Efficient Algorithms for Large Prime Characteristic Fields and Their Application to Bilinear Pairings

We propose a novel approach that generalizes interleaved modular multiplication algorithms for the computation of sums products over large prime fields. This operation has widespread use and is at core many cryptographic applications. The method reformulates widely used lazy reduction technique, crucially avoiding need storage “double-precision” operations. Moreover, it can be easily adapted to different methods exist compute multiplication, producing are significantly more efficient memory-friendly. showcase performance proposed in an extension field Fpk , demonstrate its impact with record-breaking implementations bilinear pairings. Specifically, we accomplish full optimal ate pairing popular BLS12-381 curve, designed 128-bit security level, under half millisecond on 3.2GHz Intel Coffee Lake processor, which about 1.40× faster than state-of-the-art. Similarly, perform same BLS24-509 targeting 192-bit ~ 2.6 milliseconds, achieving speedup 1.30x. also report significant other applications, including protocols based supersingular isogenies.