IACR News item: 23 February 2016
S. M. Dehnavi, A. Mahmoodi Rishakani, M. R. Mirzaee Shamsabad, Hamidreza Maimani, Einollah Pasha
ePrint Report
The operation of modular addition modulo a power of two is one of the most applied operations in symmetric cryptography.
For example, modular addition is used in RC6, MARS and Twofish block ciphers and RC4, Bluetooth and Rabbit stream ciphers.
In this paper, we study statistical and algebraic properties of modular addition modulo a power of two. We obtain probability
distribution of modular addition carry bits along with conditional probability distribution of these carry bits. Using these probability
distributions and Markovity of modular addition carry bits, we compute the joint probability distribution of arbitrary number
of modular addition carry bits. Then, we examine algebraic properties of modular addition with a constant and obtain the number
of terms as well as algebraic degrees of component Boolean functions of modular addition with a constant. Finally, we present another
formula for the ANF of the component Boolean functions of modular addition modulo a power of two. This formula
contains more information than representations which are presented in cryptographic literature, up to now.
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