For industrial control systems, ensuring the software integrity of their devices is a key security requirement. A pure software-based attestation solution is highly desirable for protecting legacy field devices that lack hardware root of trust (e.g., Trusted Platform Module). However, for the large population of field devices with ARM processors, existing software-based attestation schemes either incur long attestation time or are insecure. In this paper, we design a novel memory stride technique that significantly reduces the attestation time while remaining secure against known attacks and their advanced variants on ARM platform. We analyze the scheme's security and performance based on the formal framework proposed by Armknecht et al. [7] (with a necessary change to ensure its applicability in practical settings). We also implement memory stride on two models of real-world power grid devices that are widely deployed today, and demonstrate its superior performance.