Geodesic
The Order in the Growth of the Injective and Super-Increasing Vectors Knapsacks Quantity
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 124-135 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: injective vectors, super-increasing vectors, computer algebra. 
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D. M. Murin. The Order in the Growth of the Injective and Super-Increasing Vectors Knapsacks Quantity. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 124-135. http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a8/

[1] R. C. Merkle, M. E. Hellman, “Hiding information and signatures in trap-door knapsacks”, IEEE Trans. Inform. Theory IT, 24 (1978), 525–530 | DOI

[2] A. Salomaa, Kriptografiya s otkrytym klyuchom, Mir, M., 1995