Paper 2026/1385

Walsh LUT Evaluation on Lazy Bits for CKKS AES Transciphering

Abstract

In this work we propose a novel Boolean lookup-table evaluation methodology over binary CKKS when circuit XORs are kept lazy, i.e., evaluated as additions whose least significant bits remain correct. Our method represents a LUT in the Walsh basis, forms the required parity sums by lazy CKKS additions, and packs them into ciphertext slots. We then use CKKS binary bootstrapping as a refresh step: the StC stage maps the packed lazy parities to MSB-encoded bits, removing the overflow; CtS places the parity values in slots; and $\mathsf{EvalMod}_{f_{\mathrm{BinBoot}}}$ cleans the binary noise, leaving clean parities in the slot domain. The LUT is then evaluated by recombining these parities with plaintext Walsh coefficients. This decouples the LUT size from the multiplicative depth of the surrounding circuit: large LUTs can be handled by cleaning selected factored parity signs and spending only a small constant depth in recombination. We apply this framework to AES-CTR transciphering. The AES S-box is evaluated with a nibble-split Walsh decomposition, which supports more AES blocks at the cost of one additional multiplication depth. The AES state remains in full complex CKKS packing so real and imaginary lanes carry independent AES blocks. In CPU experiments, the Walsh S-box AES-CTR algorithm is 3.25x faster than the sparse-bootstrapping XBOOT variant at the same 1024-block batch size.