commit ment ▁protocol . ▁ ▁In ▁ 1 9 9 1 ▁Mon i ▁Na or ▁showed ▁how ▁to ▁create ▁a ▁bit - commit ment ▁scheme ▁from ▁a ▁crypt ograph ically ▁secure ▁pseud or andom ▁number ▁generator . ▁The ▁construction ▁is ▁as ▁follows . ▁If ▁G ▁is ▁pseudo - random ▁generator ▁such ▁that ▁G ▁takes ▁n ▁bits ▁to ▁ 3 n ▁bits , ▁then ▁if ▁Alice ▁wants ▁to ▁commit ▁to ▁a ▁bit ▁b : ▁ ▁Bob ▁selects ▁a ▁random ▁ 3 n - bit ▁vector ▁R ▁and ▁sends ▁R ▁to ▁Alice . ▁Alice ▁selects ▁a ▁random ▁n - bit ▁vector ▁Y ▁and ▁comput es ▁the ▁ 3 n - bit ▁vector ▁G ( Y ). ▁If ▁b = 1 ▁Alice ▁sends ▁G ( Y ) ▁to ▁Bob , ▁otherwise ▁she ▁sends ▁the ▁bit wise ▁exclusive - or ▁of ▁G ( Y ) ▁and ▁R ▁to ▁Bob . ▁ ▁To ▁de commit ▁Alice ▁sends ▁Y ▁to ▁Bob , ▁who ▁can ▁then ▁check ▁whether ▁he ▁initially ▁received ▁G ( Y ) ▁or ▁G ( Y ) ▁ ▁R . ▁ ▁This ▁scheme ▁is ▁statist ically ▁binding , ▁meaning ▁that ▁even ▁if ▁Alice ▁is ▁computation ally ▁un bounded ▁she ▁cannot ▁che at ▁with ▁probability ▁greater ▁than ▁ 2 − n . ▁For ▁Alice ▁to ▁che at , ▁she ▁would ▁need ▁to ▁find ▁a ▁Y ', ▁such ▁that ▁G ( Y ') ▁= ▁G ( Y ) ▁ ▁R . ▁If ▁she ▁could ▁find ▁such ▁a ▁value , ▁she ▁could ▁de commit ▁by ▁sending ▁the ▁truth ▁and ▁Y