New method creates complex multi-sequences for better cryptography
Construction of Multi-sequences With High Nonlinear Complexity via Narrow Ray Class Fields
Information Theory
Summary
Generating sequences that are hard to predict is very important for keeping information secure. The authors build on earlier work to create a flexible method for making multiple such sequences that are very complex in a nonlinear way. They use advanced math called narrow ray class fields to do this, which lets them create these sequences over different kinds of function fields. This approach can help improve cryptographic systems by providing stronger pseudorandom sequences.
What this means in practice
- •For cryptography engineers: Generate highly complex pseudorandom multi-sequences to improve security in cryptographic applications.
- •For communication system designers: Create sequences with strong nonlinear complexity for robust secure communication protocols.
Authors
Xiaofeng Liu, Jun Zhang, Fang-Wei Fu
Abstract
Nonlinear complexity is a fundamental criterion in the evaluation of pseudorandom sequences. The construction of multi-sequences with high nonlinear complexity is both theoretically and practically important in cryptography. Motivated by prior constructions of multi-sequences with high nonlinear complexity in [IEEE Trans. Inf. Theory, 60(10), 2014] and [IEEE Trans. Inf. Theory, 63(12), 2017], we provide a unified framework via narrow ray class fields, the cyclic descent due to Guruswami and Xing in [J. Combin. Theory Ser. A 129 (2015) ]. Then we can generate new multi-sequences with high nonlinear complexity over function fields with arbitrary genera.