1. Compute the following modular inverses. (Remember, this is*not* the same as the real inverse).

1/5 mod 14 =
1/5 mod 13 =
1/5 mod 6 =

2.Solve the following modular equations. In each case please usethe smallest positive solution.

a) 5 + x ? 4 mod 6
x =
b) 3x +1 ? 9 mod 10
x =
c) 9^x ? 9 mod 11
x =

3.Which numbers in ?26 are relatively prime to 26?Enter your answer as a comma separated list of numbers.

Sequence =

4. Which numbers in ?51 are relatively prime to 51?Enter your answer as a comma separated list of numbers.

Sequence =

5. In this problem we explore the relationship between passwordlength and cryptographic security.

Suppose a password consists of 88 ASCII characters.You can review the ASCII characters here.. Exactly 2^7 =128 of these codes are for printable characters; we willassume every character in the password is printable.

What is the size of the keyspace that consists of passwords ofthis form?

Ans.

What is the equivalent key length in bits?

Ans.

Assuming that you could check one password every 10^-12seconds, what is the worst case running time for cracking thispassword by brute force search (in days)?

Ans.

Now assume that the user used only 31 characters fromthe keyboard. What is the key length in bits in thiscase?

Ans.

How many days, in the worst case, would it take to break thisweaker password? You can't round to the nearest day here -- be asexact as possible.

Ans.

Supposing you used only 31 characters, how long is theshortest password that achieves 175175 bits ofsecurity?

Ans.

 

Transcribed Image Text:

6. (Decrypt the message DJGLRWJVC which was encrypted using the affine cipher: f(p)=(21p+9) mod 26 Alphabet: A=0,B=1,...,Z=25A=0,B=1,...,Z=25 6. (Decrypt the message DJGLRWJVC which was encrypted using the affine cipher: f(p)=(21p+9) mod 26 Alphabet: A=0,B=1,...,Z=25A=0,B=1,...,Z=25 6. (Decrypt the message DJGLRWJVC which was encrypted using the affine cipher: f(p)=(21p+9) mod 26 Alphabet: A=0,B=1,...,Z=25A=0,B=1,...,Z=25 6. (Decrypt the message DJGLRWJVC which was encrypted using the affine cipher: f(p)=(21p+9) mod 26 Alphabet: A=0,B=1,...,Z=25A=0,B=1,...,Z=25

Answer rating: 100% (QA)

Answer 1 15 mod 14 3 15 mod 13 8 15 mod 6 4 2 a x 1 b x 4 c x 10 3 Sequence 1 3 5 7 9 11 15 17 19 21 23 25 4 Sequence 1 2 3 4 6 8 9 11 12 13 16 17 18 19 22 23 24 26 28 29 31 32 33 36 37 38 39 41 42 43 ... View the full answer