Consider the RSA public key cryptosystem. The best generally known attack is to factor the modulus, and the best known factoring algorithm (for a sufficiently large modulus) is the number field sieve....

Consider the RSA public key cryptosystem. The best generally known attack is to factor the modulus, and the best known factoring algorithm (for a sufficiently large modulus) is the number field sieve. In terms of bits, the work factor for the number field sieve is

where n is the number of bits in the number being factored. For example, since /(390) « 60, the work required to factor a 390-bit RSA modulus is roughly equivalent to the work needed for an exhaustive search to recover a 61-bit symmetric key.

a. Graph the function f(n) for 1 <>

b. A 1024-bit RSA modulus N provides roughly the same security as a symmetric key of what length?

c. A 2048-bit RSA modulus N provides roughly the same security as a symmetric key of what length?

d. What size of modulus N is required to have security roughly comparable to a 256-bit symmetric key?