Secure equality testing and comparison are two important primitives widely used in many secure computation scenarios, such as privacy-preserving machine learning, private set intersection, and secure data mining, etc. This work proposes new constant-round two-party computation (2PC) protocols for secure equality testing and comparison. Our protocols are designed in the online/offline paradigm. For 32-bit inputs, the online communication cost of our equality testing protocol and secure comparison protocol are as low as 76 bits (1% of ABY) and 384 bits (5% of ABY) , respectively. Our benchmarks show that (i) for 32-bit equality testing, our scheme performs 9× faster than the Guo et al. (EUROCRYPT 2023) and 15× of the garbled circuit (GC) with the half-gate opti- mization (CRYPTO 2015). (ii) for 32-bit secure comparison, our scheme performs 3× faster than Guo et al. (EUROCRYPT 2023), 6× faster than both Rathee et al. (CCS 2020) and GC with the half-gate optimization.