Hill cipher modification based on eigenvalues HCM-EE

Mahmoud, Ahmed Y.; Chefranov, Alexander G.

doi:10.1145/1626195.1626237

Cited by 17 publications

(14 citation statements)

References 6 publications

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“…HCM-EE [14] works as follows. Sender A selects a set E = {e 1 , e 2 , ..., e m } ⊂ Z N − {0}, gcd(e j , N) = 1, gcd is the greatest common divisor, 1 ≤ j ≤ m; at least one e j should have the maximal order which is ϕ(N) 2 for N being a power of 2 [17], ϕ(N) is the Eulers totient function [5], giving the number of positive integers less than N and co-prime to it.…”

Section: Overview Of the Hill Cipher And Its Mmodificationsmentioning

confidence: 99%

“…The proposed HCM-PRE uses the same encryption/decryption technique as HCM-EE [14] does. But HCM-PRE differs from the HCM-EE in the key construction.…”

Section: The Proposed Schemementioning

confidence: 99%

“…The difference between HCM-H and HCM-HMAC is similar to the difference between HCM-PT and HCM-NPT. In [14], we introduce a modification of the HC, HCM-EE, based on the use of eigenvalues for matrix exponentiation to a pseudo-random power for a new key matrix generating for each plaintext block. In this paper we propose a new modification of HC, HCM-PRE, based on the use of pseudo-random eigenvalues to construct a key matrix [15] and modify it for each new plaintext.…”

Section: Introductionmentioning

confidence: 99%

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Hill Cipher Modification based on Pseudo-Random Eigenvalues

Mahmoud¹,

Chefranov²

2014

Appl. Math. Inf. Sci.

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Abstract:The Hill cipher is resistant to brute-force and statistical attacks, but it can be broken with a known plaintext-ciphertext attack (KPCA). In this paper, we propose a modification of the Hill cipher, HCM-PRE, which is still resistant to brute-force and statistical attacks, and is resistant also to KPCA due to dynamic encryption key matrix generating. With the modification, the new HCM-PRE can be applied widely in the systems which need high security (e.g., image encryption). Experimental results show that the proposed modification is significantly more effective in the encryption quality of images than original Hill cipher and its known modifications (HCM-PT, HCM-H, HCM-HMAC, and HCM-EE) in the case of images with large single colour areas, and slightly more effective otherwise. HCM-PRE is about two times faster than HCM-EE and HCM-HMAC and four times faster than HCM-H in the frame of our experiments.

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Section: Overview Of the Hill Cipher And Its Mmodificationsmentioning

confidence: 99%

“…The proposed HCM-PRE uses the same encryption/decryption technique as HCM-EE [14] does. But HCM-PRE differs from the HCM-EE in the key construction.…”

Section: The Proposed Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hill Cipher Modification based on Pseudo-Random Eigenvalues

Mahmoud¹,

Chefranov²

2014

Appl. Math. Inf. Sci.

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“…Instead, both sides use a pseudo-random permutation generator, and only the number of the necessary permutation is transferred to the receiver. It is shown in [7], [8] that both SHC and SHC-M fail to hide an image if it has large same colored areas. Another HC modification [5], HCM-H, also uses dynamic key matrix produced with the help of a one way hash function applied to an integer picked up randomly by the sender to get the key matrix, and a vector added to the product of the key matrix with a plain text.…”

Section: Introductionmentioning

confidence: 99%

“…Another HC modification [5], HCM-H, also uses dynamic key matrix produced with the help of a one way hash function applied to an integer picked up randomly by the sender to get the key matrix, and a vector added to the product of the key matrix with a plain text. It is shown in [7], [8] that HCM-H fails to hide an image if it has large same colored areas and it is vulnerable [9] to chosen-ciphertext attack because the selected random number is transmitted in clear over the communication link and is repeated.…”

Section: Introductionmentioning

confidence: 99%

Secure Hill Cipher Modification Based on Generalized Permutation Matrix SHC-GPM

Mahmoud¹,

Chefranov²

2012

Inf. Sci. Lett.

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Secure Hill cipher (SHC) modification based on dynamically changing generalized permutation matrix, SHC-GPM is proposed. It provides better security than that of SHC due to the significantly larger number of non-repeatedly generated keys ( 48 2 times greater for the parameters used in the conducted experiments). SHC-GPM is shown to be robust against the brute-force, statistical attacks, and is resistant also to known plaintext ciphertext attack (KPCA) due to dynamic encryption key matrix generating. The proposed modification is applied for colour images encryption. Experimental results show that the proposed modification is significantly more effective in the encryption quality of bitmap images than SHC in the case of images with large single colour areas and slightly more effective otherwise.

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The Probabilistic Encryption Algorithm Using Linear Transformation

Reddy¹,

Vishnuvardhan

2015

Advances in Intelligent Systems and Computing

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Hill cipher modification based on eigenvalues HCM-EE

Cited by 17 publications

References 6 publications

Hill Cipher Modification based on Pseudo-Random Eigenvalues

Hill Cipher Modification based on Pseudo-Random Eigenvalues

Secure Hill Cipher Modification Based on Generalized Permutation Matrix SHC-GPM

The Probabilistic Encryption Algorithm Using Linear Transformation

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