, particularly when 

one party incurs a financial loss at the expense of others. One such example is environmental 

pollution, when the expenses of pollution and cleanup incurred by a polluter are borne by 

multiple parties. Currently, the problem lies in the fact that the costs imposed on others are not 

often included in the decision-making process until the polluter takes responsibility for 

reducing the amount of pollution they are causing. During the assessment of data security, a 

situation may arise when the manufacturer of a product refuses to bear the costs associated with 

any vulnerabilities. In such cases, the law might compel the manufacturer to address the 

security concerns. Such considerations are common in the field of information technology, but, 

there are specific challenges related to security that arise for Internet of Things (IoT) devices, 

which are discussed below. Several questions arise when discussing the security of devices 

connected to the Internet of Things. Some of the important queries regarding internet security 

are as follows: [4][8] 

The issue of Cost and the Security Trade-Off involves considering how stakeholders might 

make cost-benefit decisions for Internet of Things devices. How can we systematically assess 

the risks associated with security issues? What motivates gadget developers and producers to 

accept the additional expense of implementing enhanced security measures in IoT-based 

devices? How can compatibility between functionality, usability, and security be achieved in 



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IoT devices? How can we obtain the validation of IOT security solutions to enhance the 

opportunities for IOT's social and economic advancement? [1][6] 

The vision of these questions represents the extensive security considerations associated with 

Internet of Things devices. However, it is important to remember that when a device is 

connected to the Internet, it becomes part of the Internet. This means that effective and 

improved security measures can be implemented if the users of IoT devices adopt a 

comprehensive security approach. Obtaining the answers to the aforementioned questions can 

greatly enhance the security of internet of things devices. Effective solutions to security 

concerns can only be achieved through a collaborative approach to system security and safety, 

with active participation from users who remain vigilant about the security issues affecting 

their devices and networks. The communitarian paradigm is highly effective for ensuring 

security and is widely used by many sectors to provide device security. 

Creating lightweight cryptography for IoT security involves the use of various mathematical 

tools, including permutation and combination, to develop efficient cryptographic algorithms 

suitable for devices with limited computational resources.[11] 

Basic permutation equation: 

𝑃(𝑛, 𝑘) =
𝑛!

(𝑛 − 𝑘)
 

Combination formula: 

𝐶(𝑛, 𝑘) =
𝑛!

𝑘(𝑥 − 𝑘]!
 

Permutations and combinations are fundamental in cryptography for understanding possible 

configurations, which is crucial in determining the strength of cryptographic mechanisms. 

Permutation, P(n,k), calculates the number of ways k objects can be ordered from a set of n. 

Combination, C(n,k), on the other hand, calculates the number of ways to choose k objects from 

a set of n regardless of the order. These concepts are vital in algorithm design, particularly in 

creating secure cryptographic keys.[35-40] 

Binomial theorem: 

(𝑥 + 𝑦)𝑛 = ∑  

𝑛

𝑘−0

𝐶(𝑛, 𝑘)𝑥𝑛−𝑘𝑦𝑘 

Factorial definition: 

𝑛! = 𝑛 × (𝑛 − 1) × (𝑛 − 2) × … × 2 × 1 

Euler's totient function: 

𝜙(𝑛) = 𝑛 ∏  

𝑟

𝑖−1

(1 −
1

𝕄
) 

Modular arithmetic addition: 

(𝑎 + 𝑏)mod𝑛 = ((𝑎mod𝑛) + (𝑏mod𝑛))mod𝑛 

 



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Modular arithmetic multiplication: 

(𝑎 × 𝑏)mod𝑛 = ((𝑎mod𝑛) × (𝑏mod𝑛))mod𝑛 

The binomial theorem provides a powerful way to expand expressions that are raised to a 

power. In cryptography, this theorem can be used in algorithm design, particularly in modular 

arithmetic and polynomial expansions, which are common in cryptographic functions and 

error-correcting codes.[7][9] 

The factorial function, denoted as n! is essential in computing permutations and combinations. 

It signifies the product of an integer and all the integers below it, which is crucial in determining 

the total number of possible outcomes in various cryptographic scenarios.[11][13] 

Chinese Remainder Theorem: 

𝑥 ≡ 𝑎1(mod𝑚1)

𝑥 ≡ 𝑎2(mod𝑚2)

 ⋮
𝑥 ≡ 𝑎𝑛(mod𝑚𝑛)

 

Euler's totient function, ϕ(n), is significant in cryptography, particularly in RSA encryption. It 

counts the positive integers up to a given integer n that are relatively prime to n. It's crucial in 

determining the group size for the multiplicative group of integers modulo n, which is a 

foundational aspect of RSA's public key setup. 

Modular arithmetic is the cornerstone of many cryptographic algorithms. It deals with integers 

and operates within the confines of a modulus, enabling cyclic structures crucial for encryption 

and decryption processes. It ensures that cryptographic operations can be efficiently computed, 

even with very large numbers. 

The Chinese Remainder Theorem (CRT) is pivotal in optimizing computations in 

cryptographic algorithms like RSA. CRT allows the breaking down of a large modulus 

operation into smaller, more manageable parts, significantly improving algorithm efficiency, 

which is crucial for lightweight cryptography in IoT. [15] 

5 

Extended Euclidean algorithm: 

𝑎𝑥 + 𝑏𝑦 = god (𝑎, 𝑏) 

Fermat's little theorem: 

𝑎𝑝−1 ≡ 1(mod𝑝) 

Euler's theorems 

𝑎−(𝑛) ≡ 1(mod𝑛) 

Carmichael's theorem: 

𝑎ℎ(𝑛] ≡ 1(mod𝑛) 

Discrete logarithm: 

𝑎2 ≡ 𝑏(mod𝑛) 

Diffie-Hellman key exchange: 



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𝐾 = 𝑔𝑎𝑏mod𝑝 

RSA public key: 

𝑒 ∈ {1,2, … , 𝜙(𝑛) − 1}

gcd (𝑒, 𝜙(𝑛)) = 1
 

RSA private key: 

𝑑 ≡ 𝑒−1(mod𝜙(𝑛)) 

RSA encryption: 

𝑐 ≡ 𝑚2(mod𝑛) 

RSA decryption: 

𝑚 ≡ 𝑐𝐼(mod𝑛) 

RSA encryption: 

𝑐 ≡ 𝑚𝑛(mod𝑛) 

RSA decryption: 

𝑚 ≡ 𝑐𝑙(mod𝑛) 

AES S-box transformation: 

𝑆[𝑥] =  SubBytes (𝑥) 

 

AES Round function: 

Round (𝑠, 𝑘) = AddRoundKey ( MixColumns(ShiftRows(SubBytes( 𝑠)))), 𝑘) 

Stream cipher encryption: 

𝑐𝑖 = 𝑚𝑖 ⊕ 𝑘𝑖 

Stream cipher decryption: 

𝑚𝑖 = 𝑐𝑖 ⊕ 𝑘𝑖 

Hash function property (collision resistance): 

𝐻(𝑥) = 𝐻(𝑦) ⟹ 𝑥 = 𝑦 

Merkle-Damgaird construction: 

𝐻(𝑀) = 𝐻(𝐻(𝐻(𝐻(𝐼𝑉, 𝑚1), 𝑚2), … ), 𝑚𝑛) 

Digital signature (signing): 

𝜃 = Sigpiv  (𝑚) 

Digital signature (verification): 

 Verify 
pos 

(𝑚, 𝜎) 

Elliptic curve point addition: 

𝑃 + 𝑄 = 𝑅 

Elliptic curve doubling: 

2𝑃 = 𝑅 



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Elliptic curve scalar multiplication: 

𝑘𝑃 = 𝑃 + 𝑃 + ⋯ + 𝑃(𝑘 times ) 

Shared secret = 𝑥𝑃 × 𝑦𝑄 

ECDSA signature generation: 

(𝑟, 𝑠) = ECDSA𝜇rir (𝑚) 

ECDSA signature verification: 

Verify1, (𝑚, (𝑟, 𝑘)) 

Fermat’s Little Theorem and Euler's Theorem are instrumental in public key cryptography. 

They provide the mathematical basis for many cryptographic protocols, ensuring that 

operations are reversible only with the correct key, a principle essential for secure encryption 

and decryption.[17] 

Carmichael's theorem is used to determine the smallest integer m such that m≡1(modn) for all 

integers a that are relatively prime to n. This theorem finds applications in improving the 

efficiency and security of cryptographic algorithms. 

The discrete logarithm problem is a hard problem that underpins the security of many 

cryptographic algorithms. It is a problem that is computationally difficult to solve, providing 

the security foundation for cryptographic schemes like Diffie-Hellman and ECC. 

The Diffie-Hellman algorithm allows two parties to establish a common secret key over an 

insecure channel, which is a fundamental process in secure communications. It leverages the 

difficulty of the discrete logarithm problem to ensure security. 

The RSA algorithm is a widely used public key cryptographic system that leverages the 

properties of prime numbers and modular arithmetic. It involves key generation, encryption, 

and decryption processes, with security based on the difficulty of factoring large prime 

numbers. Creating a cryptographic algorithm for IoT security involves understanding various 

mathematical principles and their application in the realm of cryptography. This extensive 

explanation will delve into the foundational concepts represented by the 35 equations listed 

above and elaborate on how these principles contribute to the development of a cryptographic 

algorithm, especially for the lightweight requirements of IoT devices. 

The Extended Euclidean Algorithm is fundamental in computing the multiplicative inverse in 

modular arithmetic, an operation central to algorithms like RSA. It's used to find integers which 

is essential for key generation and decryption processes. The Advanced Encryption Standard 

(AES) is a symmetric key encryption algorithm, crucial for securing data. It includes steps like 

SubBytes, ShiftRows, MixColumns, and AddRoundKey, each contributing to the cipher's 

strength by ensuring adequate confusion and diffusion. 

Stream ciphers encrypt plaintext digits one at a time, using a cryptographic key and a 

deterministic algorithm. They are crucial for scenarios where speed and efficiency are 

paramount, and their security often relies on the unpredictability of the key stream. Hash 

functions and digital signatures are vital for data integrity and authentication. Hash functions 

like the Merkle–Damgård construction ensure that any change to data is detectable, while 

digital signatures provide a means to verify the authenticity and integrity of a message. ECC is 



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a public key cryptography approach that offers high security with smaller key sizes, making it 

ideal for IoT devices. It involves operations on points on an elliptic curve, providing a compact 

yet secure mechanism for encryption, key exchange, and digital signatures.[18] 

Creating a Cryptographic Algorithm for IoT: 

1. Requirement Analysis: Understand the security needs and resource constraints of IoT 

devices. 

2. Algorithm Design: Use the mathematical principles outlined to design cryptographic 

processes that are efficient and secure. For IoT, focus on algorithms that require less 

computational power and memory. 

3. Implementation: Convert the mathematical models into code, ensuring that the 

implementation is optimized for the limited resources of IoT devices. 

4. Testing and Evaluation: Rigorously test the algorithm for security vulnerabilities and 

performance efficiency, ensuring it meets the required security standards without 

overburdening the IoT device. 

5. Deployment: Integrate the algorithm into IoT devices, ensuring that they can securely 

communicate and operate within their intended environments. 

By leveraging the mathematical foundations discussed and adhering to a meticulous design and 

implementation process, one can develop robust cryptographic algorithms tailored for the 

unique requirements of IoT security. 

 

2. LITERATURE SURVEY 

The literature review focuses on the burgeoning field of digital watermarking within the context 

of IoT security, highlighting the advancements and methodologies proposed by various 

researchers to enhance the robustness and efficiency of watermarking techniques. 

Wen Zhang et al. (2018) delve into watermarking technology, emphasizing a three-stage 

process encompassing generation, extraction, and identification of watermarks. Their study 

underscores the delicate balance between invisibility and robustness, particularly against 

printing-scanning attacks, and the pivotal role of color space transformation in this context. 

David-Octavio Muñoz-Ramirez et al. (2018) present a robust watermarking framework using 

Discrete Cosine Transform (DCT) and Quantization Index Modulation (QIM) for color 

watermark representation. Their method encodes watermarks in a way that ensures both high 

imperceptibility and robustness, demonstrating superior resilience against common attacks 

compared to traditional techniques. 

Anirban Patra et al. (2018) introduce a novel invisible watermarking technique employing 

alpha blending, focusing on the concealment of watermark images within main images using 

various alpha values. This method, applicable to both color and grayscale images, shows 

promise for image steganography, particularly after post-processing. 

Aoshuang Dong et al. (2017) propose a watermark embedding technique aimed at 3D model 

protection, showcasing its resistance to rotation, translation, and noise attacks. Their method, 



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based on principal component analysis and projection selection, emphasizes the watermark's 

invisibility in 3D models. 

Enjian Bai et al. (2017) introduce a novel clock-controlled generator technique for digital 

image watermarking, highlighting its effectiveness against common attacks and its reliance on 

pseudo-random characteristics like large periods and high linear complexity for performance. 

Oleg Evsutin et al. (2017) discuss an algorithm that embeds digital watermarks using block 

quantization of DWT coefficients, focusing on energy redistribution during the quantization 

process to enhance the quality of embedded regions and facilitate the detection of 

modifications. 

Ritu Gill et al. (2017) propose a combined DCT and 2DWT approach for grey image 

watermarking, showing significant improvements in data hiding and resistance to third-party 

interference, thereby bolstering image authentication and protection. 

Mohammad Shahab Goli et al. (2017) tackle the challenge of cropping attacks with a novel 

method using Sudoku tables to scatter watermarked images, enhancing the watermark's 

resistance and enabling image reconstruction post-attack. 

Muhammad Usman et al. (2017) introduce a lightweight encryption algorithm, SIT, designed 

for IoT security, emphasizing its efficiency and the balance between security and 

computational demand, particularly in the context of IoT applications. 

Noor Zaman et al. (2018) propose a lightweight authentication model for e-health IoT 

applications, employing ECC principles to ensure security while maintaining energy and 

computational efficiency. 

Muhammad Naveed Aman et al. (2017) discuss a strong authentication protocol for IoT 

systems utilizing physical unclonable functions, offering protection against a range of attacks 

while being resource-efficient. 

These studies collectively advance the digital watermarking domain, presenting innovative 

approaches to enhance the security, robustness, and efficiency of watermarking in various 

digital and IoT contexts. They reflect a significant stride toward securing digital assets and IoT 

ecosystems, employing a blend of mathematical rigor, computational efficiency, and practical 

relevance to address the multifaceted challenges of modern digital security. 

 

3. PROPOSED METHODOLOGY 

The methodology for developing a lightweight encryption algorithm for loT-based devices 

involves a series of systematic steps that ensure the security mechanism is not only robust but 

also efficient and resource-conservative. The steps in this methodology include key expansion, 

key management, encryption, decryption, and performance analysis, each integral to the 

creation of a secure and effective cryptographic solution for loT environments. 

 



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Fig 1. Flow Chart of Methodology 

Key expansion is a critical initial step in generating unique keys for encryption and decryption. 

The process involves transforming a short, initial key into an array of keys for each encryption 

round. The key expansion aims to produce a series of round keys from the initial key using 

operations like 𝑋𝑂𝑅, rotations, and substitutions to ensure that each round has a unique key, 

thereby enhancing security. Mathematically, the key expansion can be represented as follows: 

𝐾expanded = 𝑓(𝐾original , Transformations )𝐾𝑟 = 𝐾𝑟−1 ⊕ 𝑔(𝐾𝑟−𝑁 , 𝑟) 

where 𝐾expanded  is the expanded key, 𝐾original  is the original key, 𝐾𝑟 is the round key, 𝑁 is the 

key length, and 𝑔 is a transformation function involving XOR, substitutions, and rotations. 

 

 

Key Expansion Transformation: 

𝐾𝑖 − 𝐾𝑖−1 ⊕ 𝑇(𝐾𝑖−𝑁) 

Where 𝐾𝑖 is the current round key, 𝐾𝑖−1 is the previous round key, 𝑁 is the key length, and 𝑇 

is a transformation function. 

 

Round Key Selection: 

𝐾𝑟 − 𝐾expanded [𝑟 ⋅ 𝑁: (𝑟 + 1) ⋅ 𝑁 − 1] 

 

Where 𝐾𝑟 is the round key for round 𝑟, and 𝐾expanded  is the expanded key. 

 

 

Key Expansion 
Block

Key Management 
Protocol

Encryption Block

Decryption Block

Performance
Evaluation



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Encryption Function: 

𝐶𝑖 − 𝐸(𝐾, 𝑃𝑖) − 𝑃𝑖 ⊕ 𝐾𝑖 

Where 𝐶𝑖 is the ciphertext block, 𝑃𝑖 is the plaintext block, and 𝐾𝑖 is the round key. 

 

 Decryption Function: 

𝑃𝑖 − 𝐷(𝐾, 𝐶𝑖) − 𝐶𝑖 ⊕ 𝐾𝑖 

Where 𝑃𝑖 is the plaintext block, 𝐶𝑖 is the ciphertext block, and 𝐾𝑖 is the round key. 

 

Substitution Box (S-Box) Application: 

𝑆[𝑃𝑖] 

Where 𝑆 is the S-Box and 𝑃𝑖 is the input to the S-Box 

 

Permutation Box (P-Box) Application: 

𝑃[𝐶𝑖] 

Where 𝑃 is the P-Box and 𝐶𝑖 is the input to the P-Box. 

 

Key XOR Operation: 

𝐾𝑖 − 𝐾𝑖−1 ⊕ 𝐾𝑖−𝑁 

Where 𝐾𝑖 is the current key, 𝐾𝑖−1 is the previous key, and 𝐾𝑖−𝑁 is the N-th previous key. 

 

Steganographic Embedding Function: 

𝑆 − 𝑓𝐸𝑚(𝐶, 𝐶𝐼, 𝐾) 

Where 𝑆 is the stego data, 𝐶 is the cover data, 𝐶𝐼 is the critical information, and 𝐾 is the secret 

key. 

 

Steganographic Extraction Function: 

𝐶𝐼 − 𝑓𝐸𝑥(𝑆, 𝐾) 

Where 𝐶𝐼 is the extracted critical information, 𝑆 is the stego data, and 𝐾 is the secret key. 

 

Left Shift Operation: 

𝐿𝑆(𝐾, 𝑛) − (𝐾 << 𝑛) ⊕ (𝐾 >> (𝑁 − 𝑛)) 

Where 𝐿𝑆 is the left shift operation, 𝐾 is the key, 𝑛 is the number of bits to shift, and 𝑁 is the 

key size in bits. 

 

Right Shift Operation: 

𝑅𝑆(𝐾, 𝑛) − (𝐾 >> 𝑛) ⊕ (𝐾 << (𝑁 − 𝑛)) 



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Where 𝑅𝑆 is the right shift operation, 𝐾 is the key, 𝑛 is the number of bits to shift, and 𝑁 is the 

key size in bits. 

 

 XOR Operation for Encryption: 

𝐶𝑖 − 𝑃𝑖 ⊕ 𝐾𝑖 

Where 𝐶𝑖 is the ciphertext, 𝑃𝑖 is the plaintext, and 𝐾𝑖 is the key. 

 

XOR Operation for Decryption: 

𝑃𝑖 − 𝐶𝑖 ⊕ 𝐾𝑖 

Where 𝑃𝑖 is the plaintext, 𝐶𝑖 is the ciphertext, and 𝐾𝑖 is the key. 

 

Key Derivation Function: 

𝐾derived − 𝐾𝐷𝐹(𝐾, salt ) 

Where 𝐾derived  is the derived key, 𝐾𝐷𝐹 is the key derivation function, 𝐾 is the initial key, and 

salt is a random value. 

 

Composite Function for Encryption: 

𝐶𝑖 − 𝑃𝑖 ⊕ 𝐾𝑖 ⊕ 𝑆[𝑃𝑖] ⊕ 𝑃[𝐶𝑖] 

Where 𝐶𝑖 is the ciphertext, 𝑃𝑖 is the plaintext, 𝐾𝑖 is the key, 𝑆 is the S-Box, and 𝑃 is the P-Box. 

These equations form the mathematical backbone of the described methodology, providing a 

structured approach to developing a lightweight cryptographic algorithm suitable for IoT 

devices, focusing on key aspects like key expansion, encryption/decryption processes, and the 

integration of steganographic techniques for enhanced security. 



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Fig 2 Mathematical Formulation of Key Generation 

Key Management: 

Key management is essential for securely storing, exchanging, and updating cryptographic 

keys. It involves protocols to ensure keys are exchanged securely, possibly employing 

lightweight cryptographic protocols like LEAP in IOT . The management ensures that keys 

remain confidential and integral throughout their lifecycle. The process can involve personal, 

group,  

 

 

 



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Encryption Process: 

The encryption process: transforms plaintext into ciphertext using the key generated. It 

involves several operations to ensure the date's confidentiality. These operations can induced 

logical the dats. The encryption process for 𝑎 block of dats can be represented a: 

𝐶𝑖 = 𝐸(𝐾, 𝑃i) 

where 𝐶𝑖 is the ciphertect, 𝐸 is the encryption function, 𝐾 is the key, and 𝑃𝑖 is the plainted 

block. 

 

Fig 3 Generation of Text through Mathematical Operations 

Decryption Process: 

Decryption is the reverse process of encryption, converting ciphertext back into readable 

plaintext using the decryption key. The decryption process must precisely invert the steps of 

the encryption process to retrieve the original dats. For a block cipher, the decryption process 

can be represented as: 



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𝑃1 = 𝐷(𝐾, 𝐶𝑖) 

where 𝑃𝑖 is the plaintext, 𝐷 is the decryption function, 𝐾 is the 𝑘1𝑦1 and 𝐶𝑖 is the ciphertext 

block. 

Performance Analysis: 

This step involves evaluating the cryptographic system’s efficiency, security, and resource 

utilization. The analysis includes assessing the algorithm's resistance to various attacks, its 

computational requirement, and its adoptability to the constrained environments of lot devices. 

 

Crypto-Stego System for Secure Reversible Data Hiding: 

This system combines topographic and steganographic techniques to hide critical information 

(C) within non-critical cover data ( 𝐶 ), enhancing security. The embedding and extraction 

process can be represented as: 

𝑆 = ∫  
𝐸𝑚𝑚

(𝐶, 𝐶𝐼, 𝐾)𝐶𝐼 = ∫  
𝐸𝑥

(𝑆, 𝐾) 

where 𝑆 is the stego deta, 𝑓𝐸𝑚
 is the embedding function, 𝑓𝐸𝑥

 is the extraction function, 𝐶𝐼 is 

the critical information, 𝐶 is the cover data, and 𝐾 is the secret hey. 

In the proposed methodology, cryptographic operations are complemented by steganographic 

techniques, ensuring that the critical information is securely hidden within the cover data, 

thereby providing an additional layer of security. The combination of cryptographic and 

steganographic methods in IoT devices aims to create a robust defense mechanism against 

unauthorized access and data breaches, considering the limited computational and energy 

resources available in such environments. 

 

4. RESULT ANALYSIS 

The theoretical results section delves into the intricate details of the performance analysis of a 

newly introduced lightweight encryption algorithm, tailored for various image formats to gauge 

its effectiveness and efficiency across different metrics such as histogram, correlation, entropy, 

NPCR/UACI analysis, execution time, memory usage, and reversible data hiding capabilities. 



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Fig 4 Generation of Text through Mathematical Operations 

Histogram Analysis: 

The histogram analysis serves as a critical tool in evaluating the uniformity of pixel intensity 

distribution in encrypted images compared to their original counterparts. Ideally, the encrypted 

image should exhibit a uniform distribution to mask any potential clues about the original 

image, thereby enhancing security. This uniformity is crucial for thwarting any attempt to 

deduce the original content through statistical analysis. 

Correlation Analysis: 

The correlation analysis assesses the relationship between adjacent pixels in both original and 

encrypted images. For a robust encryption algorithm, the correlation in encrypted images 

should be negligible, indicating a successful disruption of discernible patterns present in the 

original image. Lower correlation values in encrypted images signify better encryption 

strength, reducing susceptibility to attacks. 

Table 1. Correlation Analysis Table 

Format Correlation Original Correlation Encrypted 

JPEG 0.9557 0.0015 

JPEG-2000 0.9615 0.0014 

GIF 0.9455 0.0009 

PNG 0.9815 0.0004 

BMP 0.9615 0.0003 

Entropy analysis measures the randomness or unpredictability in the encrypted images, which 

should ideally be high to ensure that the encryption provides substantial obscurity. Higher 

entropy values in encrypted images indicate better security, as they signify less predictability 

and more randomness. 



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Table 2. Entropy Analysis Table 

Type of Image Entropy Encrypted Image Entropy Decrypted Image 

JPEG 7.70 7.58 

JPEG-2000 7.98 7.79 

PNG 7.98 7.76 

BMP 7.98 7.86 

GIF 7.98 7.66 

 

NPCR and UACI values are pivotal in assessing the algorithm's resistance to differential 

attacks. Higher values indicate that minor changes in the plaintext result in significant 

differences in the ciphertext, which is desirable in a secure encryption algorithm. 

 

Fig 5. Analysis of Performance Parameters 

Table 3. NPCR and UACI Analysis Table 

Type of Image NPCR UACI 

JPEG 99.61 25.4751 

JPEG-2000 99.51 24.4578 

PNG 99.61 26.5997 

BMP 99.61 26.9971 

GIF 99.51 29.8075 

 



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Efficient encryption algorithms should exhibit not only robust security features but also 

optimize resource utilization, characterized by reasonable execution times and memory usage. 

Table 4. Execution Time and Memory Usage Table 

Type Execution 

Time 

Total Memory 

(MB) 

Standby Memory 

(MB) 

Effective Memory Used 

(MB) 

JPEG 27.15 Sec 1233.107872 734 499.37 

JPEG2000 20.18 Sec 1079.337536 734 345.23 

PNG 18.29 Sec 1089.659456 734 355.76 

BMP 18.99 Sec 1091.4576 734 357.66 

GIF 19292 Sec 1090.232896 734 356.12 

 

The reversible data hiding system facilitates secure encryption while allowing the original data 

to be perfectly retrieved, a vital aspect for applications demanding non-destructive recovery 

post decryption. 

Table 5.  Analysis of Result for Reversible Data Hiding 

Type of Image PSNR MSE 

JPEG 60.95 0.021 

JPEG-2000 65.16 0.016 

PNG 62.16 0.019 

BMP 64.17 0.022 

GIF 60.27 0.022 

These analyses collectively demonstrate the efficacy of the proposed lightweight encryption 

algorithm across various image formats and operational scenarios. The algorithm exhibits 

strong encryption characteristics, as evidenced by the uniform histograms, low correlation 

values, high entropy, substantial resistance to differential attacks (as indicated by NPCR and 

UACI), and efficient resource utilization in terms of execution time and memory usage. 

Furthermore, the integration of reversible data hiding illustrates the algorithm's versatility in 

ensuring data integrity and retrievability, underscoring its applicability in a range of IoT and 

image encryption contexts. 

 

5. CONCLUSION & FUTURE RESEARCH 

In this comprehensive study, we explored the efficacy of a lightweight encryption algorithm 

applied to various image formats, aiming to enhance security in the realm of digital media, 

particularly within IoT devices. Through meticulous analysis across multiple parameters—

histogram, correlation, entropy, NPCR/UACI, execution time, memory usage, and reversible 

data hiding—the algorithm's performance was scrutinized, yielding insightful findings that 

underscore its potential in securing digital assets while addressing the constraints inherent to 

IoT devices. The uniform distribution of pixel intensities in the encrypted images, as revealed 

by histogram analysis, is indicative of the algorithm's proficiency in obscuring the original 

image content. This uniformity is pivotal, ensuring that encrypted images do not retain any 

distinguishable patterns from their source, thereby bolstering security against statistical 

analysis that could potentially exploit such patterns for decryption. A fundamental aspect of 



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image encryption is disrupting the correlation between adjacent pixels to prevent any 

inference of the original content. The results demonstrated a significant reduction in 

correlation values post-encryption across all image formats, signaling a successful disruption 

of discernible patterns and affirming the algorithm's effectiveness in enhancing the 

randomness and thus the security of the encrypted images. The entropy values post-encryption 

exhibited a notable increase, reflecting the algorithm's capacity to heighten randomness within 

the encrypted images. High entropy is synonymous with unpredictability, a desirable trait in 

encryption that complicates unauthorized attempts at deciphering the encrypted content. This 

increase in entropy across various formats indicates the algorithm's consistent performance in 

securing diverse types of images. The NPCR and UACI metrics, crucial for evaluating 

resistance to differential attacks, indicated that minor alterations in the plaintext result in 

significant changes in the ciphertext. This characteristic is essential for robust encryption, as 

it ensures that the encrypted output is highly sensitive to even minute changes in the input, 

thereby fortifying the encryption against attempts to exploit similarities between different 

versions of an image. In the context of IoT devices, where resource constraints are a significant 

concern, the algorithm's performance in terms of execution time and memory usage is of 

paramount importance. The findings revealed that the algorithm maintains a balance between 

security and resource efficiency, manifesting relatively low execution times and memory 

usage across different image formats. This balance is critical for the practical application of 

the algorithm in IoT environments, where optimal resource utilization is as crucial as security. 

In conclusion, the comprehensive analysis conducted in this study elucidates the algorithm's 

robustness, versatility, and efficiency in securing digital images, a critical component in the 

ever-expanding realm of IoT. The uniformity in histogram distributions, the significant 

reduction in pixel correlations, the enhanced entropy, the strong resistance to differential 

attacks as denoted by NPCR and UACI scores, and the optimal resource utilization 

collectively attest to the algorithm's efficacy. Moreover, the reversible data hiding aspect 

underscores the algorithm's innovative approach, offering not just encryption but also a secure 

method of concealing additional data within the encrypted content. This algorithm stands as a 

testament to the potential of lightweight cryptographic solutions in addressing the nuanced 

security requirements of IoT devices. It embodies a strategic blend of security, efficiency, and 

functionality, paving the way for its integration into diverse IoT applications where 

safeguarding data integrity and privacy is paramount. As the IoT landscape continues to 

evolve, the demand for such innovative cryptographic solutions will undoubtedly escalate, 

underscoring the significance of this research in contributing to the secure and sustainable 

growth of IoT ecosystems. 

 

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