Cryptography is the science of using mathematics to encrypt and decrypt data. There are two main types: symmetric key cryptography which uses the same key for encryption and decryption, and asymmetric key cryptography which uses a public/private key pair. Symmetric algorithms include the Caesar cipher and Vigenere cipher which shift or substitute letters, while the RSA algorithm is an example of an asymmetric algorithm that uses a public/private key pair to encrypt and decrypt messages. Cryptography allows for secure storage and transmission of sensitive data over insecure networks.

1. Introduction to Cryptography
MUKESH MAHADEV
2014KUCP1012
IIIT KOTA
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2. OVERVIEW
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• Cryptography
•Some Basic Terminology
• Encryption & Decryption
• Transmission Technique
• Symmetric Cryptography
• Asymmetric Cryptography
• References

3. WHAT IS CRYPTOGRAPHY ?
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•Cryptography is the science of using
mathematics to encrypt and decrypt data.
•Cryptography enables you to store
sensitive information or transmit it across
insecure networks so that it cannot be
read by anyone except the intended
recipient.

4. Some Basic Terminology
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•Plaintext
•Encryption
•Cipher text
•Decryption
•Key

5. ENCRYPTION & DECRYPTION
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6. WHY USE CRYPTOGRAPHY ?
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• For “secret writing”
• To establish a shared secret when other
people are listening.
• TYPES
Mainly classified into two types :
1. Symmetric key cryptography
2. Asymmetric key cryptography

7. TRANSMISSION TECHNIQUE
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Cipher
msg
Plain text – in
Cipher text - out
Should understand NOTHING
about the message
Cipher text – in
Plain text - out

8. SYMMETRIC KEY CRYPTOGRAPHY
BOTH SHOULD
KNOW THE KEY
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9. where letters of plaintext are replaced by
other letters or by numbers or symbols or
if plaintext is viewed as a sequence of
bits, then substitution involves replacing
plaintext bit patterns with ciphertext bit
patterns
Classical Substitution Ciphers
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10. Caesar Cipher
Replaces each letter by 3rd letter after
example:
meet me after the toga party
phhw ph diwhu wkh wrjd sduwb
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11. Caesar Cipher
can define transformation as:
a b c d e f g h i j k l m n o p q r s t u v w x y z
D E F G H I J K L M N O P Q R S T U V W X
Y Z A B C
mathematically give each letter a number
a b c d e f g h i j k l m n o p q r s t u v
w x y z
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25
then have Caesar cipher as:
c = E(p) = (p + k) mod (26)
p = D(c) = (c – k) mod (26) 11

12. Playfair Cipher
In this scheme, pairs of letters are encrypted, instead of
single letters as in the case of simple substitution cipher.
a 5X5 matrix of letters based on a keyword
eg. using the keyword TUTORIALS
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13. Continue ..
we want to encrypt the message “hide money”
HI DE MO NE YZ
The rules of encryption are −
1).If both the letters are in the same column, take
the letter below each one
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14. Continue..
2).If both letters are in the same row, take the
letter to the right of each one
3).If neither of the preceding two rules are true
ans: - QC EF NU MF ZV 14

15. Vigenere Cipher
This scheme of cipher uses a text string (a word) as
a key, which is then used for doing a number of
shifts on the plaintext.
example:- key is ‘point’
p → 16, o → 15, i → 9, n → 14, and t → 20.
Thus, the key is: 16 15 9 14 20.
message:- ‘attack from south east’
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16. Variants of Vigenere Cipher
There are two special cases of Vigenere cipher −
1).The keyword length is same as plaintect
message. This case is called Vernam Cipher. It
is more secure than typical Vigenere cipher.
2).Vigenere cipher becomes a cryptosystem with
perfect secrecy, which is called One-time pad.
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17. One-Time Pad
● The length of the keyword is same as the length
of the plaintext.
● The keyword is a randomly generated string of
alphabets.
● The keyword is used only once
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18. Transposition Cipher
Mapping is performed by some sort of permutation
on the plaintext letters.
Example: take column length 5
plaintext is “golden statue is in eleventh cave”
ciphertext is ‘gnuneaoseenvltiltedasehetivc’ 18

19. ASYMMETRIC KEY CRYPTOGRAPHY
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• Public key cryptography is an asymmetric
scheme that uses a Pair of keys for
encryption: a Public key, which encrypts data,
and a corresponding Private key (secret key)
for decryption.

20. Rivest Shamir and Adelman(RSA)
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Encryption key- public
Decryption key- private

21. RSA Algorithm
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Choose two very large prime numbers. Denote
these numbers as p and q.
Set n= p * q
f(n)=(p-1)*(q-1)
Choose any large integer, e, such that
GCD(e, f(n)) = 1 and 1<e<f(n)
Find d such that (e * d)(mod f(n)) = 1

22. Continue..
Encryption
C=M ^ e (mod n)
C:Cipher Text
M:Plain text
e:public key
Decryption
M=C ^ d (mod n)
C:Cipher Text
M:Plain Text
D:Private key
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23. Example: RSA
Lets choose two primes: p=11 and q=13
n = p*q = 143
f(n)=(p-1)*(q-1)=120
public key, Let's choose 7 (note: both 3 and 5 do
not have a gcd of 1 with f(n)) e=7;
determine d the secret key, d=103
e⋅d=1mod f(n)
7*103=721=1mod120.
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24. Example: RSA
n=143
e=7, d=103
Lets choose our plaintext message, m to be 9
Encryption:
me mod n=97mod 143=48=c
Decryption:
cd mod n = 48103 mod 143 = 9 = m
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25. REFERENCE
•http://doctrina.org/How-RSA-Works-With-
Examples.html
•http://www.tutorialspoint.com/cryptography/tr
aditional_ciphers.htm
• http://en.wikipedia.org/wiki/Cryptography
• https://www.coursera.org/course/crypto
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26. Thank
you….
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