## A Secure Variant of the Hill Cipher (2009)

Venue: | 14TH IEEE SYMPOSIUM ON COMPUTERS AND COMMUNICATIONS (ISCC'09) |

Citations: | 1 - 0 self |

### BibTeX

@MISC{Toorani09asecure,

author = {M. Toorani and A. Falahati},

title = {A Secure Variant of the Hill Cipher},

year = {2009}

}

### OpenURL

### Abstract

The Hill cipher is a classical symmetric encryption algorithm that succumbs to the know-plaintext attack. Although its vulnerability to cryptanalysis has rendered it unusable in practice, it still serves an important pedagogical role in cryptology and linear algebra. In this paper, a variant of the Hill cipher is introduced that makes the Hill cipher secure while it retains the efficiency. The proposed scheme includes a ciphering core for which a cryptographic protocol is introduced.

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Citation Context ... calculating a modular addition, modular multiplication, and modular inverse will be of [11]: Inv (1) (2) TAdd = O(ζ ) (3) 3 TInv = O( ζ ) (5) There are also many fast algorithms for the computations =-=[12]-=- but we consider the time complexity of conventional methods since it corresponds with the worst situation and anyone can decrease the required number of operations by deploying faster algorithms. The... |

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Citation Context ...troduction The Hill cipher was invented by L.S. Hill in 1929 [1]. It is a famous polygram and a classical symmetric cipher based on matrix transformation but it succumbs to the known-plaintext attack =-=[2]-=-. Although its vulnerability to cryptanalysis has rendered it unusable in practice, it still serves an important pedagogical role in both cryptology and linear algebra. The Hill cipher is a block ciph... |

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Citation Context ...g the elements of vector V as v = k + v ~ 1a (mod p) v ~ − as i ij i− t and defining i 1 ~ ⎡γ/ 2 2 ⎤ ( mod2 ⎡γ/ 2 v ⎤ − 1 = + i−1 ) i v takes advantages of ideas behind the MQV key-exchange protocols =-=[9]-=-. v ~ i−1 is simply computed by taking the least significant half in binary representation of v i−1 and such definition will decrease the computational costs and consequently, increases the efficiency... |

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Citation Context ... multiplication, addition, and inverse calculations respectively. Total required number of operations for computing SHA-1 and MD5 hash functions are calculated as 1110 and 744 operations respectively =-=[10]-=-. Each of T Mul , T Add and T Inv requires different number of operations. Let ζ = ⎣log2 p⎦ + 1 denotes the bit-length of modulus p. Using the conventional methods, the running time fo r calculating a... |

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Citation Context ...cure while it retains the efficiency. The proposed scheme includes a ciphering core for which a cryptographic protocol is introduced. 1. Introduction The Hill cipher was invented by L.S. Hill in 1929 =-=[1]-=-. It is a famous polygram and a classical symmetric cipher based on matrix transformation but it succumbs to the known-plaintext attack [2]. Although its vulnerability to cryptanalysis has rendered it... |

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Citation Context ...troduction The Hill cipher was invented by L.S. Hill in 1929 [1]. It is a famous polygram and a classical symmetric cipher based on matrix transformation but it succumbs to the known-plaintext attack =-=[2]-=-. Although its vulnerability to cryptanalysis has rendered it unusable in practice, it still serves an important pedagogical role in both cryptology and linear algebra. The Hill cipher is a block ciph... |

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Citation Context ...r addition, modular multiplication, and modular inverse will be of [11]: Inv (1) (2) TAdd = O( ζ ) (3) 2 TMul = O( ζ ) (4) 3 TInv = O( ζ ) (5) There are also many fast algorithms for the computations =-=[12]-=- but we consider the time complexity of conventional methods since it corresponds with the worst situation and anyone can decrease the required number of operations by deploying faster algorithms. The... |

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Citation Context ...t efficient. Ismail et al. [3] used an initial vector that multiplies successively by some orders of the key matrix to produce the corresponding key of each block but it has several security problems =-=[7]-=-. In this paper, a secure cryptosystem is introduced that overcomes all the security drawbacks of the Hill cipher. The proposed scheme includes an encryption algorithm that is a variant of the Affine ... |

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Citation Context ... Although their scheme thwarts the knownplaintext attack, it is so time-consuming, requires many mathematical manipulations, and is not efficient especially when dealing with a bulk of data. Saeednia =-=[5]-=- tried to make the Hill cipher secure using some random permutations of columns and rows of the key matrix but it is proved that his cryptosystem is vulnerable to the known-plaintext attack [6], the s... |

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Citation Context .... Let ζ = ⎣log2 p⎦ + 1 denotes the bit-length of modulus p. Using the conventional methods, the running time for calculating a modular addition, modular multiplication, and modular inverse will be of =-=[11]-=-: Inv (1) (2) TAdd = O(ζ ) (3) 3 TInv = O( ζ ) (5) There are also many fast algorithms for the computations [12] but we consider the time complexity of conventional methods since it corresponds with t... |

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Citation Context ...eednia [5] tried to make the Hill cipher secure using some random permutations of columns and rows of the key matrix but it is proved that his cryptosystem is vulnerable to the known-plaintext attack =-=[6]-=-, the same vulnerability of the original Hill cipher. Lin et al. [6] tried to improve the security of the Hill cipher using several random numbers generated in a hash chain but their scheme is not eff... |

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Citation Context ... Although their scheme thwarts the knownplaintext attack, it is so time-consuming, requires many mathematical manipulations, and is not efficient especially when dealing with a bulk of data. Saeednia =-=[5]-=- tried to make the Hill cipher secure using some random permutations of columns and rows of the key matrix but it is proved that his cryptosystem is vulnerable to the known-plaintext attack [6], the s... |

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Citation Context ...matrix multiplication and inversion for encryption and decryption, and its high speed and high throughput [3]. Several researches have been done to improve the security of the Hill cipher. Yeh et al. =-=[4]-=- used two coprime base numbers that are securely shared between the participants. Although their scheme thwarts the knownplaintext attack, it is so time-consuming, requires many mathematical manipulat... |

1 |
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(Show Context)
Citation Context ... multiplication, addition, and inverse calculations respectively. Total required number of operations for computing SHA-1 and MD5 hash functions are calculated as 1110 and 744 operations respectively =-=[10]-=-. Each of TMul , TAdd and TInv requires different number of operations. Let ζ = ⎣log2 p⎦ + 1 denotes the bit-length of modulus p. Using the conventional methods, the running time for calculating a mod... |