On the index of the Diffie–Hellman mapping
Yükleniyor...
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Science and Business Media Deutschland GmbH
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Let ? be a generator of a cyclic group G of order n. The least index of a self-mapping f of G is the index of the largest subgroup U of G such that f(x) x-r is constant on each coset of U for some positive integer r. We determine the index of the univariate Diffie–Hellman mapping d(?a)=?a2, a= 0 , 1 , … , n- 1 , and show that any mapping of small index coincides with d only on a small subset of G. Moreover, we prove similar results for the bivariate Diffie–Hellman mapping D(?a, ?b) = ?ab, a, b= 0 , 1 , … , n- 1. In the special case that G is a subgroup of the multiplicative group of a finite field we present improvements
Açıklama
Anahtar Kelimeler
Cryptography, Cyclic Groups, Cyclotomic Mappings, Diffie–Hellman Mapping, Index
Kaynak
Applicable Algebra in Engineering, Communications and Computing
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
Sayı
Künye
Işık, L., & Winterhof, A. (2020). On the index of the Diffie–Hellman mapping. Applicable Algebra in Engineering, Communication and Computing, 1-9.
