GMC-crypto: Low latency implementation of ECC point multiplication for generic Montgomery curves over GF(p)

Elliptic Curve Cryptography (ECC) is the front-runner among available public key cryptography (PKC) schemes due to its potential to offer higher security per key bit. All ECC-based cryptosystems heavily rely on point multiplication operation where its efficient realization has attained notable focus in the research community. Low latency implementation of the point multiplication operation is frequently required in high-speed applications such as online authentication and web server certification. This paper presents a low latency ECC point multiplication architecture for Montgomery curves over generic prime filed $GF\left(p\right)$. The proposed architecture is able to operate for a general prime modulus without any constraints on its structure. It is based on a new novel pipelined modular multiplier developed using the Montgomery multiplication and the Karatsuba-Offman technique with a four-part splitting methodology. The Montgomery ladder approach is adopted on a system level, where a high-speed scheduling strategy to efficiently execute $GF\left(p\right)$ operations is also presented. Due to these circuit and system-level optimizations, the proposed design delivers low-latency results without a significant increase in resource consumption. The proposed architecture is described in Verilog-HDL for 256-bit key lengths and implemented on Virtex-7 and Virtex-6 FPGA platforms using Xilinx ISE Design Suite. On the Virtex-7 FPGA platform, it performs a 256-bit point multiplication operation in just 110.9 us with a throughput of almost 9017 operations per second. The implementation results demonstrate that despite its generic nature, it produces low latency as compared to the state-of-the-art. Therefore, it has prominent prospects to be used in high-speed authentication and certification applications.