Lightweight Key Encapsulation Using LDPC Codes on FPGAs

In this paper, we present a lightweight hardware design for a recently proposed quantum-safe key encapsulation mechanism based on QC-LDPC codes called LEDAkem, which has been admitted as a round-2 candidate to the NIST post-quantum standardization project. Existing implementations focus on high speed while few of them take into account area or power efficiency, which are particularly decisive for low-cost or power constrained IoT applications. The solution we propose aims at maximizing the metric of area efficiency by rotating the QC-LDPC code representations amongst the block RAMs in digit level. Moreover, optimized parallelized computing techniques, lazy accumulation and block partition are exploited to improve key decapsulation in terms of area and timing efficiency. We show for instance that our area-optimized implementation for 128-bit security requires $6.82\times 10^5$mml:mathmml:mrowmml:mn6mml:mo.mml:mn82mml:mo×mml:msupmml:mn10mml:mn5 cycles and $2.26\times 10^6$mml:mathmml:mrowmml:mn2mml:mo.mml:mn26mml:mo×mml:msupmml:mn10mml:mn6 cycles to encapsulate and decapsulate a shared secret, respectively. The area-optimized design uses only 39 slices (3 percent of the available logic) and 809 slices (39 percent of the available logic) for key encapsulation and key decapsulation respectively, on a small-size low-end Xilinx Spartan-6 FPGA.