Author

# Ghulam Murtaza

Bio: Ghulam Murtaza is an academic researcher. The author has contributed to research in topics: MDS matrix & Cipher. The author has an hindex of 2, co-authored 4 publications receiving 18 citations.

Topics: MDS matrix, Cipher, Block cipher, Hash chain, Double hashing

##### Papers

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11 Dec 2017

TL;DR: In this article, the authors proposed a Dynamic Mix Column Transformation (DCT) based on the default MDS Matrix of AES and mbit additional key, where m is a variable length that does not exceed the product of 31.97 and one less the number of encryption rounds.

Abstract: MDS Matrix has an important role in the design of Rijndael Cipher and is the most expensive component of the cipher. It is also used as a perfect diffusion primitive in some other block ciphers. In this paper, we propose a replacement of Mix Column Transformation in AES by equivalent Dynamic Mix Column Transformation. A Dynamic Mix Column Transformation comprises dynamic MDS Matrices which are based on default MDS Matrix of AES and mbit additional key. Here m is a variable length that does not exceed the product of 31.97 and one less the number of encryption rounds. This mechanism increases a brute force attack complexity by m-bit to the original key and enforces the attackers to design new frameworks for different modern cryptanalytic techniques applicable to the cipher. We also present efficient implementation of this technique in Texas Instrument’s DSP C64x+ with no extra cost to default AES and in Xilinx Spartan3 FPGA with no change in AES throughput. We also briefly analyze the security achieved over it.

9 citations

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TL;DR: Ghulam Murtaza, Nassar Ikram as discussed by the authors presented an idea of direct exponent and direct square of a matrix and showed that direct exponent may not be an MDS matrix.

Abstract: Ghulam Murtaza, Nassar Ikram 1,2 National University of Sciences and Technology, Pakistan azarmurtaza@hotmail.com dr_nassar_ikram@yahoo.com Abstract. An MDS matrix is an important building block adopted by different algorithms that provides diffusion and therefore, has been an area of active research. In this paper, we present an idea of direct exponent and direct square of a matrix. We prove that direct square of an MDS matrix results in an MDS matrix whereas direct exponent may not be an MDS matrix. We also delineate direct exponent class and scalar multiplication class of an MDS matrix and determine the number of elements in these classes. In the end, we discuss the standing of design properties of a cryptographic primitive by replacing MDS matrix by dynamic one.

8 citations

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TL;DR: MAYHAM is designed as a simple and efficient hash function as compared to other dedicated hash functions and supports parallel processing in its compression function and can be efficiently implemented by using lookup tables.

Abstract: With the succumbing of various Hash functions to collision attacks, there have been serious research efforts to design new Hash functions which are robust against various contemporary attacks. MAYHAM is one such hash function that has been designed keeping in view the cryptographic properties needed yet resistant to all the publically known attacks. MAYHAM is designed as a simple and efficient hash function as compared to other dedicated hash functions. Main operations involved in MAYHAM’s hash computation include S-box, MDS Matrix multiplication, data mixing, XOR, addition and interleaving. MAYHAM supports parallel processing in its compression function and can be efficiently implemented by using lookup tables.

1 citations

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TL;DR: In this paper, a fast implementation of the cipher using Texas Instrument's DSP C64x+ is presented, which is based on the strategy of multiple layered security and derived from AES-128.

Abstract: Grand Cru, a candidate cipher algorithm of NESSIE project, is based on the strategy of multiple layered security and derived from AES-128. This algorithm was not selected for second phase evaluation of NESSIE project due to implementation and processing cost. In this paper we present relatively a fast implementation of the cipher using Texas Instrument’s DSP C64x+.

##### Cited by

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TL;DR: In this article, the question of what happens if we replace all the constants in Rijndael, including the irreducible polynomial, the coefficients of the MixColumn operation, the affine transformation in the S box, etc.

Abstract: In this paper we ask the question what happens if we replace all the constants in Rijndael, including the replacement of the irreducible polynomial, the coefficients of the MixColumn operation, the affine transformation in the S box, etc. We show that such replacements can create new dual ciphers, which are equivalent to the original in all aspects. We present several such dual ciphers of Rijndael, such as the square of Rijndael, and dual ciphers with the irreducible polynomial replaced by primitive polynomials. We also describe another family of dual ciphers consisting of the logarithms of Rijndael.We then discuss self-dual ciphers, and extend our results to other ciphers.

84 citations

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TL;DR: The results show that the proposed method efficiently generated cipher images with very low correlation coefficients of adjacent pixels and provided better encryption speed and high security as a result of the dependence of the S-box on the key characteristics of the chaotic system.

Abstract: With the rapid development of the Internet and communication networks, the confidentiality of digital images transmitted over public networks must be preserved by using encryption techniques. Advanced Encryption Standard (AES) is one of the most commonly used encryption algorithms at present. Although AES has several advantages, such as security in data encryption, it also has a number of drawbacks, such as high computations, pattern problems when used for encrypting images, and fixed S-box weak points. This paper proposes a method that overcomes the fixed S-box weak points and improves the performance of AES when used for encrypting images, particularly when the image data are large. In addition, the MixColumn stage is replaced by chaotic mapping and XOR operation to reduce the high computations in MixColumn transform. The proposed method is tested on several images, and the results show that the proposed method efficiently generated cipher images with very low correlation coefficients of adjacent pixels and provided better encryption speed and high security as a result of the dependence of the S-box on the key characteristics of the chaotic system.

25 citations

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11 Dec 2017

TL;DR: In this article, the authors proposed a Dynamic Mix Column Transformation (DCT) based on the default MDS Matrix of AES and mbit additional key, where m is a variable length that does not exceed the product of 31.97 and one less the number of encryption rounds.

Abstract: MDS Matrix has an important role in the design of Rijndael Cipher and is the most expensive component of the cipher. It is also used as a perfect diffusion primitive in some other block ciphers. In this paper, we propose a replacement of Mix Column Transformation in AES by equivalent Dynamic Mix Column Transformation. A Dynamic Mix Column Transformation comprises dynamic MDS Matrices which are based on default MDS Matrix of AES and mbit additional key. Here m is a variable length that does not exceed the product of 31.97 and one less the number of encryption rounds. This mechanism increases a brute force attack complexity by m-bit to the original key and enforces the attackers to design new frameworks for different modern cryptanalytic techniques applicable to the cipher. We also present efficient implementation of this technique in Texas Instrument’s DSP C64x+ with no extra cost to default AES and in Xilinx Spartan3 FPGA with no change in AES throughput. We also briefly analyze the security achieved over it.

9 citations

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TL;DR: Some new results on the preservation of many good cryptographic properties of MDS matrices under direct exponent transformation are presented and are shown to have important applications in constructing dynamic diffusion layers for block ciphers.

Abstract: Maximum Distance Separable (MDS) code has been studied for a long time in the coding theory and has been applied widely in cryptography. The methods for transforming an MDS into other ones have been proposed by many authors in the literature. These methods are called MDS matrix transformations in order to generate different MDS matrices (dynamic MDS matrices) from an existing one. In this paper, some new results on the preservation of many good cryptographic properties of MDS matrices under direct exponent transformation are presented. These good cryptographic properties include MDS, involutory, symmetric, recursive (exponent of a companion matrix), the number of 1's and distinct elements in a matrix, circulant and circulant-like . In addition, these results are shown to have important applications in constructing dynamic diffusion layers for block ciphers. The strength of the ciphers against developing cryptanalytic techniques can be enhanced by the dynamic MDS diffusion layers.

4 citations

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17 Jun 2011

TL;DR: In this paper, the authors presented a method of linear transformation in substitution-permutation network symmetric-key block cipher (SPSC) for key-dependent MDS matrices.

Abstract: One embodiment of the present invention is a method of linear transformation in Substitution-Permutation Network symmetric-key block cipher producing n x n key-dependent MDS matrices from given n x n MDS matrix by scalar multiplication and permutations of elements of given matrix where multiplicative scalar and permutations are derived from binary inputs of length l . The method comprising deriving multiplicative scalar from binary input; multiplying given matrix with multiplicative scalar, producing first intermediate matrix; deriving first permutation of n objects from binary input; permuting rows of first intermediate matrix according to first permutation, producing second intermediate matrix; deriving second permutation of n objects from binary input; and permuting columns of second intermediate matrix according to second permutation to produce final MDS matrix. Another embodiment of the present invention is a method of linear transformation in Substitution-Permutation Network symmetric-key block cipher producing n x n key-dependent MDS matrices from given n x n MDS matrix by scalar multiplication and permutations of elements of given matrix where multiplicative scalar and permutations are derived from binary inputs of length l . The method comprising deriving multiplicative scalar from the key (202); multiplying given matrix with multiplicative scalar to produce first intermediate matrix (204); deriving first permutation of n objects from the key (206); permuting rows of first intermediate matrix according to first permutation to produce second intermediate matrix (208); deriving second permutation of n objects from the key (304); and permuting columns of second intermediate matrix according to second permutation (212) to produce final MDS matrix (214).

4 citations