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Within a broader context of mobile and embedded computing, the design of practical, secure tokens that can store and/or process security-critical information remains an ongoing challenge. One aspect of this challenge is the threat of information leakage through side-channel attacks, which is exacerbated by any resource constraints. Along these lines, this paper extends previous work on use of Yao circuits via two contributions. First, we show how careful analysis can fix the maximum number of leakage occurrences observed during a DPA attack, effectively bounding leakage from a Yao-based token. To achieve this we use modularised Yao circuits, which also support our second contribution: the first Yao-based implementation of a secure authentication payload, namely HMAC based on SHA-256.