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Classified in Mathematics

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What is a one-way function?
A one-way function is a function that is easy to compute in one direction but difficult to
compute in the reverse. For example given an input a hash is easy to compute. However
given the output it is extremely difficult (time consuming) to determine the input.
● What is a trapdoor function?
A trapdoor function is like a one-way function, however a trapdoor function can reverse
the one-way function if the trapdoor is known. For example finding the 2 prime divisors of
6895601 is difficult. However if you know that 1931 is one of the numbers it will be easy to
divide 6895601 by 1931 to determine the answer. In this case 1931 is the trapdoor.
● What makes RSA difficult to break? <ans = the large number factorisation
problem/>
The large number factorisation problem makes RSA difficult to break. The modulus used
in RSA is usually 1024 bits long, which is a number that has more than 300 digits.
Computing the divisors is infeasible.
● What is Euler’s Phi (Totient) Function? How is it used in RSA? <probably too
specific./>
Euler’s Phi Function is used to calculate the count of numbers in the set ???? N*. If n is a
prime the count of numbers in the set ???? N* is n-1, i.E. phi(n) = n-1. Euler’s totient function
is distributive i.E. If n = p*q, phi(n) = phi(p)*phi(q). Calculating phi(n) is difficult (large
number factorisation difficult) but because p and q are known and chosen during the
RSA process it is easy to calculate phi(n). From the set of numbers in phi(n) a value e
(the encryption key) is selected such that e is coprime to phi(n). A value d (decryption
key) is also selected such that d is the inverse of e mod phi(n).
<AS I TYPE THIS I REALISE THAT THIS QUESTION IS TOO SPECIFIC AND I
REALLY DOUBT IT WILL BE USED IN THE TEST/>
● What can asymmetric encryption be used for besides message encryption?
Asymmetric encryption can also be used for digital signatures and key exchange.
● RSA uses long key lengths, what is an alternative to RSA?
Elliptic Curve Cryptography is an alternative to RSA.

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