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MSIT 543 Cryptography Concepts and Techniques How RSA Encryption Works

Learn how RSA encryption works, including asymmetric key exchange, prime numbers usage, and decryption process. Explore the origin of RSA and its significance in cryptography.

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MSIT 543 Cryptography Concepts and Techniques How RSA Encryption Works

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  1. MSIT 543 Cryptography Concepts and TechniquesHow RSA Encryption Works Dr Jeffrey A Robinson

  2. How Encryption Works • From http://www.youtube.com/watch?v=wXB-V_Keiu8 The Kahn Academy • Prior to the 1970’s encryption depended upoinsymmetric keys, which can be safely exchanged. • But if keys need to be shared with MANY people, thousands of messages need to be transmitted to establish those many different keys. • This specific key exchange scenario is know as the Diffie-Hellman key exchange

  3. RSA Encryption • RSA encryption is based on Asymmetric keys • One to encrypt • And another to decrypt • The first is known as the public key..and anyone can encrypt • The second is the private key and can be used to decrypt the encoded message

  4. RSA Encryption • The secret is the relation below (the enclosed link shows the origin and development of this function) • where K and n are very large primes

  5. RSA Encryption • Uses very large prime numbers • p1 is a large prime • p2 is another large prime • n = p1*p2

  6. RSA Encryption • Alice picks some numbers and does some math. She then publishes e and n (which together make up her public key). (d in this case = 2011)

  7. RSA Encryption • Encryption is performed by me mod n = c Where m is the message And c is the encrypted result (Note: all digital objects are all numbers)

  8. RSA Encryption • If the message, in our case, is 89, then c is 1394 • (Remember, in real world cases, the numbers are many, many digits long)

  9. RSA Encryption • Alice can then decrypt the message using her secret key “d” • By raising c to the power of d (which is m mod n)

  10. RSA Encryption • The result is decrypted cd mod n = m or 13942011 mod 3127 = 89 revealing the original message

  11. RSA Encryption • When first discovered, it was immediately classified. • But it was rediscovered and published in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman at MIT • And is now known as RSA encryption • The letters RSA are the initials of their surnames, listed in the same order as on the paper

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