Key Recovery Attacks on Grain-Like Keystream Generators with Key Injection

Abstract

A common structure in stream ciphers makes use of linear and nonlinear shift registers with a nonlinear output function drawing from both registers. We refer to these as Grain-like keystream generators. A recent development in lightweight ciphers is a modification of this structure to include a non-volatile key register, which allows key bits to be fed into the state update of the nonlinear register. Sprout and Plantlet are examples of this modified structure. The authors of these ciphers argue that including these key bits in the internal state update provides increased security, enabling the use of reduced register sizes below the commonly accepted rule of thumb that the state size should be at least twice the key size. In this paper, we analyse Plantlet and show that the security of this design depends entirely on the choice of the output function. Specifically, the contribution from the nonlinear register to the output function determines whether a key recovery attack is possible. We make a minor modification to Plantlet’s output function which allows the contents of the linear register to be recovered using an algebraic attack during keystream generation. This information then allows partial recovery of the contents of the nonlinear register, after which the key bits and the remaining register contents can be obtained using a guess and check approach, with a complexity significantly lower than exhaustive key search. Note that our attack is not successful on the existing version of Plantlet, though it only requires minor modifications to the filter function in order for the attack to succeed. However, our results clearly demonstrate that including the key in the state update during keystream generation does not increase the security of Plantlet. In fact, this feature was exploited to recover the key during keystream generation without the need to consider the initialisation process. This paper provides design guidelines for choosing both suitable output functions and the register stages used for inputs to these functions in order to resist the attacks we applied.