CSE 2500 Computer Security and Privacy
Tutorial Sheet 06
Q1) Given a modular exponentiation algorithm for n-bit integers that needs about n3
operations, how much does performance deteriorate by moving from 512-bit to 1024-bit
RSA?
Q2) Consider a block cipher algorithm with the following properties:
- Input and output block length of 64 bits and the key size is 56 bits
- Given a key K, the key scheduling requires 2 microseconds (2 x 10 -6 secs)
- After the key scheduling produces all the sub-keys (if required), the
encryption of a single block of 64 bits block takes 0.5 microseconds.
Compute the following information:
- The total time required (of course in microseconds) to encrypt 1MBytes (2
20
bytes) of data.
- Given 2 values C and M such that C = EK(M) under the unknown key value
K, how many years (at most) are required to crack the cipher on a single
computer.
Q3) Consider the following scheme of encryption and decryption scheme:
- Let P be a data block of arbitrary length.
- EK(P) and DK(P) represent the secret key encryption and decryption
algorithms of a secret key cryptosystems (such as DES) where K is the secret
key.
- PEU (P) and PDV(P) represent the public-key encryption and decryption
algorithms of a public-key cryptosystem (such as RSA), where U is the public
key and V is the private key of the user.
- Let X and Y be the public and private key of Srini in the above public-key
cryptosystem.
Consider the following sequence of operations (and explain what are they in English)
-
C = EK(P)
destroy P
D = PEU (K)
E = PEX (K)
destroy K
F = { C, D, E }
Is it possible to obtain P from F knowing V? If so how?
Is it possible to obtain P from F knowing Y? if so how?
Is it possible to obtain V if we know Y? If so how?
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Is it possible to obtain P from F if we lose V? If so how?
Is it possible to obtain P from F if we lose Y? If so how?
Is it possible to obtain P from F if we lose both V and Y? If so how?
Q4) Consider a password system which uses all the 102 printable characters of the
English (or American) key board and the password is of 8 characters long.
- How many distinct passwords are possible under the above scheme? (give
the numbers approximately as a.b x 10 c).
- If the password scheme is limited to 26 lowercase English alphabets only (still
password length remains as 8 characters), how many passwords will there be?
- If the password length is limited to 6 characters (still the number of
characters is 102), how many passwords will there be?
Q5) Think
of application(s) where private key encryption may not be suitable.
Q6) Assume that passwords have length six and all alphanumerical characters, upper and
lower case, can be used in their construction. How long will a brute force attack take on
average if:
- it takes one tenth of a second to check a password?
- it takes a microsecond to check a password?
Q7) Passwords are entered by users and checked by computers. Thus, there has to be
some communications channel between user and computer. So far we have taken a very
abstract view of this channel and assumed that it exists and that it is adequately secure.
When this assumption is justified? When it is not justified?
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