A new algebraic attack on DASTA

As a fully homomorphic encryption friendly symmetric-key primitive, DASTA was invented by Hebborn at Fast Software Encryption 2020. A new fixed linear layer design concept is introduced in the DASTA stream cipher so that its AND depth and the number of ANDs per encrypted bit are quite small. Currently, the security of the DASTA stream cipher has received extensive attention. Note that the best-known attack (i.e., algebraic attack) on DASTA still has a very high data complexity. It appears to be an important task to reduce the data complexity of the attack on DASTA. In this article, a new algebraic attack on DASTA is proposed. More specifically, the key feed-forward operation, the properties of the nonlinear layer and the invariance from the linear layer are successfully utilized in the attack. In particular, the nonlinear relation of internal states in DASTA is linearized effectively. In this case, more secret key bit equations with low algebraic degrees are collected by fixing the bit. It is illustrated that four ( r − 1 )-round instances of the DASTA cipher family are theoretically broken by the attack, where r is the iterative number of round operations. Compared with the results of previous algebraic attacks, our approach achieves more favorable data complexity.