Explore BrainMass

# Numerical example of encryption using the RSA method

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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.)

https://brainmass.com/math/number-theory/numerical-encryption-rsa-method-598049

## 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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!