# GSFedSec: Group Signature-Based Secure Aggregation for Privacy Preservation in Federated Learning
## 1 Introduction
Hence, the most trusted party, the admin, must compute the secret key only once. This reduces the computational cost of each client and the communication costs of sending messages to every other client on the network. After adding the secret keys to their updates, clients send their updates by signing them with a GS. When the server receives a signed message, it verifies the GS and aggregates the secured message. Group signature scheme has its own limitations. The size of the signature significantly depends upon the size of the group. If the group size increases, the GS size also increases. Verification and key management complexity also increase with the increase in group size. However, this increase in complexity is still very minimal when compared with the increase in complexity of the SA algorithm. Increase in one member in SA increases (\(n+1\)) communications. It also increases the computational overhead for each client to generate the secret key part for the new member. There are various factors explained later in this article that prove that SA is not scalable. Moreover, an increase in signature size depends upon the increase in group size. It does not depend on how many clients are selected for \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Properties** & **SA** & **DP** & **HE** & **GS** & **GSFedSec (Proposed)** \\ \hline Privacy Protection & Data & Data & Data & User & Data and User \\ Client-Client Communication & Required & No & No & No & No \\ Participant List & Required & No & No & No & No \\ Computational Complexity & High & Low & High & Low & Low \\ Space Complexity & High & Low & Low & Low & Low \\ Efficiency & Low & Low & High & High & High \\ Accuracy & High & Low & High & High & High \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of various techniques used in FL to provide privacy. the FL process. However, an increase in members for the FL process affects the performance of SA significantly. Hence, GS performs better than existing algorithms even when group size increases. This is explained later in Performance analysis, Section 5. To validate the secrecy, confidentiality, and other security aspects of the method, we verify it using a mathematical logic tool: Burrows-Abadi-Needham (BAN) logic. This operates on a set of rules that we define and helps determine the likelihood of attacks in our algorithm. We also simulate our algorithm using the Automated Validation of Internet Security Protocols and Applications (AVISPA) [16] and High-level Protocol Specification Language (HLPSL). AVISPA is a robust tool that uses HLPSL to specify algorithms and their security properties, and it integrates different backend tools to provide automated validation. We also compare our results with existing algorithms in terms of their cost, size, and security. The contributions of this study are outlined below:  
* **Protection of data and user privacy**: We introduce a novel SA with GS to provide privacy to clients and their data. Contrary to data privacy or user privacy algorithms, this is the first work to address data security and user privacy simultaneously. The server cannot know the identity of the user because of GS, and it cannot guess the previous sequence of updates because of SA. Our work combines the best features of both technologies to produce an algorithm that completely mitigates inference attacks. * **Improved computation and communication efficiency**: Our algorithm has much lower computation and communication costs than existing algorithms. This is achieved by eliminating the need for peer-to-peer communication during key exchanges in the existing SA model. We provide a detailed analysis of the computation, communication, and signaling costs via comparisons with the existing algorithms. * **Security proof of FL algorithm using BAN logic and AVISPA**: We provide a formal mathematical proof using BAN logic and simulation analyses using AVISPA. This paper is based on the assumption that the group admin is a trusted entity, like a certificate authority.