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2 Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

2 2014

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On New Examples of Families of Multivariate Stable Maps and their Cryptographical Applications

Wróblewska A., Ustimenko V.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

2014

Vol. 14, no. 1

19--36

Let K be a general finite commutative ring. We refer to a family gn, n = 1, 2, . . . of bijective polynomial multivariate maps of Kn as a family with invertible decomposition gn = gn1 gn2 . . . g gnk, such that the knowledge of the composition of gni allows computation of gni for O(ns) (s > 0) elementary steps. A polynomial map g is stable if all non-identical elements of kind gt, t > 0 are of the same degree. We construct a new family of stable elements with invertible decomposition. This is the first construction of the family of maps based on walks on the bipartite algebraic graphs defined over K, which are not edge transitive. We describe the application of the above mentioned construction for the development of stream ciphers, public key algorithms and key exchange protocols. The absence of edge transitive group essentially complicates cryptanalysis.

Cryptographic Applications of the Duplex Construction

Borowski M.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

2014

Vol. 14, no. 1

37--48

Assured security is the desirable feature of modern cryptography. Most of modern cryptography primitives have no provably secure constructions. Their safety is defined on the basis of well-known in the given time cryptanalytic attacks. The duplex construction equipped with one ideal permutation and appropriate security parameters is suitable for building provably secure cryptographic primitives. The constructions can be used for unclassified information of different sensitivity levels protection. Some of them can secure classified information up to the TOP SECRET level. The applications based on the duplex construction can be used for key wrapping, authenticated encryptionand can work as a pseudo-random bit sequence generator. They are not covered by any known intellectual property.