24 Jul HashQuestion (Use Sage):The following describes the simple hash
HashQuestion (Use Sage):The following describes the simple hash function:Choose p, q primes and compute N = pq.Choose g relatively prime to N and less than N.Then a number n is hashed as follows:H = gn mod NIf there is an m that hashes to the same value as n, thengm ≡ gn mod Nsogm-n ≡ 1 mod Nwhich implies thatm –n ≡ 0 mod φ (N)So breaking this amounts to finding a multiple of φ (N), which is the hard problem in RSA. Write a function that takes a bit length n and generates a modulus N of bitlength n and g less than N and relatively prime to it. Show the output of your function from part (a) for a few outputs. Using N, g, n as arguments write a function to perform the hashing. For the following parts (a)-(d) compute the simple hash: N = 600107, g = 154835, n = 239715 N = 548155966307, g = 189830397891, n = 44344313866 N = 604766153, g = 12075635, n = 443096843 Write a function that creates a collision given p and q. Show that your function works for a couple of examples.
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