On Non-Polynomial Latin Squares

A Latin Square (LS) of order n is an arrangement of n symbols in an nxn matrix form so that each symbol occurs in each row and each column exactly once. The total number of Latin Squares LS(n) of order n increases rapidly with n. This helps to design cryptosystems using Latin Squares with a very large key-space. We define encryption and decryption using simple operations on Latin Squares. Different schemes are designed to make the system secure and easy to implement. Use of keyed permutations and construction of large quasigroups ensure that the system is resistant to different practical cryptographic attacks. Computer implementations show the simplicity and power of these schemes for future cryptographic applications in resource-constrained networks or in mobile devices.

In this paper we present a new 128-bit block cipher called SQUARE. The original design of SQUARE concentrates on the resistance against differential and linear cryptanalysis. However, after the initial design a dedicated attack was mounted that forced us to augment the number of rounds. The goal of this paper is the publication of the resulting cipher for public scrutiny. A C implementation of SQUARE is available that runs at 2.63 MByte/s on a 100 MHz Pentium. Our M68HC05 Smart Card implementation fits in 547 bytes and takes less than 2 msec. (4 MHz Clock). The high degree of parallellism allows hardware implementations in the Gbit/s range today.

Journal of Cryptology, 2001

In this paper an attack on block ciphers is introduced, the interpolation attack. This method is useful for attacking ciphers that use simple algebraic functions (in particular quadratic functions) as S-boxes. Also, attacks based on higher-order differentials are introduced. They are special and important cases of the interpolation attacks. The attacks are applied to several block ciphers, the six-round prototype cipher by Nyberg and Knudsen, which is provably secure against ordinary differential cryptanalysis, a modified version of the block cipher SHARK, and a block cipher suggested by Kiefer.

In this paper we present a new 128-bit block cipher called Square. The original design of Square concentrates on the resistance against differential and linear cryptanalysis. However, after the initial design a dedicated attack was mounted that forced us to augment the number of rounds. The goal of this paper is the publication of the resulting cipher for public scrutiny. A C implementation of Square is available that runs at 2.63 MByte/s on a 100 MHz Pentium. Our M68HC05 Smart Card implementation fits in 547 bytes and takes less than 2 msec. (4 MHz Clock). The high degree of parallellism allows hardware implementations in the Gbit/s range today.

In this paper the main cryptography technique we will use is caesar cipher involving replacing each letter of the alphabet with the letter standing 3 places further down the alphabet. Here the encryption algorithm takes plaintext letters as input, and produc es cipher text letters for them .

Discrete Applied Mathematics, 1989

The classical definition of Latin squares is generalized by allowing multiple occurrences of symbols in each row and each column. A perfect (k, I)-Latin square is an N x N array in which any row or column contains every distinct symbol and the symbol at position (i, j) appears exactly k times in the ith row and I times in the jth column, or vice versa. Existence of such squares and the notion of orthogonality for such squares are studied. Several algorithms for constructing such squares are presented.

… Journal of Network …, 2009

In this paper, we propose a new block cipher called BC2 (Block Cipher 2). We make a cipher using components that are believed secure. The structure of BC2 is very simple. We use Feistel network with input-output 128 bits, matrix Maximum Distance Separable (MDS) 8x8 with branch number 9 to give high diffusion, a function affine equivalent to the inverse function in GF(2 8 ) that we get from Camellia and Hierocrypt S-Box for confusion and we make FN function, based on FL function of Camellia. We use a heuristic method to count the minimum number of active substitution box at Feistel Network. And we also construct a new key schedule that is fast and secure.

Latin squares of order n exist for each n ≥ 1. There are severalways of constructing Latin squares. Also for n≥ 2, if the number of reduced Latin squares isknown, then the number of general Latin squares canbecalculated. This paperproposed a generalmethod to constructsymmetric Latin squares of orderí µí±ž í µí±› by using blocks of order q which have the basic property of a recursivealgorithmwith the use of cyclicshiftingmethod. Further, the resultingsymmetric Latin squares have the property of reduced Latin squares. The proposedalgorithmwastestedmannualy for q=2,3,4 and 5.For higherorder Latin squares wastestedusing Java progaramm.Thisalgorithmcouldbegeneralized for any q ≥ 2 and n ≥1.

Literature shows that there are several ways of generating Latin squares, but there is not enough implementation about Supersymmetric Latin squares. This paper proposes a mathematical algorithm to construct Super-symmetric Latin squares of order 2 ୬ by substituting blocks of order 2 n which has the basic properties of a recursive algorithm. The proposed algorithm was tested for a large number of orders and the results proved that the algorithm could be generalized for any input order n where n is a positive integer.

Advanced Encryption Standard–AES, 2005

This paper is motivated by the design of AES. We consider a broader question of cryptanalysis of block ciphers having very good non-linearity and diffusion. Can we expect anyway, to attacks such ciphers, clearly designed to render hopeless the main classical attacks ? Recently a lot of attention have been drawn to the existence of multivariate algebraic relations for AES (and other) S-boxes. Then, if the XSL-type algebraic attacks on block ciphers [11] are shown to work well, the answer would be positive. In this paper we show that the answer is certainly positive for many other constructions of ciphers. This is not due to an algebraic attack, but to new types of generalised linear cryptanalysis, highly-nonlinear in flavour. We present several constructions of somewhat special practical block ciphers, seemingly satisfying all the design criteria of AES and using similar S-boxes, and yet being extremely weak. They can be generalised, and evolve into general attacks that can be applied-potentially-to any block cipher.