▁the ▁algebraic ▁properties ▁of ▁the ▁underlying ▁groups , ▁and ▁the ▁notion ▁originally ▁seemed ▁to ▁be ▁very ▁much ▁related ▁to ▁the ▁algebra . ▁However , ▁it ▁was ▁shown ▁that ▁bas ing ▁statist ically ▁binding ▁commit ment ▁schemes ▁on ▁general ▁un struct ured ▁assumption ▁is ▁possible , ▁via ▁the ▁notion ▁of ▁interactive ▁has hing ▁ ▁for ▁commit ments ▁from ▁general ▁complexity ▁assumptions ▁( specific ally ▁and ▁originally , ▁based ▁on ▁any ▁one ▁way ▁permut ation ) ▁as ▁in ▁ ▁. ▁ ▁Quant um ▁bit ▁commit ment ▁It ▁is ▁an ▁interesting ▁question ▁in ▁quantum ▁crypt ography ▁if ▁un condition ally ▁secure '' ▁bit ▁commit ment ▁protocol s ▁exist ▁on ▁the ▁quantum ▁level , ▁that ▁is , ▁protocol s ▁which ▁are ▁( at ▁least ▁asympt ot ically ) ▁binding ▁and ▁conce aling ▁even ▁if ▁there ▁are ▁no ▁restrictions ▁on ▁the ▁computational ▁resources . ▁One ▁could ▁hope ▁that ▁there ▁might ▁be ▁a ▁way ▁to ▁explo it ▁the ▁intr insic ▁properties ▁of ▁quantum ▁mechan ics , ▁as ▁in ▁the ▁protocol s ▁for ▁un condition ally ▁secure ▁key ▁distribution . ▁ ▁However , ▁this ▁is ▁impossible , ▁as ▁Domin ic ▁May ers ▁showed ▁in ▁ 1 9 9 6 ▁( see ▁ ▁for ▁the ▁original ▁proof ). ▁Any ▁such ▁protocol ▁can ▁be ▁reduced ▁to ▁a ▁protocol ▁where ▁the ▁system ▁is ▁in ▁one ▁of ▁two ▁pure ▁states ▁after ▁the ▁commit ment ▁phase , ▁depending ▁on ▁the ▁bit ▁Alice ▁wants ▁to ▁commit . ▁If ▁the ▁protocol ▁is ▁un condition ally ▁conce aling , ▁then ▁Alice ▁can ▁un itar ily ▁transform ▁these ▁states