International Association for Cryptologic Research

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Paper: Racing BIKE: Improved Polynomial Multiplication and Inversion in Hardware

Authors:
Jan Richter-Brockmann , Ruhr University Bochum, Intel Labs
Ming-Shing Chen , Ruhr University Bochum
Santosh Ghosh , Intel Labs
Tim Güneysu , Ruhr University Bochum, DFKI
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Abstract: BIKE is a Key Encapsulation Mechanism selected as an alternate candidate in NIST’s PQC standardization process, in which performance plays a significant role in the third round. This paper presents FPGA implementations of BIKE with the best area-time performance reported in literature. We optimize two key arithmetic operations, which are the sparse polynomial multiplication and the polynomial inversion. Our sparse multiplier achieves time-constancy for sparse polynomials of indefinite Hamming weight used in BIKE’s encapsulation. The polynomial inversion is based on the extended Euclidean algorithm, which is unprecedented in current BIKE implementations. Our optimized design results in a 5.5 times faster key generation compared to previous implementations based on Fermat’s little theorem. Besides the arithmetic optimizations, we present a united hardware design of BIKE with shared resources and shared sub-modules among KEM functionalities. On Xilinx Artix-7 FPGAs, our lightweight implementation consumes only 3 777 slices and performs a key generation, encapsulation, and decapsulation in 3 797 µs, 443 µs, and 6 896 µs, respectively. Our high-speed design requires 7 332 slices and performs the three KEM operations in 1 672 µs, 132 µs, and 1 892 µs, respectively.
BibTeX
@article{tches-2022-31640,
  title={Racing BIKE: Improved Polynomial Multiplication and Inversion in Hardware},
  journal={IACR Transactions on Cryptographic Hardware and Embedded Systems},
  publisher={RUB},
  author={Jan Richter-Brockmann and Ming-Shing Chen and Santosh Ghosh and Tim Güneysu},
  year=2022
}