# s

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**tocompute 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**factorisationproblem/>

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 functionis 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 (decryptionkey) 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.