, ▁most ▁of ▁the ▁popular ▁public ▁key ▁ci ph ers ▁are ▁based ▁on ▁the ▁difficulty ▁of ▁factor ing ▁integers ▁or ▁the ▁discrete ▁log arith m ▁problem , ▁both ▁of ▁which ▁can ▁be ▁solved ▁by ▁Sh or ' s ▁algorithm . ▁In ▁particular , ▁the ▁R SA , ▁D iff ie – H ell man , ▁and ▁elli ptic ▁curve ▁D iff ie – H ell man ▁algorithms ▁could ▁be ▁broken . ▁These ▁are ▁used ▁to ▁protect ▁secure ▁Web ▁pages , ▁encrypted ▁email , ▁and ▁many ▁other ▁types ▁of ▁data . ▁Bre aking ▁these ▁would ▁have ▁significant ▁ram ifications ▁for ▁electronic ▁priv acy ▁and ▁security . ▁ ▁However , ▁other ▁crypt ographic ▁algorithms ▁do ▁not ▁appear ▁to ▁be ▁broken ▁by ▁those ▁algorithms . ▁Some ▁public - key ▁algorithms ▁are ▁based ▁on ▁problems ▁other ▁than ▁the ▁integer ▁factor ization ▁and ▁discrete ▁log arith m ▁problems ▁to ▁which ▁Sh or ' s ▁algorithm ▁applies , ▁like ▁the ▁Mc E lie ce ▁crypt os ystem ▁based ▁on ▁a ▁problem ▁in ▁coding ▁theory . ▁L attice - based ▁crypt os ystem s ▁are ▁also ▁not ▁known ▁to ▁be ▁broken ▁by ▁quantum ▁computers , ▁and ▁finding ▁a ▁polynomial ▁time ▁algorithm ▁for ▁solving ▁the ▁di hed ral ▁hidden ▁subgroup ▁problem , ▁which ▁would ▁break ▁many ▁lattice ▁based ▁crypt os ystem s , ▁is ▁a ▁well - stud ied ▁open ▁problem . ▁It ▁has ▁been ▁proven ▁that ▁applying ▁Gro ver ' s ▁algorithm ▁to ▁break ▁a ▁symmetric ▁( secret ▁key ) ▁algorithm ▁by ▁br ute ▁force ▁requires ▁time ▁equal ▁to ▁roughly