Algebraic Countermeasure to Enhance the Improved Summation Generator with 2-Bit Memory

Recently proposed algebraic attack has been shown to be very effective on several stream ciphers. In this paper, we have investigated the resistance of PingPong family of stream ciphers against algebraic attacks. This stream cipher was proposed in 2008 to enhance the security of the improved summation generator against the algebraic attack. In particular, we focus on the PingPong-128 stream cipher’s resistance against algebraic attack in this paper. In our analysis, it is found that an algebraic attack on PingPong family of stream ciphers require much more operations compare to the exhaustive key search on the internal state of the LFSRs. It will be shown that due to the irregular and mutual clock controlling in PingPong stream cipher the degree of the generated equation tends to grow up with each successive clock which in turn increases the overall complexity of an algebraic attack. Along with the PingPong 128 stream cipher the other instances of PingPong family stream ciphers are also investigated against the algebraic attack. Our analysis shows that, PingPong family stream ciphers are highly resistant against the algebraic attack due to their mutual and irregular clocking function.