CRYPTOGRAPHY/PROBABILITY QUESTION PLEASE SHOW ALL WORK!!!!!!!! CRYPTOGRAPHY/PROB
ID: 2989985 • Letter: C
Question
CRYPTOGRAPHY/PROBABILITY QUESTION PLEASE SHOW ALL WORK!!!!!!!!
CRYPTOGRAPHY/PROBABILITY QUESTION PLEASE SHOW ALL WORK! Likelihood ratio test: Alice generates random 4-bit numbers by flipping 4 coins. Bob generates random 4-bit numbers by rolling 3 dice, summing them, and subtracting 3. Complete the following table: x Palice(x) Pbob(x) LR(x) 0 1 2 3 4 5 6 7 1/16 1/216 27/2 x Palice(x) Pbob(x) LR(x) 8 9 a b c d e f Text Each of the following strings is generated by either Alice or Bob. Compute the likelihood ratio for each: (a) 9fb781 (b) a57c89 (c) d2f3ed (d) b87268Explanation / Answer
for alice 4-bit number is generated using 4 coins.So each comibantion is unique.And 0 to f are equally probable
for bob
are possible combination and subtracting 3 from it gives 0 to 15
x Palice (x) Pbob(x)
0 1/16 1/216
1 1/16 3/216
2 1/16 6/216
3 1/16 10/216
4 1/16 15/216
5 1/16 21/216
6 1/16 25/216
7 1/16 27/216
8 1/16 27/216
9 1/16 25/216
a 1/16 21/216
b 1/16 15/216
c 1/16 10/216
d 1/16 6/216
e 1/16 3/216
f 1/16 1/216
U can get LR(x) be P(bob)/P(alice)
a)9fb781
P(alice)=(1/16)^6
P(bob)=25*1*15*27*27*3/(216)^6=8.07*10^-9
b)a57c89
P(alice)=(1/16)^6
P(bob)=21*21*27*10*27*25/(216)^6 =7.91*10^-7
c)d2f3ed
P(alice)=(1/16)^6
p(bob)=6*6*1*10*3*6/(216)^6=6.38*10^-11
d)b87268
P(alice)=(1/16)^6
p(bob)=15*27*27*6*25*27/(216)^6=4.36*10^-7