4 research outputs found
Novel Area-Efficient and Flexible Architectures for Optimal Ate Pairing on FPGA
While FPGA is a suitable platform for implementing cryptographic algorithms,
there are several challenges associated with implementing Optimal Ate pairing
on FPGA, such as security, limited computing resources, and high power
consumption. To overcome these issues, this study introduces three approaches
that can execute the optimal Ate pairing on Barreto-Naehrig curves using
Jacobean coordinates with the goal of reaching 128-bit security on the Genesys
board. The first approach is a pure software implementation utilizing the
MicroBlaze processor. The second involves a combination of software and
hardware, with key operations in and being transformed into
IP cores for the MicroBlaze. The third approach builds on the second by
incorporating parallelism to improve the pairing process. The utilization of
multiple MicroBlaze processors within a single system offers both versatility
and parallelism to speed up pairing calculations. A variety of methods and
parameters are used to optimize the pairing computation, including Montgomery
modular multiplication, the Karatsuba method, Jacobean coordinates, the Complex
squaring method, sparse multiplication, squaring in , and
the addition chain method. The proposed systems are designed to efficiently
utilize limited resources in restricted environments, while still completing
tasks in a timely manner.Comment: 13 pages, 8 figures, and 5 table
Efficient Algorithms for Large Prime Characteristic Fields and Their Application to Bilinear Pairings
We propose a novel approach that generalizes interleaved modular multiplication algorithms to the computation of sums of products over large prime fields. This operation has widespread use and is at the core of many cryptographic applications. The method reformulates the widely used lazy reduction technique, crucially avoiding the need for storage and computation of double-precision operations. Moreover, it can be easily adapted to the different methods that exist to compute modular multiplication, producing algorithms that are significantly more efficient and memory-friendly.
We showcase the performance of the proposed approach in the computation of multiplication over an extension field , and demonstrate its impact with a record-breaking implementation for bilinear pairings: a full optimal ate pairing over the popular BLS12-381 curve is computed in under half a millisecond on a 3.2GHz Intel Coffee Lake processor, which is about faster than the state-of-the-art