A nice animated presentation explaining the method of RSA algorithm. Its definition, explanation, advantages, disadvantages.

1. PUBLIC KEY CRYPTOGRAPHY
RSA ENCRYPTION ALGORITHM
Meenakshi Shetti
Muthu Gomahty V

2. CONTENTS
• CRYPTOGRAPHY
• WHAT IS A KEY ?
• PRIVATE KEY CRYPTOGRAPHY
• PUBLIC KEY CRYPTOGRAPHY
• RSA ALGORITHM
• ADVANTAGES
• DISADVANTAGES
• REFERENCES

3. CRYPTOGRAPHY
•It’s a greek word which means hidden secret in
writing
•Cryptography is the practice and study of
techniques for secure communication in the
presence of third parties(called adversaries).

4. What is a “key”?
A key is a piece of information (a parameter) that
determines the functional output of a
cryptographic algorithm or cipher.

5. PRIVATE KEY CRYPTOGRAPHY
• Also called as Symmetric-key algorithms
• They are a class of algorithms for cryptography that
use the same cryptographic keys for both encryption
of plaintext and decryption of ciphertext.

6. Public key cryptography
• Also known as asymmetric cryptography
• Refers to a cryptographic algorithm which requires two separate keys, one
of which is secret (or private) and one of which is public.

7. Non secret ENCRYTION USING LOCK
ALICE BOB

8. ENCRYPTION
DECRYPTION

9. EVE
ALICE BOB

10. TRAP DOOR –ONE WAY FUNCTION
EASY
HARD

11. EXPONENET
REMAINDER
12345
mod 17 ≡ 135903
346 mod 12 ≡10
BASE
MODULUS

12. memod N ≡ c

13. EASY
memod N ≡ c
HARD
?emod N ≡ c

14. memod N ≡ c
emod N- public key
C -remainder
m- message

15. me mod N ≡ c
cd mod N ≡ m
medmod N ≡ m
e- encryption
d - decryption

16. For computation of e and d
STEP 1 -> PRIME FACTORIZATION
STEP 2 -> PHI FUNCTION
STEP 3-> EULER’S THEOREM

17. Multiplication of two extra large
numbers are easy to compute.
But prime factorization of a
number is the hardness of the
problem .
Prime factorization is what used
to build the trap door

18. STEP 1 -> PRIME FACTORIZATION
P1 – 150 digits long
P2 – 150 digits long
P1 * P2 = N
N- 300 digits long

19. STEP 2 -> PHI FUNCTION
- breakability of a number
Given a number N – it output’s how many integers are
less than or equal to N that do not share a common
factor with N
ɸ[8] = 1
2
3
4
5
6
7
8
ɸ[8] = 1
2
3
4
5
6
7
8
We want to find ɸ[8] ,
we look at all integers
from 1 to 8 , then we
count how many
integers does not
share a factor greater
than 1
ɸ[8] = 4

20. • In the case of ɸ of a prime number –
As prime numbers does not share common
factor of any number greater than
ɸ[P]=P-1
i.e, ɸ[7] = 1
2
3
4
5
6
7
As none of them share a common
factor with 7
ɸ[7] = 7-1
ɸ[7] = 6

21. ɸ[N] is also multiplicative
ɸ[A*B] = ɸ[A] * ɸ[B]
= (A-1) * (B-1)
ɸ[N] = ɸ[P1] * ɸ[P2]
ɸ[N] = (P1-1) * (P2-1)
77=7*11
ɸ[7] = ɸ[7] * ɸ[11]
ɸ[7] = (7-1) * (11-1) = 6 * 10 =60

22. STEP 3-> EULER’S THEOREM
- Relation between the phi function and modular
exponentiation
mɸ[N]= 1 mod N
Pick 2 numbers that do not share a common factor
m=5, n=8
5ɸ[8]= 1 mod 8
54= 1 mod 8
625=1 mod 8

23. Modify this equation using 2 simple rules
1) 1k=1
mk*ɸ[N]= 1 mod N
We multiply eponent ɸ[N] by any number k,
the solution is still 1
2) 1*m=m
m*mk*ɸ[N]= m mod N
mk*ɸ[N]+1= m mod N

24. We now have an equation to find e and d which depends
on ɸ[N]
mk*ɸ[N]+1= m mod N
me*d= m mod N
Where d= k*ɸ[N]+1
e
Meaning d is ALICE’s private key .
It is the trap door which will perform undo operation

25. EVE
N=3127
ALICE BOB
P1=53
d=2011
P1=59
N= 53* 59
N=3127
ɸ[N]=52*58
e=3
d=2*(3016)+1
3
d=2011
e=3
hi
m=hi
m=89
893 mod 3127=1394
c=1394
ɸ[N]=3016
cd mod N = m
13942011 mod 3127 = 89
m=89
m=hi
c=1394

26. • Any one wth N, e and c can find d if and only if they know
the prime factorization of N
• If N is large enough it requirs 100 to 1000 years to find
factorize
• It is the most widely used public key cryptography
algorithm and most copied software in the history
• Every internet user is using RSA whether they realise on
the hardness of prime factorization which results in deep
question of distribution of prime numbers.

27. APPLICATIONS
• When it comes to assymetric cryptography the most
popular and widely used application that comes to
anyone's mind is PGP. PGP stands for “Pretty Good
Privacy” and is the standard public key cryptography
application used today. In the examples of this project
we chose to use PGP Desktop. The reason for this
choice is that PGP Desktop is easier to use than other
text-based versions of PGP such as gnuPGP. PGP
Desktop provides us with a very intuitive GUI
accessible from the Windows Start Menu ,the PGP
taskbar icon and from Windows explorer (shell
integration). So from now on, every time we mention
PGP, we will be referring to the PGP Desktop version.

28. ADVANTAGES
1. Convenience: It solves the problem of distributing the key for encryption.
2. Provides for message authentication: Public key encryption allows the use
of digital signatures which enables the recipient of a message to verify that
the message is truly from a particular sender.
3. Detection of tampering: The use of digital signatures in public key
encryption allows the receiver to detect if the message was altered in transit.
A digitally signed message cannot be modified without invalidating the
signature.
4. Provide for non-repudiation: Digitally signing a message is akin to
physically signing a document. It is an acknowledgement of the message and
thus, the sender cannot deny it.

29. DISADVANTAGES
1. Public keys should/must be authenticated: No one can be absolutely sure that a
public key belongs to the person it specifies and so everyone must verify that their public
keys belong to them.
2. Slow: Public key encryption is slow compared to symmetric encryption. Not feasible for
use in decrypting bulk messages.
3. Uses up more computer resources: It requires a lot more computer supplies
compared to single-key encryption.
4. Widespread security compromise is possible: If an attacker determines a
person's private key, his or her entire messages can be read.
5. Loss of private key may be irreparable: The loss of a private key means that all
received messages cannot be decrypted

30. REFERENCES
1. Frederick J. Hirsch. "SSL/TLS Strong Encryption: An
Introduction". Apache HTTP Server. Retrieved
2013-04-17.. The first two sections contain a very
good introduction to public-key cryptography.
2. N. Ferguson; B. Schneier (2003). Practical
Cryptography. Wiley. ISBN 0-471-22357-3.
3. J. Katz; Y. Lindell (2007). Introduction to Modern
Cryptography. CRC Press. ISBN 1-58488-551-3.
4. A. J. Menezes; P. C. van Oorschot; S. A.
Vanstone (1997). Handbook of Applied
Cryptography. ISBN 0-8493-8523-7.

31. THANK YOU