Fast polynomial inversion for post quantum QC-MDPC cryptography

New post-quantum Key Encapsulation Mechanism (KEM) designs, evaluated as part of the NIST PQC standardization Project, pose challenging tradeoffs between communication bandwidth and computational overheads. Several KEM designs evaluated in Round-2 of the project are based on QC-MDPC codes. BIKE-2 uses the smallest communication bandwidth, but its key generation requires a costly polynomial inversion. In this paper, we provide details on the optimized polynomial inversion algorithm for QC-MDPC codes (originally proposed in the conference version of this work). This algorithm makes the runtime of BIKE-2 key generation tolerable. It brings a speedup of 11. 4× over the commonly used NTL library, and 83. 5× over OpenSSL. We achieve additional speedups by leveraging the latest Intel's Vector-PCLMULQDQ instructions, 14. 3× over NTL and 103. 9× over OpenSSL. Our algorithm and implementation were the reason that BIKE team chose BIKE-2 as the only scheme for its Round-3 specification (now called BIKE).

Authors

• Nir Drucker
• Shay Gueron
• Dusan Kostic

Keywords

• Polynomial inversion
• BIKE
• QC-MDPC codes
• Constant-time algorithm
• Constant-time implementation
• NIST PQC round-3