Public Key Cryptography Lecture 3 Chantilly Academy Poorvi
Public Key Cryptography Lecture 3: Chantilly Academy Poorvi Vora Department of Computer Science George Washington University
How do you exchange keys? • Main issue with encryption we have studied so far: – how does one get the key to the other party? • Problem occupied cryptographers in the early 70’s. – Interested in enabling lay people to talk to each other freely and secretly without fear of government snooping. 9/9/2020 Chantilly Academy Crypto Lecture 2: Spring 07 2
Public Key Cryptography • Famous paper by Diffie and Hellman (1976) – Suppose two keys: one public; other private – Anything encrypted with one can be decrypted by other – Not possible to determine private key through: • Encrypted messages • Public key • Based on asymmetry of problems using today’s computers: – Forward direction of problem harder than inverse 9/9/2020 Chantilly Academy Crypto Lecture 2: Spring 07 3
Make Public Key Available • To exchange keys used for AES • Alice encrypts AES key with public key of Bob • Sends to Bob, who decrypts with his private key • They have a conversation using AES and the key exchanged 9/9/2020 Chantilly Academy Crypto Lecture 2: Spring 07 4
Example Public-Key Scheme: RSA (Rivest Shamir Adleman) • Most popular public-key encryption scheme • Developed in mid-70 s • Turns out it was developed two years earlier by a British intelligence agent (Cocks) who could not make it public. • This was revealed in the early 2000 s • RSA won Turing Award for their work, and the company made billions 9/9/2020 Chantilly Academy Crypto Lecture 2: Spring 07 5
Example • So far we used addition to encrypt • For RSA, we use exponentiation: raising numbers to a power • Additionally, we take the remainder • For example, encrypt 3 using the key 3 33 mod 15 = 27 mod 15 = 12 Where “mod 15” denotes “remainder when dividing by 15” 9/9/2020 Chantilly Academy Crypto Lecture 2: Spring 07 6
Difficult to invert It is hard to find the message if we know the ciphertext, and the power (the public key) For example, 13 mod 15 is x 3 mod 15 for some x Can you guess x? You end up trying every possibility, or something that is almost as difficult. 9/9/2020 Chantilly Academy Crypto Lecture 2: Spring 07 7
The answer • However, if you know the private key, you can quickly find the answer. • When 13 mod 15 = x 3 mod 15 X can be found by raising 13 to the power of the private key. In this case, the private key is also 3, however this is not typical. 133 mod 15 = 7 mod 15 = x 9/9/2020 Chantilly Academy Crypto Lecture 2: Spring 07 8
- Slides: 8