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’
• • ’•
•
Alice Bob
sA sB
Pr[sA = sB ] > 0:99
sEPr[sE = sA]< 0:51
H01n01n
H
H
8n9On²
PrsEsAPrsAsB²
Alice
sA sB
HBob
q201nqH
8n9On²
Pr’1²
sAsB
8n9On²
Pr’1–O²
Alice
sA sB
HBob
’·On²
8iqiqjji·²n
’’
8iqiqjji·10²n
’ithqqi
••
’’’
’
’
¹ (¸10²n
’A= rAhA10²n
>²nq
• • ’
“”
•
8iqiqjji·²n
’ithqqi
••
’’’
’
’
’A=rAhA10²n
¹>5²n
8AB
“”
Thus theorem follows from:
Depends only on A,A
Depends only on B,B
Cor: Probabilities in product and non-product are same up to mult factor of 0.99
N
M
®M
8n9On²
Pr’1–O²
Alice
sA sB
HBob
’·On²
8iqiqjji·10²n
·10²
’·On²’·On²
• ’
“”
• !
• “”
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