Open AccessThe Order in the Growth of the Injective and Super-Increasing Vectors Knapsacks Quantity
Author(s) -
D. M. Murin
Publication year - 2015
Publication title -
modelirovanie i analiz informacionnyh sistem
Language(s) - English
Resource type - Journals
eISSN - 2313-5417
pISSN - 1818-1015
DOI - 10.18255/1818-1015-2012-3-124-135
Subject(s) - injective function , cryptosystem , order (exchange) , set (abstract data type) , class (philosophy) , knapsack problem , computer science , cryptography , mathematics , discrete mathematics , combinatorics , algorithm , business , artificial intelligence , finance , programming language
In 1978 R. Mercle and M. Hellman offered to use the subset sum problem for constructing cryptographic systems. The proposed cryptosystems were based on a class of the knapsacks with super-increasing vectors. This class is a subset of the set of knapsacks with injective (cryptographic) vectors that allow the single-valued decoding (decryption) result. In this paper we consider the problems related to the order in the growth of the injective vectors knapsacks quantity and to the order in the growth of knapsacks quantity with the super-increasing vectors through the knapsack maximal element increasing.