We count the number of permutations with k occurrences of the pattern 2–13 in permutations by lattice path enumeration. We give closed forms for k ≤ 8, extending results of Claesson and Mansour.

The r-round (iterated) Even-Mansour cipher (also known as key-alternating cipher) defines a block cipher from r fixed public n-bit permutations P1, . . . , Pr as follows: given a sequence of n-bit round keys k0, . . . , kr, an n-bit plaintext x is encrypted by xoring round key k0, applying permutation P1, xoring round key k1, etc. The (strong) pseudorandomness of this construction in the random...

BACKGROUND The science of toxicology has a long history and been highly valued in Islamic countries. Numerous scientists were the expert in this field, particularly during the third and fourth centuries. Through reading such literature and gaining the experience of the scientists, one can use such valuable information to promote this science. METHODS In this article, different sources of trad...

In 1396 (798/799), two hundred years before Vesalius, the Persian author Mans: ur ibn Muh:ammad ibn Ah:mad ibn Y usuf ibn Faq h Ily as composed a treatise on anatomy entitled Tas:r h: -i Mans: ur that summarized many of the observations of Galen. It was not the first such treatise to be composed in the Islamic world, but it was the first to be accompanied by drawings of the human body in anatom...

Akıl İslam düşünce geleneğinde geçmişten günümüze önemini korumuş, epistemoloji ve ontolojinin konusu olmuş, kelam, felsefe tasavvufun ortak kavramı olarak her zaman tartışılmış bir kavram güncelliğini korumaktadır. felsefesi özelinde bakıldığında özellikle Fârâbî akıl konusunda sudûr teorisi ekseninde ontolojiyi ile harmanlanmış şekilde aklı izah etmeye çalışmıştır. İbn Sînâ diğer konularda ol...

We propose new key recovery attacks on the two minimal two-round n-bit Even-Mansour ciphers that are secure up to 2 queries against distinguishing attacks proved by Chen et al. Our attacks are based on the meet-in-the-middle technique which can significantly reduce the data complexity. In particular, we introduce novel matching techniques which enable us to compute one of the two permutations w...