| Sažetak: | The threat of quantum computing has spurred research into post-quantum cryptography. SQI<span style="font-variant: small-caps;">sign</span>, a candidate submitted to the standardization process of the National Institute of Standards and Technology, is emerging as a promising isogeny-based signature scheme. This work aimed to enhance SQI<span style="font-variant: small-caps;">sign</span>’s practical deployment by optimizing its low-level arithmetic operations. Through hierarchical decomposition and performance profiling, we identified the ideal-to-isogeny translation, primarily involving elliptic curve operations, as the main bottleneck. We developed efficient 32-bit finite field arithmetic for elliptic curves, such as basic operations, like addition with carry, subtraction with borrow, and conditional move. We then implemented arithmetic operations in the Montgomery domain, and extended these to quadratic field extensions. Our implementation offers improved compatibility with 32-bit architectures and enables more fine-grained SIMD acceleration. Performance evaluations demonstrated the practicality in low-level operations. Our work has potential in easing the development of SQI<span style="font-variant: small-caps;">sign</span> in practice, making SQI<span style="font-variant: small-caps;">sign</span> more efficient and practical for real-world post-quantum cryptographic applications.
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