# Numerical example of encryption using the RSA method

Please see the file below about encoding a birthday.

For example the birthday is 250692, how to calculate?

Exercise 2: Encode your date of birth (format DDMMYY) using the public key:

n = 536813567

a = 7582663

(Use the correspondence 0 <-> 0, 1 <-> 1, ..., 9 <-> 9 and work in base 10 to encode this message.)

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

The theory of RSA encryption states the following

Choose two large numbers p and q and compute n = p*q

Compute phi = (p-1)*(q-1)

Choose a prime number a that is coprime with phi

Compute the multiplicative inverse of phi w.r.t. i.e. d = a-1(phi)

The numbers n and a shared as the public and private keys

The encryption algorithm for any given number M is

N = Ma mod n

The encrypted number N along with the keys n and a are shared

The decryption algorithm for crypted value N is

M = Nd mod n

In the present case

n = 536813567 and a = 7582663

Breaking it into factors we find 536813567 = 8191 X 65537

Hence phi = 8190 X 65536 = 536739840

(Hint: the following weblink can help www.math.wustl.edu/cgi-bin/primes)

Now d = 7582663-1 536739840 = 38411

(Hint: The following weblink can help www.cs.princeton.edu/~dsri)

Let's assume 25061992 as the date of birth

The encrypted number is N = 250619927582663 mod 536813567

The decryption algorithm is M = N38411 mod 536813567

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