Işık Lavrauw, LeylaWinterhof, Arne2020-11-302020-11-302020Işık, L., & Winterhof, A. (2020). On the index of the Diffie–Hellman mapping. Applicable Algebra in Engineering, Communication and Computing, 1-9.0938-1279https://www.doi.org/10.1007/s00200-020-00475-3https://hdl.handle.net/20.500.12713/1257Let ? 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 improvementseninfo:eu-repo/semantics/openAccessCryptographyCyclic GroupsCyclotomic MappingsDiffie–Hellman MappingIndexArticleWOS:0005919800000012-s2.0-85096453834Q310.1007/s00200-020-00475-3Q3