Cryptographic

Algorithms:

DES & RSAPresented By:

Aritra Ranjan Das (13000112077)

Arnab Bhattacharjee (13000112078)

Ipshita Das (13000112103)

Arpan Mondal (13000112081)

OverviewNeeds for Security

Types of Attack

What is Cryptography?

Basic Terms

Techniques for Cryptography

Types of Cryptography

DES Algorithm for Symmetric key Cryptography

Problems with Symmetric Key Cryptography

RSA Algorithm for Asymmetric Key Cryptography

Real Life Applications of Cryptography

Conclusion

References

Needs for Security in India

• Computer Applications has been developed to handle financial and personal data.

• India has bypassed Japan to become the world’s third largest Internet user after China and the United States.

• This encourages a group of people to indulge in cyber crime activities.

• India ranked 11th in the cyber crime activities in the world [1].

Alice (Sender)

Bob (Receiver)

Medium

Eve (Unauthorized

Person)

Needs for Security in India

Figure: Number of cyber crime complaints registered in India [2]

Types of Attack

ATTACKS

INTERCEPTION FABRICATION MODIFICATION INTERRUPTION

Passive Attacks Active Attacks

CRYPTOGRAPHY

What is Cryptography?

• Cryptography came from Greek kryptós, "hidden", + gráphein, "to

write".

• Cryptography is the art of achieving security by encoding messages to messages to make them non-readable.

• It provides Confidentiality, Integrity, Accuracy.

CRYPTOGRAPHY

Basic Terms• Plain Text: Message before encryption.

• Cipher Text: Message after encryption.

• Cipher: Encryption algorithm

• Encryption: the process of converting Plain text to Ciphertext

• Decryption: the process of converting ciphertext back to the original plaintext.

• Key: Sequence that controls the operation and behavior of the cryptographic algorithm.

Figure: General working principle of Cryptography [3]

Techniques for Cryptography

1. Substitution Technique: In substitution cipher technique, the

characters of a plain text message are replaced by other Characters, Characters, Number or Symbols.

Example: Caesar Cipher.

• Caesar Cipher is a special case of substitution technique wherein each message message is replaced by an alphabet three place down the line.

• To decrypt Caesar Cipher we have to replace each alphabet in cipher text text message with the alphabet that is three place up the line.

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

F R P H K H U H

C O M E H E R E

Techniques for Cryptography (Contd..)2. Transposition Technique: Transposition techniques differ from

substitution techniques in the way that they do not simply replace replace one alphabet with another; they also perform some permutation over the plain text alphabets.

Example: Rail Fence Technique

• Write down the plain text message as a sequence of diagonals.

• Read the plain text written in step 1 as a sequence of rows.

Original plain text message: Come home tomorrow

C m h m t m r o

o e o e o o r w

Cipher Text: cmhmtmrooeoeoorw

Types of Cryptography1. Symmetric Key Cryptography:

• Symmetric key cryptography involves the usage of the same key for encryption encryption and decryption [4].

• Both sender and receiver must know the common key.

• The common key need to be exchanged before hand by some other secure secure method.

Figure: Working principle of Symmetric Key Cryptography [5]

Data Encryption Standard(DES)

• Symmetric Key Algorithm

• Derived from IBM’s Lucifer

• Approved as a standard in 1977 by the U.S Government

64-bit

Plain Text

DES

64-bit

Cipher Text

64-bit

Plain Text

64-bit

Plain Text

DES DES

64-bit

Cipher Text

64-bit

Cipher Text

56-bit key 56-bit key 56-bit key…

Block 1 Block 2 Block n

The 56-bit key is derived from a 64-bit key by eliminating

all 8 bit positions.

In other words bits positions 8,16,24,32,40,48,56 and 64

are discarded.

Key Derivation:

…

Initial Permutation : Before the plain text is

encrypted with the key the bit positions of the plain plain text are transposed .

Bit position in plain text block Overwritten by contents of bit position

1 58

2 50

3 42

… …

64 7

The permuted block is divided into two blocks, namely Left Plain Text (LPT) and Right Plain Text (RPT).

Original Plain Text of 64 bits

Left Plain Text (LPT) of 32 bits Right Plain Text (RPT) of 32 bits

Key Transformation:

• The 56-bit key is divided into two 28-bit segments. Each segment undergoes a circular left shift of 1 or 2 bits depending on the round of encryption (16 total rounds).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1

Round

Number of bits shifted

• After appropriate bit shifting 48 of the 56 bits are selected to form the final encryption key. This is known as compression permutation.

14 17 11 24 1 5 3 28 15 6 21 10

23 19 12 4 26 8 16 7 27 20 13 2

41 52 31 37 47 55 30 40 51 45 33 48

44 49 39 56 34 53 46 42 50 36 29 32

Expansion Permutation:

Right Plain Text (RPT) of 32 bits from previous step

Block 1 (4 bits) Block 2 (4 bits) Block 8 (4 bits)

Input Block 1 (4 bits)

1 2 3 4

Input Block 2 (4 bits)

5 6 7 8

Input Block 8 (4 bits)

29 30 31 32

1 2 3 4 5 6

Output Block 1 (6 bits)

7 8 9 10 11 12

Output Block 2 (6 bits)

43 44 45 46 47 48

Output Block 8 (6 bits)

48-bit Key 48-bit RPTXOR

S-box Substitution

S-box Substitution:

In S-box substitution the 48-bit encrypted text is broken into 6-bit blocks and each block is used to generate a 4-bit output block by using an S-box

48-bit input block

6-bit sub block 6-bit sub block 6-bit sub block

S-box 1 S-box 8S-box 2

4-bit output 4-bit output4-bit output

…

32-bit output block

From each 6-bit block the MSB and LSB combine together to select the row number and the intermediate bits select the column number in the 4x16 S-box which contains a corresponding 4-bit number.

…

1.Key Transformation

2.Expansion Permutation

3.S-box Substitution

4.P-box Permutation

P-Box Permutation: The output of S-box consists of 32 bits. These bits

are permuted using P-box with a straight forward permutation mechanism.XOR & Swap:

Original 64-bit Plain Text Block

32-bit Left Plain Text (LPT) 32-bit Right Plain Text (RPT)

32-bit Left Plain Text (LPT) 32-bit Right Plain Text (RPT)

XOR

Next Round

Final Permutation: At the end of 16 rounds, the Final Permutation is performed (only once) which is a simple transposition.

Strength Of DES Algorithm:

• The Strength of DES Algorithm lies in its key, which must be secret.

• DES uses 64-bits key.

• Thus, there are 264 possible keys

• Hence, Brute-Force attack on DES is impractical

• It would require more than 1,000 years to break DES.

Problems with Symmetric Key Cryptography:

• Problem of Key Distribution

• Large number of keys required (One for each pair of communicating parties)

For n persons, the number of lock-and-key pairs are :

n*(n-1)/2!

Hence, for 1000 persons we will have 499,500 lock-and-key pairs!!!

• A trusted party is required to manage all the keys

Parties Involved Lock-and-Key pairs Number of lock-key pair

2 (A,B) (A-B) 1

3 (A,B,C) (A-B, A-C, B-C) 3

4 (A,B,C,D) (A-B, A-C, A-D, B-C, B-D, C-D) 6

Types of Cryptography (Contd…)

2. Asymmetric Key Cryptography:

• Two different keys are used to encrypt and decrypt the message.

• Receiver generates a public and private key pair.

• Receiver broadcasts the public key.

• Encryption is done by public key and private key is used for decryption.

Figure: Working principle of Asymmetric Key Cryptography [6]

RSA Algorithm

• by Rivest , Shamir & Adleman of MIT in 1977

• best known & widely used public-key scheme

• security due to cost of factoring large numbers

RSA Algorithm

• by Rivest , Shamir & Adleman of MIT in 1977

• best known & widely used public-key scheme

• security due to cost of factoring large numbers

RSA Key Setup

• each user generates a public/private key pair by:

• selecting two large primes at random : p, q

• computing their system modulus N=p * q

• Note : ø(N)=(p-1)(q-1)

• selecting at random the encryption key : e

• where 1<e<ø(N), gcd(e,ø(N))=1

• solve following equation to find decryption key : d

• d ≡ e−1 (mod φ(n)) and 0≤d≤N

• publish their public encryption key: KU= {e , N}

• keep secret private decryption key: KR={d , p , q}

RSA Use

• To encrypt a message M the sender:

• obtains public key of recipient KU={e , N}

• computes: C ≡ Me mod N, where 0≤M<N

• To decrypt the ciphertext C the owner:

• uses their private key KR={d , p, q}

• computes: M ≡ Cd mod N

• Note that the message M must be smaller than the

modulus N (block if needed)

EXAMPLE OF RSA ALGORITHM

C

BOB wants to send a message

(M) to ALICE.

*Public Key KU{ e , N} is available

to

sender(BOB)

*Encrypting M, to create the cipher

text(C).

*Sending C to receiver ALICE

*Decrypting Cipher text (C):

Figure: Explanation Of RSA [7]

Setting up RSA Cryptosystem(RECEIVER’S SIDE)

• Algorithm

1. A user must first choose two large prime numbers, say p and q

2.Calculate n = p * q

3.Calculate φ(n) = (p-1) * (q-1)

• Example

1.Let Alice choose.

p=11 and q=19

2.Alice calculated p * q as 11 * 19 and got the value of n = 209.

3.Alice calculated (p-1) * (q-1) as 10 * 18 and got the

value of φ(n) = 180.

Setting up RSA Cryptosystem(RECEIVER’S SIDE)

Algorithm

4.Choose a value of e such that GCD(e,φ(n)) = 1.

5.Calculate d such that e * d(mod φ(n))=1 , or in other words, find the modular multiplicative inverse of e.

• Applying Euclid's:

180 = 1 * 103 + 77

103 = 1 * 77 + 26

77 = 2 * 26 + 25

26 = 1 * 25 + 1

Example

4.Alice randomly chose e as 103 which is co-prime to 180.

5.To find the required inverse, Alice would use Euclid's Algorithm in reverse manner and then use its extension to find the inverse. Here's how:

Remember, Alice chose e = 103 and φ(n) = 180

Setting up RSA Cryptosystem(RECEIVER’S SIDE)

Algorithm

Reversing Euclid's:

1 = 26 – 25

= 26 – (77 – 2*26)

= 3 * 26 – 77

= 3 * (103 – 77) – 77

= 3 * 103 – 4 * 77

= 3 *(103) – 4 * (180 – 103)

1 = 7 * 103 – 4 * 180

(Bezout's Identity)

Example

Remember, Bezout's Identity is in the

form

ax + by = gcd ( a, b)

Setting up RSA Cryptosystem(RECEIVER’S SIDE)

• Finding Inverse:

We now write our Bézout's Identity as ex + φ(n)y = 1, and we just determined x as 7.

Now, the inverse of e is e-1≡ x (mod φ(n)) ≡ 7 (mod 180)

Hence, d = 7

Setting up RSA Cryptosystem(RECEIVER’S SIDE)

Algorithm

6.The Public keys are (e,n),

Example

6.Alice thus obtained her Public Key as (103,209) and

7.Private Key as (7, 209)

Encryption Process(SENDER’S SIDE)

Algorithm

In order to encrypt a number m, we calculate c≡me (mod n), where c is the the encrypted number and and m is less than n, keeping in mind that the encryption (public) key is (e,n).

Example

Bob wants to send Alice and important number, say 10. The cipher using Alice's public key would be

c≡10103 (mod 209)

On calculating this, which comes out to be 32, Bob sends it to Alice.

Decryption Process(RECEIVER’S SIDE)

Algorithm

In order to decrypt a cipher cipher c, we calculate m≡cd

Example

Alice receives the encrypted number. The decrypted number using her private key would be

m≡327 (mod 209)

On calculating this, she gets m=10, which was desired.

ADVANTAGES

1. Convenience

2. Provides for message authentication

3. Detection of tampering

4. Provide for non-repudiation

DISADVANTAGES

1. Public keys should/must be authenticated

2. Slow

3. Uses up more computer resources

4. Widespread security compromise is possible

5. Loss of private key may be irreparable

Real Life Application Of Cryptography [8]

• Authentication and Digital Signatures

• Time stamping

• Electronic Cash transaction

• Disk encryption

Conclusion

• Cryptography is literally everywhere.

• Do not rely on ‘security by obscurity’.

• Cryptographic theory is a very active field of research.

References• [1]: http://www.dnaindia.com/india/report-indore-industries-lose-rs-18k-

cryr-to-cyber-crimes-1930610

• [2]: http://www.medianama.com

• [3]: http://www.slideshare.net/priyavinkal/cryptography-10858819(slide number: 7)

• [4]: Cryptography and Network Security By Atul Kahate (ISBN: 0-07-049483-5)

• [5]: http://www.slideshare.net/priyavinkal/cryptography-108588(slide number: 11)

• [6]: http://www.slideshare.net/priyavinkal/cryptography-108588(slide number: 14)

• [7]: www.youtube.com

• [8]: www.laits.utexas.edu/../life.html

Thank You

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