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Dehnavi, S., Mahmoodi Rishakani, A., Mirzaee Shamsabad, M., Pasha, E. (2014). Statistical properties of the square map. Iranian Journal of Science and Technology (Sciences), 38(3.1), 349-353. doi: 10.22099/ijsts.2014.2433
S. M. Dehnavi; A. Mahmoodi Rishakani; M. R. Mirzaee Shamsabad; E. Pasha. "Statistical properties of the square map". Iranian Journal of Science and Technology (Sciences), 38, 3.1, 2014, 349-353. doi: 10.22099/ijsts.2014.2433
Dehnavi, S., Mahmoodi Rishakani, A., Mirzaee Shamsabad, M., Pasha, E. (2014). 'Statistical properties of the square map', Iranian Journal of Science and Technology (Sciences), 38(3.1), pp. 349-353. doi: 10.22099/ijsts.2014.2433
Dehnavi, S., Mahmoodi Rishakani, A., Mirzaee Shamsabad, M., Pasha, E. Statistical properties of the square map. Iranian Journal of Science and Technology (Sciences), 2014; 38(3.1): 349-353. doi: 10.22099/ijsts.2014.2433

Statistical properties of the square map

Article 8, Volume 38, Issue 3.1, Autumn 2014, Page 349-353  XML PDF (75 K)
Document Type: Regular Paper
DOI: 10.22099/ijsts.2014.2433
Authors
S. M. Dehnavi 1; A. Mahmoodi Rishakani2; M. R. Mirzaee Shamsabad3; E. Pasha1
1Faculty of Mathematical and Computer Sciences, Kharazmi University,Tehran, Islamic Republic of Iran
2Faculty of Sciences, Shahid Rajaee Teacher Training University, Tehran, Islamic Republic of Iran
3Faculty of Mathematics and Computer Science, Shahid Bahonar University, Kerman, Islamic Republic of Iran
Abstract
The square map is one of the functions used in cryptography. For instance, the square map is used in Rabin
encryption scheme, block cipher RC6 and stream cipher Rabbit, in different forms. In this paper, we study
statistical properties of the output of the square map as a vectorial Boolean function. We obtain the joint
probability distribution of arbitrary number of the upper and the lower bits of the output of square map along with
the asymptotic probability distribution of the upper bits of its output. Based upon a measure for evaluating the
imbalance of maps, we study the imbalance of limit distribution of the restriction of square map to its upper bits.
Last, we introduce the square root map and examine this map as a vectorial Boolean function; we compute
probability distribution of the component Boolean functions of this new map and also obtain the imbalance of the
square root map.
Keywords
Square Map; square root map; vectorial boolean function; component boolean function; asymptotic probability distribution
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