# Comprehensive Evaluation on an ID-Based Side-Channel Authentication with FPGA-Based AES
## 2 Preliminaries
### Protocol in Side-Channel Authentication  
The possible protocols for side-channel authentication were discussed in [1]. In this paper, we only discuss the Challenge-S-Response authentication and the Challenge-S authentication, as shown in  
Figure 1: Two types of side-channel data with Advanced Encryption Standard (AES).  
Figure 2a,b. Here, challenge \(c\) and response \(r\) are the same with conventional authentication schemes, and \(S\) denotes the side-channel information.  
For both schemes, prover \(X_{i}\) registers its secret key \(sk_{i}\) in the verifier before the authentication. The authentication starts when the verifier sends a challenge \(c\) to a prover \(X_{i}\). Prover \(X_{i}\) calculates \(f(c,sk_{i})\) using its secret key \(sk_{i}\), where \(f(\hat{)}\) is a cryptographic calculation. The verifier measures the side-channel information \(S\) during the encryption process.  
The major difference between these two schemes is whether the response \(r\) is sent back from the prover to the verifier to be used in the verification.  
For Challenge-S-Response authentication, the response \(r\) is sent to the verifier. The identification of the prover is performed using both side-channel information \(S\) and the conventional challenge-response verification. First, the verifier searches the secret key \(sk_{i}\in\{sk_{1},sk_{2},\ldots,sk_{q}\}\) to find the \(sk_{i}\) such that \(f(c,sk_{i})=r\). Then, the found \(sk_{i}\) is used with \(c\) and a leakage model to estimate the side-channel information as \(L(c,sk_{i})\). After that, Pearson's correlation coefficient between the measurement of real side-channel information \(S\) and the estimation \(L(c,sk_{i})\) is calculated and compared with a pre-determined threshold \(h\). The authentication is passed only when both the response and the side-channel information match the expectation. This scheme is similar to conventional challenge-response authentication.  
For Challenge-S authentication, only the side-channel information \(S\) is used in the authentication. The response of the encryption process is not returned to the verifier. The verifier is required to  
Figure 2: Two types of authentication methods proposed in [1]. (a) Challenge-S-Response method; (b) Challenge-S method.  
calculate the expected leakage for all registered keys as \(\{sk_{1},sk_{2},\ldots,sk_{q}\}\). Then, for each registered key, a correlation calculation is conducted. The key with the largest correlation among all possible keys is compared with a pre-determined threshold \(h\). Only when the maximal correlation is larger than the threshold, is the prover considered to be a legitimate prover. The comparison with the threshold is done to prevent a situation where the invalid keys can pass the authentication.  
For Challenge-S authentication, the response \(r\) is not transmitted in the communication channel. The benefits of omitting \(r\) transmission are two-fold. First, the response \(r\) is not available for the attacker for any key recovery attack. Second, the communication for the authentication in the main channel can be reduced. Furthermore, the communication can be omitted entirely if the challenge \(c\) is predefined between the prover device and the verifier.  
For the Challenge-S authentication scheme in conventional side-channel authentication [1], the correlation coefficients are calculated for all the pre-registered keys. Thus, it is expected to be time consuming when the number of registered provers is large. In this paper, we want to accelerate the Challenge-S authentication scheme of the side-channel authentication.