# GSFedSec: Group Signature-Based Secure Aggregation for Privacy Preservation in Federated Learning
## 1 Introduction
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Abbreviation** & **Description** & **Abbreviation** & **Description** \\ \hline \(A\) & Admin & \(A_{i}\) & Secret key of client \(i\) \\ \(B_{1},B_{2},B_{3},B_{4},B_{5}\) & Binding variables & \(c,\xi\) & Challengers \\ \(C_{1},C_{2},C_{3}\) & Tracing variables & \(c_{1},c_{2},c_{3}\) & Ciphertext set \\ \(C_{BV}\) & Cost of binding variables & \(C_{SV}\) & Cost of signing variables \\ \(C_{TV}\) & Cost of tracing variables & \(C_{ENC}\) & Cost of encryption \\ \(C_{DEC}\) & Cost of decryption & \(C_{VER}\) & Cost of verification \\ \(C_{AGG}\) & Cost of aggregation & \(Dp\) & Differential privacy \\ \(\varepsilon\) & Bilinear map & \(Enc\) & Encryption \\ \(FL\) & Federated learning & \(FLReq\) & Participation request for FL \\ \(FLRep\) & Confirmation reply of FLReq & \(G_{1},G_{2},G_{T}\) & Cyclic isomorphic group \\ \(g_{1},g_{2},g_{T}\) & Generators of \(G_{1},G_{2},G_{T}\) & \(\sigma_{GS}\) or \(GS\) & Group signature \\ \(GSReq\) & Request for sending GS & \(GSRep\) & Reply with the latest GS \\ \(HE\) & Homomorphic encryption & \(m\) & Total number of clients \\ \(n\) & Number of clients selected for FL & \(\eta\) & Fixed learning rate of client \\ \(\omega_{k}\) & Current model update & \(\omega_{k+1}\) & Updated model update \\ \(s_{1},s_{2},s_{3},s_{4},s_{5}\) & Signing variables & \(SA\) & Secure aggregation \\ \(S_{i}\) & Secret Key part in SA & \(s_{pk}\) & Public key of the server \\ \(Upd\), \(\omega\) & Updated gradient & \(Upd_{s}\) & \(Upd\) with \(S_{i}\) \\ \(Upd_{sc}\) & Encrypted \(Upd\) with \(s_{pk}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of symbols and abbreviations used. Figure 1: Federated learning model and privacy breach. on 5 June 2024). Hence, the security of the data and the privacy of their source must be ensured, even in FL. Three popular techniques are available to provide privacy in FL: secure aggregation (SA) (using masking), differential privacy (DP), and homomorphic encryption (HE) [10; 11; 12]. SA is very costly (as explained later in this article); DP adds noise to the data, therefore reducing its accuracy; HE has a relatively high complexity, raising concerns regarding the feasibility of its real-time implementation. The properties of these schemes have been given in Table 2, in which schemes are compared based on their advantages and disadvantages. Group signature was first introduced to FL in 2021 to solve the issue of privacy preservation for users in the network [13]. The main purpose of using a group signature (GS) is to preserve a sender's privacy. The idea is to hide the individual signature so the receiver can verify the source's identity without explicitly knowing it [14]. The GS must be changed if membership is revoked or a member willingly leaves the group. Otherwise, the former member can misuse the GS for their advantage [15]. The membership table is updated with a list of existing members and ex-members. Only authenticated members can sign a message using the GS; thus, the GS maintains its privacy with proper authentication. It achieves the main aim of FL: to preserve the user's privacy. If the user's identity is not revealed to the receiver, personal information linked to the user can be protected. In this study, we aim to enhance the privacy of clients in the FL model using GS while also preserving updates using SA. In a conventional SA, clients share secret information with all other participating clients in the network, and the server aggregates them with client updates. All secret keys cancel each other out during the SA process. Each client must communicate with others selected for the FL process, significantly increasing the computation and communication costs. Signaling overheads also increase significantly, complicating the entire information collection process. As indicated in [12], this basic SA model is not scalable. Therefore, we adopted a GS-based SA technique, in which a secret key is shared with the participating clients by the admin of the group while sharing the GS.