2016/06/09 by László Mérai, Harald Niederreiter, Arne Winterhof · 1 citation
Computer Science · Mathematics · #Binomial (polynomial) #Coding theory and cryptography #Computational complexity theory #Cryptographic Implementations and Security #Cryptography #Cryptography and Data Security #Finite field #Measure (data warehouse) #Modulo #Probabilistic logic #Sequence (biology) #Time complexity #math.NT
paper · pdf · doi:10.1007/s12095-016-0189-2
openalex publication_date 2016/06/09 · arxiv created 2016/06/21 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. We study the relationship between linear complexity and expansion complexity. In particular, we show that for purely periodic sequences both figures of merit provide essentially the same quality test for a sufficiently long part of the sequence. However, if we study shorter parts of the period or nonperiodic sequences, then we can show, roughly speaking, that the expansion complexity provides a stronger test. We demonstrate this by analyzing a sequence of binomial coefficients modulo p. Finally, we establish a probabilistic result on the behavior of the expansion complexity of random sequences over a finite field.