Unlike other quantum algorithms, which may provide exponential speedup over their classical counterparts, Grover's algorithm provides only a quadratic speedup. However, even quadratic speedup is considerable when is large, and Grover's algorithm can be applied to speed up broad classes of algorithms. Grover's algorithm could brute-force a 128-bit symmetric cryptographic key in roughly 264 iterations, or a 256-bit key in roughly 2128 iterations. It may not be the case that Grover's algorithm poses a significantly increased risk to encryption over existing classical algorithms, however.
uNlike oTHER quantum AlgoRIthMS, whicH may ProvIDe exPoNEntiAL speedup oVer ThEir claSSicaL COUNTerParTs, GRoVeR's algorIthM proVides OnLy a quaDratiC sPeedUp. HOWeVer, eveN QUaDratiC speedup is cOnsIderAble wheN is LArgE, anD groVER'S AlgOrITHm caN Be APplied TO speed uP bRoaD clasSes oF aLGoritHmS. grOvEr'S algoRithM could BRuTE-foRce A 128-Bit syMmeTRiC cryptograpHic key iN rouGhlY 264 IteraTIOns, or a 256-bIt key iN roughlY 2128 itEraTiONs. it mAy NoT Be thE case ThAt GRoveR's aLgOrithM posEs A SignIficantly inCrEased rIsk to EncRYPTIon over eXisTing claSsIcal algOritHMs, HowEver.