Probabilistically Generated Ternary Quasigroup Based Stream Cipher
Presently the crypto-research based on n-quasigroup for n = 3 or higher is at its nascent stages. The recent ternary quasigroup cipher was illustrated using ternary quasigroups of order 4. Practically the ternary quasigroup needs to be of order 256. Strea
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Abstract Presently the crypto-research based on n-quasigroup for n = 3 or higher is at its nascent stages. The recent ternary quasigroup cipher was illustrated using ternary quasigroups of order 4. Practically the ternary quasigroup needs to be of order 256. Stream ciphers to be used for real-world applications need to have ternary quasigroup of order 256. The present paper is an extension of Ternary Quasigroup Stream Cipher for practical applicability. The current work introduces the concept of probabilistically generated quasigroup. The probabilistically generated ternary quasigroup of order 256 improves the cryptographic strength of the cipher.Ternary quasigroups are more desirable options over quasigroup, but they impose serious memory constraints, particularly for large orders, e.g., 256 or more. The current study dynamically generates 3-quasigroup of the order 256 without any requisite to store them. The current study employs a selection criterion to choose suitable probabilistically generated ternary quasigroup with improved cryptographic strength. Keywords Data encryption Stream cipher
⋅ Quasigroups ⋅ Latin squares ⋅ Linear equations ⋅
The present research motive is to find mathematical accessories to design cryptographic primitives. Several cryptographic algorithms based on quasigroups have been developed [1–4]. The goal of present paper is to upgrade the available ciphers [5–9] on ternary quasigroup and quasigroups to improved stream cipher (based on ternary quasigroup). The current paper introduces a method for construction of probabilistic ternary quasigroup (of the order 256). The structure of our paper: Probabilistic quasigroup generators are discussed in Sect. 1. Wherein Sect. 1.1 introduces the probabilistic quasigroup generators enlisting different generators. Section 1.2 discusses the probabilistic ternary quasigroup generators. The modified cipher of present paper is given in Sect. 2. Result and discussions are listed in Sect. 3. Section 4 gives the test cases. The test cases comprises D. Haridas (✉) ⋅ K.C. Emmanuel Sanjay Raj ⋅ V. Sarma ⋅ S. Chowdhury Department of Space, Government of India, Advanced Data Processing Research Institute (ADRIN), Secunderabad, Telangana 500009, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2018 P.K. Sa et al. (eds.), Progress in Intelligent Computing Techniques: Theory, Practice, and Applications, Advances in Intelligent Systems and Computing 719, DOI 10.1007/978-981-10-3376-6_17
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of the comparative study of certain examples of the plaintext ciphertext pairs using previous cipher and the present modified ternary quasigroup based stream cipher results. Conclusions for the present work are given in Sect. 5.
1 Probabilistic Quasigroup Generation of Seed Quasigroup 1.1 Induction of Probabilistic Quasigroup Generators Different ternary quasigroups are generated for different initial seed quasigroups. In the present work, quasigroups of order 256 have been used. If there corresponds a methodology to generate quasigrou
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