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This paper studies the information-theoretic secrecy rates of wireless two-way relay systems where two users wish to exchange information through a single relay with an eavesdropper observing all communications. We formulate and compare the achievable secrecy rates of the system that employs one of the three common relay protocols: conventional decode-and-forward (DF), DF with network coding (NC), and compute-and-forward (CF) based on physical-layer network coding (PNC). We show that CF based on PNC achieves the highest secrecy rate at high signal-to- noise ratio (SNR), while, interestingly, the other two protocols have mixed performance depending on the power allocation scheme and network topology. Our study offers insights into designing wireless two-way relay protocols from a secrecy perspective.