Recent advancements in post-quantum cryptographic algorithms have led to their standardization by the National Institute of Standards and Technology (NIST) to safeguard information security in the post-quantum era. These algorithms, however, employ public keys and signatures that are 3 to 9$\times$ longer than those used in pre-quantum cryptography, resulting in significant performance and energy efficiency overheads. A critical bottleneck identified in our analysis is the cache bandwidth. This limitation motivates the adoption of on-chip in-/near-cache computing, a computing paradigm that offers high-performance, exceptional energy efficiency, and flexibility to accelerate post-quantum cryptographic algorithms. Our analysis of existing works reveals challenges in integrating in-/near-cache computing into modern computer systems and performance limitations due to external bandwidth limitation, highlighting the need for innovative solutions that can seamlessly integrate into existing systems without performance and energy efficiency issues. In this paper, we introduce a near-cache-slice computing paradigm with support of customization and virtual address, named Crypto-Near-Cache (CNC), designed to accelerate post-quantum cryptographic algorithms and other applications. By placing SRAM arrays with bitline computing capability near cache slices, high internal bandwidth and short data movement are achieved with native support of virtual addressing. An ISA extension to facilitate CNC is also proposed, with detailed discussion on the implementation aspects of the core/cache datapath.