XCRYPT: Accelerating Lattice Based Cryptography with Memristor Crossbar Arrays

This paper makes a case for accelerating lattice-based post quantum cryptography (PQC) with memristor based crossbars, and shows that these inherently error-tolerant algorithms are a good fit for noisy analog MAC operations in crossbars. We compare different NIST round-3 lattice-based candidates for PQC, and identify that SABER is not only a front-runner when executing on traditional systems, but it is also amenable to acceleration with crossbars. SABER is a module-LWR based approach, which performs modular polynomial multiplications with rounding. We map the polynomial multiplications in SABER on crossbars and show that analog dot-products can yield a $1.7-32.5\times$ performance and energy efficiency improvement, compared to recent hardware proposals. This initial design combines the innovations in multiple state-of-the-art works -- the algorithm in SABER and the memristive acceleration principles proposed in ISAAC (for deep neural network acceleration). We then identify the bottlenecks in this initial design and introduce several additional techniques to improve its efficiency. These techniques are synergistic and especially benefit from SABER's power-of-two modulo operation. First, we show that some of the software techniques used in SABER, that are effective on CPU platforms, are unhelpful in crossbar-based accelerators. Relying on simpler algorithms further improves our efficiencies by $1.3-3.6\times$. Second, we exploit the nature of SABER's computations to stagger the operations in crossbars and share a few variable precision ADCs, resulting in up to $1.8\times$ higher efficiency. Third, to further reduce ADC pressure, we propose a simple analog Shift-and-Add technique, which results in a $1.3-6.3\times$ increase in the efficiency. Overall, our designs achieve $3-15\times$ higher efficiency over initial design, and $3-51\times$ higher than prior work.