Name: Shri Ramswaroop Memorial University
Uploaded: 2022-03-05
Duration: 6 min 56 s
Description: Shri Ramswaroop Memorial University. 1. SRMU Lucknow YouTube.

Shri Ramswaroop Memorial University. 1. SRMU Lucknow YouTube. 

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Submitted To:  							            Submitted By: Mr.  Neeraj  Kumar								     Abhay  Singh  Chauhan (079) 											     Sitlendra   Pratap  Singh(096) 											     Sakshi   Sohane (113) 											     Komal  Gupta(117) 											     B.Tech (CS -73,74) , 7 th   Sem

Table of Contents. 2. Introduction Techniques for Encryption History Diffie -Hellman Algorithm Security of the Diffie -Hellman Algorithm Uses Advantages Disadvantes Project Execution Screenshots Conclusion. 

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Introduction     Techniques for Encryption     History      Diffie -Hellman Algorithm     Security of the  Diffie -Hellman  Algorithm     Uses     Advantages      Disadvantes     Project Execution Screenshots     Conclusion

Introduction. 3. The first published public-key algorithm that defined public-key cryptography was published by Diffie and Hellman.. 

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The first published public-key algorithm that defined public-key cryptography was published by  Diffie  and Hellman.

It is generally referred to as the  Diffie  –Hellman key exchange.

A number of commercial products employ this key exchange technique.

Purpose of the algorithm is to enable two users to exchange a secret key securely that then can be used for subsequent encryption of messages.

The algorithm itself is limited to the exchange of the keys .

Depends for its effectiveness on the difficulty of computing discrete logarithms.

Techniques for Encryption. 4. • There are two basic techniques for encrypting information: • Symmetric Encryption (also called secret key encryption). • Asymmetric Encryption (also called public and private key encryption).. 

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•   There are two basic techniques for encrypting information: •   Symmetric Encryption (also called secret key encryption). •   Asymmetric Encryption (also called public and private key encryption).

History. 5. • The Diffie -Hellman algorithm was developed by Whitfield Diffie and Martin Hellman in 1976. • This algorithm was devices not to encrypt the data but to generate same private cryptographic key at both ends so that there is no need to transfer this key from one communication end to another.. 

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•    The  Diffie -Hellman algorithm was developed by Whitfield  Diffie  and Martin Hellman in 1976.  •   This algorithm was devices not to encrypt the data but to generate same private cryptographic key at both ends so that there is no need to transfer this key from one communication end to another.

Diffie -Hellman Algorithm. 6. The Algorithm Lets assume that there are two publicly known numbers: a prime number q and an integer α that is a primitive root of q.. 

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The Algorithm    Lets assume that there are two publicly known numbers: a prime number q and an integer  α  that is a primitive root of q.

For a prime number  p , if  α   is a primitive root of  p , then  α ,  α 2 ,…,  α p -1  are distinct (mod  p ).     E.g. for prime number 19, its primitive roots are 2, 3, 10, 13, 14, and 15.    Suppose the users A and B wish to create a shared key.

User A selects a random integer X A  < q and computes Y A  =  α XA  mod q.    Similarly, user B independently selects a random integer X B  < q and computes Y B  =  α XB  mod q.

Each side keeps the X value private and makes the Y value available publicly to the other side. Thus , X A is A’s private key and Y A is A’s corresponding public key, The same applies for B.. 

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Each side keeps the X value private and makes the Y value  available publicly  to the other side.  Thus , X A  is A’s private key and Y A  is A’s  corresponding public  key,  The same applies  for B.

User A computes the key as K = (Y B ) XA  mod q and      User B computes the key as K = (Y A ) XB  mod q.     The result is that the two sides have exchanged a secret value.

Diffie -Hellman Algorithm. 8. Alice Alice and Bob share a prime number q and an integer a, such that a < q and ais a primitive root of q Alice generates a private key XA such that XA < q Alice calculates a public key YA = OXA mod q Alice receives Bob's public key YB in plaintext Alice calculates shared secret key K = (YB)XA mod q Bob Alice and Bob share a prime number q and an integer a, such that a < q and a is a primitive root of q Bob generates a private key XB such that XB < q Bob calculates a public key YB = a B mod q Bob receives Alice's public key YA in plaintext Bob calculates shared secret key K = (YA)XB mod q. 

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Alice
Alice and Bob share a
prime number q and an
integer a, such that a < q and
ais a primitive root of q
Alice generates a private
key XA such that XA < q
Alice calculates a public
key YA = OXA mod q
Alice receives Bob's
public key YB in plaintext
Alice calculates shared
secret key K = (YB)XA mod q
Bob
Alice and Bob share a
prime number q and an
integer a, such that a < q and
a is a primitive root of q
Bob generates a private
key XB such that XB < q
Bob calculates a public
key YB = a B mod q
Bob receives Alice's
public key YA in plaintext
Bob calculates shared
secret key K = (YA)XB mod q

Example: Lets take q = 353 and a primitive root of 353, α = 3 . A and B select private keys X A = 97 and X B = 233, respectively .. 

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Example: Lets take q  = 353 and a primitive root of 353,  α =  3 . A and B select private  keys X A   = 97 and X B  = 233, respectively .

Each computes its public key:    A computes Y A  = 3 97   mod  353 = 40.    B computes  Y B   = 3 233  mod 353 = 248.    After they exchange public keys, each can compute the common secret key:

A computes K = (Y B ) XA mod 353 = 248 97 mod 353 = 160. B computes K = (Y A ) XB mod 353 = 40 233 mod 353 = 160 . an attacker would have available the following information: q = 353; α = 3; Y A = 40; Y B = 248.. 

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A computes K = (Y B ) XA  mod 353 = 248 97  mod 353 = 160. B computes K = (Y A ) XB  mod 353 = 40 233  mod 353 = 160 . an attacker would have available the following information: q  = 353;  α   = 3;  Y A   = 40;  Y B   =  248.

In this simple example, it would be possible by brute force to determine the secret key 160.

While it is relatively easy to calculate exponentials modulo a prime, it is very difficult to calculate discrete logarithms . For large primes, the latter task is considered infeasible .. 

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While it  is relatively easy to calculate exponentials modulo a prime, it is very  difficult to  calculate discrete logarithms . For  large primes, the latter task is  considered infeasible .

Security of the  Diffie -Hellman  Algorithm

The  Diffie -Hellman key-exchange algorithm is a secure algorithm that offers high performance, allowing two computers to publicly exchange a shared value without using data encryption.

Uses. 12. Aside from using the algorithm for generating public keys, there are some other places where DH Algorithm can be used: Encryption: The Diffie Hellman key exchange algorithm can be used to encrypt. One modern example of it is called Integrated Encryption Scheme, which provides security against chosen plain text and chosen clipboard attacks. Password Authenticated Agreement: When two parties share a password, a password-authenticated key agreement can be used to prevent the Man in the middle attack. This key Agreement can be in the form of Diffie -Hellman. Secure Remote Password Protocol is a good example that is based on this technique.. 

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Aside from using the algorithm for generating public keys, there are some other places where DH Algorithm can be used: Encryption:  The   Diffie  Hellman key exchange algorithm can be used to encrypt. One modern example of it is called Integrated Encryption Scheme, which provides security against chosen plain text and chosen clipboard attacks. Password Authenticated Agreement:   When two parties share a password, a password-authenticated key agreement can be used to prevent the Man in the middle attack. This key Agreement can be in the form of  Diffie -Hellman. Secure Remote Password Protocol is a good example that is based on this technique.

Contd ….. 13. Forward Secrecy: Forward secrecy-based protocols can generate new key pairs for each new session, and they can automatically discard them when the session is finished. In these forward Secrecy protocols, more often than not, the Diffie Hellman key exchange is used.. 

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Forward Secrecy:   Forward secrecy-based protocols can generate new key pairs for each new session, and they can automatically discard them when the session is finished. In these forward Secrecy protocols, more often than not, the  Diffie  Hellman key exchange is used.

Adavantages. 14. The sender and receiver have no prior knowledge of each other. Communication can take place through an insecure channel. Sharing of secret key is safe.. 

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The sender and receiver have no prior knowledge of each other.     Communication can take place through an insecure channel.     Sharing of secret key is safe.

Disadvantages. 15. A problem with asymmetric encryption, however, is that it is slower than symmetric encryption. It requires far more processing power to both encrypt and decrypt the content of the message.. 

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A problem with asymmetric encryption, however, is that it is slower than symmetric encryption.     It requires far more processing power to both encrypt and decrypt the content of the message.

The algorithm can not be sued for any asymmetric key exchange.     Similarly, it can not be used for signing digital signatures.

Project Execution Screenshots. 16. blob:https://web.whatsapp.com/56b268e4-8b9d-43a8-87ee-45b662480dc5. 

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blob:https://web.whatsapp.com/56b268e4-8b9d-43a8-87ee-45b662480dc5

Welcome to the World of Keys
Diffi-Hellman
Algorithm

Contd ….. 17. Diffi-Hellman Algorithm Alice public Value G: Alice private value x: SENDER Enter our Message Encryption Generate Key Encrypted Message Bob value p: Bob private value RECEVIER Enter key Submit Receive Message Decryption. 

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Diffi-Hellman Algorithm
Alice public Value
G:
Alice private value
x:
SENDER
Enter our Message
Encryption
Generate Key
Encrypted Message
Bob
value
p:
Bob private value
RECEVIER
Enter key
Submit
Receive Message
Decryption

Contd ….. 18. Diffi-Hellman Algorithm Alice Alice private value x: SENDER Enter our Message hello mike Encryption Generate Encrypted Message Send Key Bob p: Bob private value RECEVIER Enter key Submit Receive Message CE•cryption. 

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Diffi-Hellman Algorithm
Alice
Alice private value
x:
SENDER
Enter our Message
hello mike
Encryption
Generate
Encrypted Message
Send
Key
Bob
p:
Bob private value
RECEVIER
Enter key
Submit
Receive Message
CE•cryption

Conclusion. 19. The Diffie Hellman key Exchange has proved to be a useful key exchange system due to its advantages. it is really tough for someone snooping the network to decrypt the data and get the keys, it is still possible if the numbers generated are not entirely random. Also, the key exchange system makes it possible to do a man in the middle attack; to avoid it, both parties should be very careful at the beginning of the exchange.. 

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The  Diffie  Hellman key Exchange has proved to be a useful key exchange system due to its advantages.      it is really tough for someone snooping the network to decrypt the data and get the keys, it is still possible if the numbers generated are not entirely random.     Also, the key exchange system makes it possible to do a man in the middle attack; to avoid it, both parties should be very careful at the beginning of the exchange.