## A Cryptanalysis of PRINTcipher: The Invariant
Subspace Attack

** Gregor Leander, Mohamed Ahmed Abdelraheem, Hoda AlKhzaimi, and
Erik Zenner**

* Technical University of Denmark, Lyngby, Denmark*
**Abstract.**
At CHES 2010, the new block cipher PRINTcipher was
presented as a light-weight encryption solution for printable circuits [15].
The best attack to date is a differential attack [1] that breaks less than
half of the rounds. In this paper, we will present a new attack called
invariant subspace attack that breaks the full cipher for a significant
fraction of its keys. This attack can be seen as a weak-key variant of a
statistical saturation attack. For such weak keys, a chosen plaintext
distinguishing attack can be mounted in unit time. In addition to breaking
PRINTcipher, the new attack also gives us new insights into other, more
well-established attacks. We derive a truncated differential characteristic
with a round-independent but highly key-dependent probability. In
addition, we also show that for weak keys, strongly biased linear
approximations exists for any number of rounds. In this sense, PRINTcipher
behaves very differently to what is usually – often implicitly – assumed.

** Keywords.**
Symmetric cryptography, block cipher, invariant subspace attack.