Solving an equation system is a very important step in algebraic attack.For a cryptosystem

after being transformed to equations

we often need to employ guess-and-determine algorithm to estimate computational complexity of this attack.In this paper

we introduce a model to estimate average time in solving subsystems more accurately

and propose some criteria on selecting specific guessed variables to speed up the solving efficiency

which based on static weight and dynamic weight etc.For comupting Grbner bases

we use serveral varible order which are AB

S

S-rev etc.Meanwhile

we introduce the concept of conflicting equations

and show the importance for correct analysis and narrow guessing space.In the end

we estimate the time of attacking Bivium.Experiments showed that

in the worst cases

guessing 60 varibles in the Evy3 position and with DM-rev varible order will have the optimal result

that is about 2 exp(39.16) seconds.