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Using Vojvoda approach [34] we demonstrate that cryptographical primitives proposed in [26] are vulnerable relative to chosen ciphertext attack and chosen plaintext attack. We develop proposed in [31] modifications and add some new modifications of known quasigroup based stream ciphers [19, 26]. Systems of orthogonal n-ary groupoids are used.

Buchsteiner loops are those which satisfy the identity x\(xy · z) = (y · zx)/x. We show that a Buchsteiner loop modulo its nucleus is an abelian group of exponent four, and construct an example where the factor achieves this exponent. A loop (Q, ·) is a set Q together with a binary operation · such that for each a, b ∈ Q, the equations a · x = b and y · a =… (More)

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