Ciphertext-only attack on d × d Hill in O(d13d)

Hill is a classical cipher which is generally believed to be resistant against ciphertext-only attack. In this paper, by using a divide-and-conquer technique, it is first shown that Hill with d×d key matrix over Z26 can be broken with computational complexity of O(d26d), for the English language. This is much less than the only publicly known attack, i.e., the brute-force with complexity of O(d326d2). Then by using the Chinese Remainder Theorem, it is shown that the computational complexity of the proposed attack can be reduced down to O(d13d). Using an information-theoretic approach, it is shown that the minimum ciphertext length required for a successful attack increases by a factor of about 7 and 9.8, respectively for these two attacks in comparison with the brute-force attack. This is the only serious attack on Hill since its invention in 1929.