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sasc:laboratoare:03 [2017/03/06 12:42] dan.dragan |
sasc:laboratoare:03 [2017/03/07 15:32] (current) dan.dragan |
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| - | ==== Exercise 1 (2p) ==== | + | ==== Exercise 1 (4p) ==== |
| In this exercise we'll try to break a Linear Congruential Generator, that may be used to generate "poor" random numbers. | In this exercise we'll try to break a Linear Congruential Generator, that may be used to generate "poor" random numbers. | ||
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| </code> | </code> | ||
| + | ==== Exercise 2 (3p) ==== | ||
| - | ==== Exercise 2 - LFSR (2p) ==== | + | Let's use the experiment defined earlier as a pseudorandom generator ($\mathsf{PRG}$) as follows: |
| + | - Set a desired output length $n$ | ||
| + | - Obtain a random sequence $R$ of bits of length $n$ (e.g. using the Linear-congruential generator from Exercise 1) | ||
| + | - For each bit $r$ in the random sequence $R$ generated in the previous step, output a bit $b$ as follows: | ||
| + | * if the bit $r$ is $0$, then output a random bit $b \in \{0, 1\}$ | ||
| + | * if the bit $r$ is $1$, then output $1$ | ||
| + | |||
| + | a. Implement the frequency (monobit) test from [[http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf | NIST (see section 2.1)]] and check if a sequence generated by the above $\mathsf{PRG}$ (say $n=100$) seems random or not. | ||
| + | |||
| + | b. Run the test on a random bitstring (e.g. a string such as R used by the above $\mathsf{PRG}$), and compare the result of the test. | ||
| + | |||
| + | If the two results are different across many iterations, this test already gives you an attacker that breaks the $\mathsf{PRG}$. | ||
| + | |||
| + | <note tip>You may use a function like this to generate a random bitstring</note> | ||
| + | <code python> | ||
| + | import random | ||
| + | |||
| + | def get_random_string(n): #generate random bit string | ||
| + | bstr = bin(random.getrandbits(n)).lstrip('0b').zfill(n) | ||
| + | return bstr | ||
| + | </code> | ||
| + | |||
| + | <note tip>Also, in Python you may find the functions sqrt, fabs and erfc from the module math useful</note> | ||
| + | |||
| + | ==== Exercise 3 - LFSR (3p) ==== | ||
| In this exercise we'll build a simple Linear Feedback Shift Register (LFSR). LFSRs produce random bit strings with good statistical properties, but are very easy to predict. | In this exercise we'll build a simple Linear Feedback Shift Register (LFSR). LFSRs produce random bit strings with good statistical properties, but are very easy to predict. | ||
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| Using the above starting state and polynomial, generate $100$ random bits and run the monobit statistical test from the previous exercise to see if their frequency seems random. | Using the above starting state and polynomial, generate $100$ random bits and run the monobit statistical test from the previous exercise to see if their frequency seems random. | ||
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