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2022•Unpublished venueOpen access

Evaluation of the maximum proportion of invertible submatrices in invertible binary matrices

Jiayi Hu

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Abstract

The research on all-or-nothing transform in cryptography leads to the problem that, for a given positive integer , what is the density of invertible submatrices of any invertible matrix? For binary matrices, previous work shows that in the case , , where denotes the maximum proportion of invertible submatrices in invertible matrices. In this paper we study the case . It is proved that and an upper bound of is given as well.

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The research on all-or-nothing transform in cryptography leads to the problem that, for a given positive integer , what is the density of invertible submatrices of any invertible matrix? For binary matrices, previous work shows that in the case , , where denotes the maximum proportion of invertible submatrices in invertible matrices. In this paper we study the case . It is proved that and an upper bound of is given as well.

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Available abstract

The research on all-or-nothing transform in cryptography leads to the problem that, for a given positive integer , what is the density of invertible submatrices of any invertible matrix? For binary matrices, previous work shows that in the case , , where denotes the maximum proportion of invertible submatrices in invertible matrices. In this paper we study the case . It is proved that and an upper bound of is given as well.

Key concepts: Invertible matrix, Block matrix, Mathematics, Binary number, Combinatorics, Integer (computer science), Block (permutation group theory), Matrix (chemical analysis)

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