ALGEBRICAL PROPERTIES OF MODULAR ADDITION MODULO 2TWITH R OPERANT

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ALAEIYAN M.; RAHIMPOUR A.R.; DEHNAVI S.M.

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Journal: Advanced Defense Science and Technology Year:2011 | Volume:1 | Issue:2 Page(s): 25-31

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Information Journal Paper

Title

ALGEBRICAL PROPERTIES OF MODULAR ADDITION MODULO 2TWITH R OPERANT

Author(s)

ALAEIYAN M. | RAHIMPOUR A.R. | DEHNAVI S.M. | Issue Writer Certificate

Keywords

MODULAR ADDITION MODULO 2TQ3

BOOLEAN FUNCTIONSQ3

Abstract

Modular addition modulo 2t is one of the most applicable operators in symmetric cryptography Therefore, investigating the properties of this operator has a significant role in design and analysis of symmetric ciphers. Algebraic properties of this operator have been studied for two operands in [1]. In this contribution, to obtain more accurate results in this area, we generalize some of the algebraic properties of this operator for r ³ 2 operands. More precisely, we consider the algebraic degree of the component BOOLEAN FUNCTIONS of modular addition as a vectorial Boolean function and determine the number of terms and variables in these BOOLEAN FUNCTIONS. After some theoretical analysis in special cases, we propose an efficient algorithm for finding the degree of these BOOLEAN FUNCTIONS general case. Using this algorithm, the algebraic degree of the component BOOLEAN FUNCTIONS for modular addition modulo 232, with three up to eight operands is calculated.

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APA: Copy

ALAEIYAN, M., RAHIMPOUR, A.R., & DEHNAVI, S.M.. (2011). ALGEBRICAL PROPERTIES OF MODULAR ADDITION MODULO 2^TWITH R OPERANT. (JOURNAL OF ADVANCED DEFENCE SCIENCE AND TECHNOLOGY) JOURNAL OF PASSIVE DEFENCE SCIENCE AND TECHNOLOGY, 1(2), 25-31. SID. https://sid.ir/paper/167403/en

Vancouver: Copy

ALAEIYAN M., RAHIMPOUR A.R., DEHNAVI S.M.. ALGEBRICAL PROPERTIES OF MODULAR ADDITION MODULO 2^TWITH R OPERANT. (JOURNAL OF ADVANCED DEFENCE SCIENCE AND TECHNOLOGY) JOURNAL OF PASSIVE DEFENCE SCIENCE AND TECHNOLOGY[Internet]. 2011;1(2):25-31. Available from: https://sid.ir/paper/167403/en

IEEE: Copy

M. ALAEIYAN, A.R. RAHIMPOUR, and S.M. DEHNAVI, “ALGEBRICAL PROPERTIES OF MODULAR ADDITION MODULO 2^TWITH R OPERANT,” (JOURNAL OF ADVANCED DEFENCE SCIENCE AND TECHNOLOGY) JOURNAL OF PASSIVE DEFENCE SCIENCE AND TECHNOLOGY, vol. 1, no. 2, pp. 25–31, 2011, [Online]. Available: https://sid.ir/paper/167403/en

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