Papers by Kondwani Magamba
We obtain upper bounds on the number of irreducible and extended irreducible Goppa codes over GF(... more We obtain upper bounds on the number of irreducible and extended irreducible Goppa codes over GF(p) of length q and q+1, respectively defined by polynomials of degree r, where q=p^t and r≥ 3 is a positive integer.
ArXiv, 2012
The Hill Cipher is a classical symmetric cipher which breaks plaintext into blocks of size m and ... more The Hill Cipher is a classical symmetric cipher which breaks plaintext into blocks of size m and then multiplies each block by an m by m key matrix to yield ciphertext. However, it is well known that the Hill cipher succumbs to cryptanalysis relatively easily. As a result, there have been efforts to strengthen the cipher through the use of various techniques e.g. permuting rows and columns of the key matrix to encrypt each plaintext vector with a new key matrix. In this paper, we strengthen the security of the Hill cipher against a known-plaintext attack by encrypting each plaintext matrix by a variable-length key matrix obtained from a Maximum Distance Separable (MDS) master key matrix.
We obtain an upper bound on the number of extended irreducible q- ary Goppa codes of degree $r$ a... more We obtain an upper bound on the number of extended irreducible q- ary Goppa codes of degree $r$ and length $q^n+1$ , where $q=p^t$ and $n$ and $r>2$ are prime numbers.
We obtain upper bounds on the number of irreducible and extended irreducible Goppa codes over $GF... more We obtain upper bounds on the number of irreducible and extended irreducible Goppa codes over $GF(p)$ of length $q$ and $q+1$, respectively defined by polynomials of degree $r$, where $q=p^t$ and $r\geq 3$ is a positive integer.
Journal of Algebra Combinatorics Discrete Structures and Applications
Let n be an odd prime and m > 1 be a positive integer. We produce an upper bound on the number of... more Let n be an odd prime and m > 1 be a positive integer. We produce an upper bound on the number of inequivalent extended irreducible binary Goppa codes of degree 2 m and length 2 n + 1. Some examples are given to illustrate our results.
We produce an upper bound on the number of extended irreducible Goppa codes over any finite field.
Journal of Discrete Mathematics, 2014
ABSTRACT The problem of finding the number of irreducible monic polynomials of degree r over F_{q... more ABSTRACT The problem of finding the number of irreducible monic polynomials of degree r over F_{q^n} is considered in this paper. By considering the fact that an irreducible polynomial of degree r over F_{q^n} has a root in a subfield F_{q^s} of F_{q^{nr}} if and only if (nr/s,r)=1 , we show that Gauss’s formula for the number of monic irreducible polynomials can be derived by merely considering the lattice of subfields of F_{q^{nr}} . We also use the lattice of subfields of F_{q^{nr}} to determine if it is possible to generate a Goppa code using an element lying in a proper subfield of F_{q^{nr}} .
A linear code C with parameters [n, k, d] over F q is said to be a maximum distance separable(MDS... more A linear code C with parameters [n, k, d] over F q is said to be a maximum distance separable(MDS) code if and only if d = n − k + 1. Goppa codes are linear codes with a beautiful structure and have attracted a lot of attention as they form the backbone of the secure McEliece and Neiderreter public key cryptosytems. In this paper, we consider MDS Goppa codes and show that for any prime q > 2 and there exists a Goppa polynomial of degree r such that the Goppa code [n, k, d] is MDS.
Super-regular matrices are well known for their different applications. For example, it is well k... more Super-regular matrices are well known for their different applications. For example, it is well known that if we append an k ×k super-regular matrix A to an I k identity matrix then [I k |A k×k ] forms a generator matrix of aa [2k, k, k+1] MDS code. Recently, super-regular matrices have been shown to have applications in cryptography and have been used as linear transformations in AES and other block ciphers. In this paper we enumerate super-regular matrices of dimension 3 ≤ k ≤ 9 over 3 ≤ F q ≤ 5.
arXiv preprint arXiv:1210.1940, 2012
The Hill Cipher is a classical symmetric cipher which breaks plaintext into blocks of size and th... more The Hill Cipher is a classical symmetric cipher which breaks plaintext into blocks of size and then multiplies each block by an × key matrix to yield ciphertext. However, it is well known that the Hill cipher succumbs to cryptanalysis relatively easily. As a result, there have been efforts to strengthen the cipher through the use of various techniques e.g. permuting rows and columns of the key matrix to encrypt each plaintext vector with a new key matrix. In this paper, we strengthen the security of the Hill cipher against a known-plaintext attack by encrypting each plaintext matrix by a variable-length key matrix obtained from a Maximum Distance Separable (MDS) master key matrix.
In mobile devices, data compression is important in that it is an
essential tool to decrease stor... more In mobile devices, data compression is important in that it is an
essential tool to decrease storage size, maximise power supply and increase the speed of data transmission. In this paper, a hybrid compression system is proposed which uses static Hu ffman codes to encode bit streams and the resulting bits are further compressed using Hamming Codes. The paper also discusses an application of the proposed method to Short Messaging Service (SMS) compression.
The Hill Cipher is a classical symmetric cipher which breaks plaintext into blocks of size n and ... more The Hill Cipher is a classical symmetric cipher which breaks plaintext into blocks of size n and then multiplies each block by an mxm key matrix to yield ciphertext. However,it is well known that the Hill cipher succumbs to cryptanalysis relatively easily. Recently, there have been e forts to strengthen the cipher through the use of modern techniques e.g. the use of S-boxes and P-boxes which have improved the security of the cipher quite signi cantly. In this paper, we examine the level of security of the Hill cipher when it is required that the key matrix be Maximum Distance Separable (MDS).
"In this paper, we survey the state of Text Message Compression protocols and levels of compressi... more "In this paper, we survey the state of Text Message Compression protocols and levels of compression achieved through their use. We start by reviewing statistical-based compression protocols.We pay special attention to their design and then make a comparative analysis of these methods and
other compression methods e.g Dictionary Methods. We also propose a combined approach to Short Messaging Service(SMS) compression. Finally, we discuss how feasible and under what conditions Compression protocols can be applied in hand-held devices."
AFRICON 2007, Jan 1, 2007
In this paper, by defining an irreducible Goppa code in terms of a single field element, we give ... more In this paper, by defining an irreducible Goppa code in terms of a single field element, we give a simple proof of the well known result, namely that if one irreducible Goppa polynomial can be transformed into another by a combination of an affine map and a Frobenius automorphism, then the corresponding codes are equivalent. We give the details of the proof for the most general case, namely for irreducible Goppa codes over any finite field and further show that the equivalence in question is one of the simplest types, that is a permutation of coordinate positions. Finally, by giving a full categorisation of irreducible Goppa codes of length 32, we show 1) that contrary to a previous claim, even if two Goppa polynomials are not related by the above two maps, the Goppa codes can still be equivalent and 2) the upper bound on the number of irreducible Goppa codes given in a recent publication is not tight.
Conference Presentations by Kondwani Magamba
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Papers by Kondwani Magamba
essential tool to decrease storage size, maximise power supply and increase the speed of data transmission. In this paper, a hybrid compression system is proposed which uses static Hu ffman codes to encode bit streams and the resulting bits are further compressed using Hamming Codes. The paper also discusses an application of the proposed method to Short Messaging Service (SMS) compression.
other compression methods e.g Dictionary Methods. We also propose a combined approach to Short Messaging Service(SMS) compression. Finally, we discuss how feasible and under what conditions Compression protocols can be applied in hand-held devices."
Conference Presentations by Kondwani Magamba
Books by Kondwani Magamba
essential tool to decrease storage size, maximise power supply and increase the speed of data transmission. In this paper, a hybrid compression system is proposed which uses static Hu ffman codes to encode bit streams and the resulting bits are further compressed using Hamming Codes. The paper also discusses an application of the proposed method to Short Messaging Service (SMS) compression.
other compression methods e.g Dictionary Methods. We also propose a combined approach to Short Messaging Service(SMS) compression. Finally, we discuss how feasible and under what conditions Compression protocols can be applied in hand-held devices."