Rotation-equivalence classes of binary vectors. (English) Zbl 1436.94069
Summary: In this paper we study equivalence classes of binary vectors with regards to their rotation by using an algebraic approach based on the theory of linear feedback shift registers. We state the necessary and sufficient condition for existence of an equivalence class with given cardinality and provide two formulas. The first represents the sharp distribution of cardinalities for given length and Hamming weight of binary vectors and the second enables us to determine the number of different classes with the same cardinality.
MSC:
| 94A60 | Cryptography |
| 11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |
| 94A55 | Shift register sequences and sequences over finite alphabets in information and communication theory |
Keywords:
rotational equivalence classes; binary vectors; binary vector rotation; rotational classes cardinality; linear feedback shift registersSoftware:
McElieceReferences:
| [1] | REPKA, Overview of the McEliece cryptosystem and its security Tatra Mt, Math Publ pp 57– (2014) |
| [2] | ZAJAC, Rotational cryptanalysis ofGOSTwith identicalS - boxes Tatra Mt, Math Publ pp 1– (2013) |
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