Resistance of Stream Ciphers to Algebraic Recovery of Internal Secret States

Cryptanalysis is also a tool to measure the strength of a cipher in terms of its resistance against different types of attacks. Every new proposed design ensures at least that it is resistant to the existing attacks. Algebraic attack is now quite a familiar threat for stream ciphers. Moreover, to make out the design components that can strengthen a cipher against algebraic cryptanalysis must also be of interest to stream cipher designers. Algebraic cryptanalysis, in its general form, aims to recover the internal secret state bits of the registers of the cipher by solving non-linear algebraic equations. That is why it is considered to be not applicable on stream ciphers where registers are updated non-linearly. Since in this case degree of algebraic equations, which relate internal states with key-stream bits, increase with each clock. However different designs with nonlinear update may offer disparate levels of resistance. In this article we compare some recently proposed structures of stream ciphers and identify the level of resistance their design shows against gaining the secret internal states. We analyze eSTREAM proposed stream ciphers Grain, Trivium and Mickey and also compare their key generating structures. Mickey and Grain-128 are found to be more resistant than Grain-v1 and Trivium.