# SC-SA: Byte-Oriented Lightweight Stream Ciphers Based on S-Box Substitution
## 2 SC-SA Cipher
The S-box used in the cryptographic algorithm proposed in this paper is generated from Figure 5. The specific values of the S-box are listed in Figure 6.  
An S-box is a way to substitute bits in plaintext by mapping input bits to output bits, performing both confusion and diffusion functions. Confusion ensures that there is no apparent relationship between the input and output, making the cipher algorithm more difficult to crack. A well-designed S-box in cryptography should possess good nonlinearity, uniformity, and other cryptographic characteristics. Next, this paper will analyze the S-box proposed in this paper. 1. Bijectiveness  
In cryptography, bijectiveness refers to the property of a cryptographic function or transformation being both injective and surjective. A bijective cryptographic function ensures a one-to-one correspondence between the input and output, providing reversible mapping. Bijectiveness helps ensure the security and integrity of cryptographic operations, such as encryption and decryption, by allowing a clear and unique relationship between plaintext and ciphertext;  
2. Differential Probability  
In cryptography, an S-box is often crucial in block cipher algorithms. The concept of \"Differential Probability\" is related to the probability of a specific difference in the input affecting a particular difference in the output of an S-box. Differential Cryptanalysis is a technique used to analyze the differences between pairs of plaintexts and their  
Figure 1:0 The random S-box generation process. Figure 1:1 The S-box generation process. corresponding ciphertexts. It explores how changes in the input (plaintext) affect the changes in the output (ciphertext). Differential Cryptanalysis is particularly applicable to block ciphers. Differential probability measures the likelihood of a particular difference in the input leading to a specific difference in the output of the S-box. In other words, it quantifies the probability of a specific \"input difference \(\rightarrow\) output difference\" scenario. High differential probability indicates that a distinct difference in input bits is likely to result in a particular difference in the output bits with high probability. Cryptographic designers aim to create S-boxes with low differential probabilities to enhance security. A lower differential probability makes it more difficult for attackers to exploit differences in plaintexts to deduce information about the key or the internal state of the cryptographic algorithm. Designing S-boxes with good differential properties is critical to creating secure block ciphers. In the cryptographic scheme proposed in this paper, the S-box used has a maximum differential probability of \(5/128\), indicating good differential characteristics, as calculated using Formula (4). Figure 1:2 (4)
3. Walsh Spectrum of S-box Let \(\mathrm{F}\mathrm{:F}\mathrm{:F}\mathrm{{}^{2}_{2}}\rightarrow\mathrm{F}\mathrm{ {}^{m}_{2}}\), then \(\mathrm{W}_{\mathrm{F}}(\mathrm{u},\mathrm{v})=\sum_{\mathrm{x}\in\mathrm{F} \mathrm{{}^{2}_{n}}}(-1)^{\mathrm{u}\cdot\mathrm{x}\oplus\mathrm{v}\cdot \mathrm{F}(\mathrm{x})}\) is called the Walsh Spectrum of \(\mathrm{F}\), where \(\mathrm{u}\in\mathrm{F}\mathrm{{}^{2}_{2}}\) and \(\mathrm{v}\in\mathrm{F}\mathrm{{}^{m}_{2}}\backslash\{0\}\). In fact, the Walsh Spectrum of a Boolean function \(\mathrm{F}\) indicates the degree of approximation between \(\mathrm{F}\) and a linear function, so \(\mathrm{W}_{\mathrm{F}}(\mathrm{u},\mathrm{v})\) represents the degree of approximation between the component function \(\mathrm{v}\cdot\mathrm{F}(\mathrm{x})\) of \(\mathrm{F}\) and the linear function \(\mathrm{u}\cdot\mathrm{x}\). The value of the Walsh transform at the point \((\mathrm{u},\mathrm{v})\) is called the Walsh coefficient of \(\mathrm{F}\) at \((\mathrm{u},\mathrm{v})\). The Walsh Spectrum of the S-box is an important step in calculating the nonlinearity of the S-box;  
Figure 1:3 The selected \(8\times 8\) S-box.