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Cryptography 101

Cryptography 101. How is data actually secured. RSA Public Key Encryption. RSA – names after the inventors Rivest, Shamir, and Adleman Basic Idea: Your private key is the only key that can unlock (decrypt) messages that were locked (encrypted) with your public key. Public & Private Keys.

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Cryptography 101

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  1. Cryptography 101 How is data actually secured

  2. RSA Public Key Encryption • RSA – names after the inventors • Rivest, Shamir, and Adleman • Basic Idea: • Your private key is the only key that can unlock (decrypt) messages that were locked (encrypted) with your public key.

  3. Public & Private Keys • Share you public key • Thus, users can send you encrypted data • Never share your private key • Thus, no one else can decrypt messages that are sent to you and encrypted with you public key

  4. How does it work? • Answer: Math • Background: • What are the factors of 30? • What are prime numbers. • What are the prime factors of 30?

  5. Public Key • Public Key = PK = p*q • Example: • p = 5 • q = 11 • PK = 55 • 55 is special; Its the product of two prime numbers.

  6. Example • http://www.antilles.k12.vi.us/math/cryptotut/rsa3.htm • PK = 55 • Here I’m going to encrypt the letter ‘E’ • ‘E’ is represent in ASCII as 69 • The encryption technique will actually transform the letter ‘E’ (69) into the number ‘1’ (49)

  7. Encryption • Take your text (T = 69) • Enlarge it by raising it to a power (e = 3) • Here I can pick E to be whatever I want • Divide by Public Key (PK = 55) • The remainder is the encrypted cipher-text (C =49) • 693 = 328,509 • 328,509 / 55 = 5972 R 49

  8. Decryption • How do you decrypt 49 back into a 69? • You have to compute a special value • The book calls this value s • Most other books call this value d • s = (1/e) * (2 * (p-1) * (q-1) + 1) • s = 1/3 * (2*4*10 + 1) • s = 1/3 * 81 • s = 27

  9. Decryption • How do you decrypt 49 (C) back into a 69 (T)? • Take your ciphertext (C = 49) • Enlarge it by raising it to a power (s = 27) • Here s depends on your choice of p, q, and e. • Divide by Public Key (PK = 55) • The remainder is the original (C =49) • 4927 = a really big number • really big number / 55 = 5972 R 69

  10. Summary • Encryption • uses the Public Key (PK) and specially selected value (e) • These are both Public knowledge • In fact, the Public key is both PK and e • Decryption • uses a specially computed value s (some books call it d) • This value is kept private. • It computationally impossible to figure out s unless you know p and q. • The private key is s. But keep in mind that s is computed from p, q, and e.

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