the rsa algorithm...public key cryptography diffie-hellman is the first use of asymmetric key. it...
TRANSCRIPT
![Page 1: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/1.jpg)
The RSA Algorithm
![Page 2: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/2.jpg)
Public Key Cryptography● Diffie-Hellman is the first use of asymmetric key.
![Page 3: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/3.jpg)
Public Key Cryptography● Diffie-Hellman is the first use of asymmetric key.● It has some impracticalities:
![Page 4: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/4.jpg)
Public Key Cryptography● Diffie-Hellman is the first use of asymmetric key.● It has some impracticalities:
○ Setup phase: Alice has to exchange public information with each Bob.
![Page 5: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/5.jpg)
Public Key Cryptography● Diffie-Hellman is the first use of asymmetric key.● It has some impracticalities:
○ Setup phase: Alice has to exchange public information with each Bob.
● These impracticalities are avoided by the Rivest-Shamir-Adleman (RSA) algorithm.
![Page 6: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/6.jpg)
Public Key Model● The key is broken into a public and private part.
![Page 7: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/7.jpg)
Public Key Model● The key is broken into a public and private part.
![Page 8: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/8.jpg)
Public Key Model● The key is broken into a public and private part.● Bob and Alice publish their public keys.
![Page 9: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/9.jpg)
Public Key Model● The key is broken into a public and private part.● Bob and Alice publish their public keys -- for all.
![Page 10: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/10.jpg)
Public Key Model● The key is broken into a public and private part.● Bob and Alice publish their public keys -- for all.● Alice encrypts “hello” using Bob’s public key.
![Page 11: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/11.jpg)
Public Key Model● The key is broken into a public and private part.● Bob and Alice publish their public keys -- for all.● Alice encrypts “hello” using Bob’s public key.● Alice sends the encrypted “g#bzr&*h” to Bob.
![Page 12: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/12.jpg)
Public Key Model● The key is broken into a public and private part.● Bob and Alice publish their public keys -- for all.● Alice encrypts “hello” using Bob’s public key.● Alice sends the encrypted “g#bzr&*h” to Bob.● Bob decrypts with his private key.
![Page 13: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/13.jpg)
Public Key Model● The key is broken into a public and private part.● Bob and Alice publish their public keys -- for all.● Alice encrypts “hello” using Bob’s public key.● Alice sends the encrypted “g#bzr&*h” to Bob.● Bob decrypts with his private key.● Bob reads “hello”.
![Page 14: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/14.jpg)
Rivest Shamir Adleman (RSA)● Based on a one-way function -- i.e., a function that
is easy in one direction and hard in the other.
me mod N → c
![Page 15: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/15.jpg)
Rivest Shamir Adleman (RSA)● Based on a one-way function -- i.e., a function that
is easy in one direction and hard in the other.
me mod N → c
m: message (a number)
![Page 16: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/16.jpg)
Rivest Shamir Adleman (RSA)● Based on a one-way function -- i.e., a function that
is easy in one direction and hard in the other.
me mod N → c
m: message (a number)e: public exponent
![Page 17: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/17.jpg)
Rivest Shamir Adleman (RSA)● Based on a one-way function -- i.e., a function that
is easy in one direction and hard in the other.
me mod N → c
m: message (a number)e: public exponentN: public modulus
![Page 18: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/18.jpg)
Rivest Shamir Adleman (RSA)● Based on a one-way function -- i.e., a function that
is easy in one direction and hard in the other.
me mod N → c
m: message (a number)e: public exponentN: public modulusc: encrypted message
![Page 19: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/19.jpg)
Rivest Shamir Adleman (RSA)● Based on a one-way function -- i.e., a function that
is easy in one direction and hard in the other.
me mod N → c
m: message (a number)e: public exponentN: public modulusc: encrypted message
Easy: Compute me mod N
![Page 20: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/20.jpg)
Rivest Shamir Adleman (RSA)● Based on a one-way function -- i.e., a function that
is easy in one direction and hard in the other.
me mod N → c
m: message (a number)e: public exponentN: public modulusc: encrypted message
Easy: Compute me mod N Hard: Find m given (e,N)
![Page 21: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/21.jpg)
Rivest Shamir Adleman (RSA)● Basic structure of RSA
med mod N → c
publicmodulus
privatekeypublic
key
![Page 22: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/22.jpg)
Rivest Shamir Adleman (RSA)● Prime factorization problem:
○ Find the prime factors of N
![Page 23: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/23.jpg)
Rivest Shamir Adleman (RSA)● Prime factorization problem:
○ Find the prime factors of N○ E.g: N= 20 20 = 2 x 2 x 5
![Page 24: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/24.jpg)
Rivest Shamir Adleman (RSA)● Prime factorization problem:
○ Find the prime factors of N○ E.g: N= 20 20 = 2 x 2 x 5○ E.g: N= 45 45 = 3 x 3 x 5
![Page 25: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/25.jpg)
Rivest Shamir Adleman (RSA)● Prime factorization problem:
○ Find the prime factors of N○ E.g: N= 20 20 = 2 x 2 x 5○ E.g: N= 45 45 = 3 x 3 x 5
● Easy for small values of N
![Page 26: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/26.jpg)
Rivest Shamir Adleman (RSA)● Prime factorization problem:
○ Find the prime factors of N○ E.g: N= 20 20 = 2 x 2 x 5○ E.g: N= 45 45 = 3 x 3 x 5
● Easy for small values of N● Intractable for large values of N
![Page 27: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/27.jpg)
Rivest Shamir Adleman (RSA)● Prime factorization problem:
○ Find the prime factors of N○ E.g: N= 20 20 = 2 x 2 x 5○ E.g: N= 45 45 = 3 x 3 x 5
● Easy for small values of N● Intractable for large values of N● RSA uses very large numbers for N : > 300 digits
![Page 28: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/28.jpg)
RSA Summary
![Page 29: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/29.jpg)
RSA Summary● Solves the key-exchange problem.
![Page 30: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/30.jpg)
RSA Summary● Solves the key-exchange problem.
● Public keys can be published and distributed.
![Page 31: The RSA Algorithm...Public Key Cryptography Diffie-Hellman is the first use of asymmetric key. It has some impracticalities: Setup phase: Alice has to exchange public information with](https://reader033.vdocuments.mx/reader033/viewer/2022041707/5e45ab462c41937f72590061/html5/thumbnails/31.jpg)
RSA Summary● Solves the key-exchange problem.
● Public keys can be published and distributed.
● Secured by the intractability of the prime factorization problem -- i.e., the problem of discovering the prime factors of a large number.