Homomorphic Encryption (HE) provides strong data privacy for cloud services but at the cost of prohibitive computational overhead. While GPUs have emerged as a practical platform for accelerating HE, there remains an order-ofmagnitude energy-efficiency gap compared to specialized (but expensive) HE ASICs. This paper explores an alternate direction: leveraging existing AI accelerators, like Google's TPUs with coarse-grained compute and memory architectures, to offer a path toward ASIC-level energy efficiency for HE. However, this architectural paradigm creates a fundamental mismatch with SoTA HE algorithms designed for GPUs. These algorithms rely heavily on: (1) high-precision (32-bit) integer arithmetic to now run on a TPU's low-throughput vector unit, leaving its high-throughput low-precision (8-bit) matrix engine (MXU) idle, and (2) fine-grained data permutations that are inefficient on the TPU's coarse-grained memory subsystem. Consequently, porting GPU-optimized HE libraries to TPUs results in severe resource under-utilization and performance degradation. To tackle above challenges, we introduce CROSS, a compiler framework that systematically transforms HE workloads to align with the TPU's architecture. CROSS makes two key contributions: (1) Basis-Aligned Transformation (BAT), a novel technique that converts high-precision modular arithmetic into dense, low-precision (INT8) matrix multiplications, unlocking and improving the utilization of TPU's MXU for HE, and (2) Memory-Aligned Transformation (MAT), which eliminates costly runtime data reordering by embedding reordering into compute kernels through offline parameter transformation. Our evaluation on a real single-host Google TPU v6e refreshes the SoTA Number Theoretic Transform (NTT) throughput record with up-to$1.43 \times$throughput improvement over WarpDrive on a NVIDIA A100. Furthermore, CROSS achieves$451 \times, 7.81 \times, 1.83 \times, 1.31 \times, 1.86 \times$, and$1.15 \times$higher throughput per watt than OpenFHE, WarpDrive, FIDESlib, FAB, HEAP, and Cheddar, respectively, establishing AI ASIC as the SotA efficient platform for HE operators. Code: https://github.com/EfficientPPML/CROSS.