Compact representation for division property

Abstract

The division property, which is a new method to find integral characteristics, was proposed at Eurocrypt 2015. Thereafter, some applications and improvements have been proposed. The bit-based division property is also one of such improvements, and the accurate integral characteristic of Simon32 is theoretically proved. In this paper, we propose the compact representation for the bit-based division property. The disadvantage of the bit-based division property is that it cannot be applied to block ciphers whose block length is over 32 because of high time and memory complexity. The compact representation partially solves this problem, and we apply this technique to 64-bit block cipher PRESENT to illustrate our method. We can accurately evaluate the propagation characteristic of the bit-based division property thanks to the compact representation. As a result, we find 9-round integral characteristics, and the characteristic is improved by two rounds than previous best characteristic. Moreover, we attack 12-round PRESENT-80 and 13- round PRESENT-128 by using this new characteristic.