Randomness and Statistical Tests

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Presentation transcript:

Randomness and Statistical Tests Sayed Mahdi Mohammad Hasanzadeh Hasanzadeh@Raymandcrypto.ir Spring 2004

Goals in cryptography 1) Cryptography remove the redundancy from sequence Pr(1)=Pr(0)=1/2 2) Cryptography is a mapping in the sequence space 3)Cryptography provide security in some cases: data integrity, Authentication and identification ,…

Stream Cipher Pr(Pi=0) Pr(Pi=1) 1/2 Pr(ai=0) =Pr(ai=1) =1/2 Pr(Ci=0) =Pr(Ci=1) =1/2

Generator Properties Randomness Provable security Bit rate Key length Complexity of algorithm Memory Resistant against every attack

Randomness Golomb rules Statistical tests Linear Complexity

Golomb rules Maximum period Pseudorandom 01010001101111100111 #’1’ - #’0’ =0,1 #run1=R/2^1, #run2=R/2^2,…,#runi=R/2^I t : C(t)= 01010001101111100111 #run1=5,#run2=2,#run3=2,#run4=0,#run5=1 #gap=5 , #block=5

Randomness Golomb rules Statistical tests Linear Complexity

Why Statistical tests impossible to give a mathematical proof that a generator is indeed a random bit generator, the tests help detect certain kinds of weaknesses the generator may have. This is accomplished by taking a sample output sequence of the generator and subjecting it to various statistical tests.

Statistical tests the term “accepted” should be replaced by “not rejected” six Basic Test (Using Chi-square analysis) Frequency Test: # of 0 and 1 Serial Test: # of 00, 01, 10, 11 Poker-k Test: # of each k-bit string Run Test: comparing with expected run length Autocorrelation test: correlations between s and shifted version Binary derivation

Working with a Software for Statistical Tests