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Cryptography

ElGamal encryption is a public-key cryptosystem based on the Diffie-Hellman key exchange, emphasizing security through the discrete logarithm problem (DLP) rather than integer factorization. This system allows for secure key generation and encryption/decryption processes. With a recommended order for the generator ( g ) of at least ( 2^{160} ), ElGamal prevents attacks like the Pohlig-Hellman. Additionally, the algorithm involves using hash functions such as SHA-1 for message integrity and authentication through digital signatures, ensuring robust security in modern cryptographic applications.

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Cryptography

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  1. Cryptography

  2. Public KeyCryptosystems

  3. ElGamal Encryption:Based on Diffie Hellman Key Exchange Security of Diffie Hellman key exchange not based on integer factoring (like RSA and Rabin)but on the discrete logarithm problem (DLP).

  4. Discrete Logarithm

  5. Diffie Hellman Key Exchange

  6. Diffie Hellman Key Exchange Choose order g at least 2^160 to prevent Pohlig Hellman.

  7. ElGamal Key Generation

  8. ElGamal Key Encryption

  9. ElGamal Key Decryption

  10. ElGamal

  11. ElGamal and Diffie Hellman

  12. Hash functions

  13. Hash Function

  14. Compression Function

  15. One-way Function

  16. One-way Function

  17. Collisions

  18. Collisions

  19. Collisions

  20. Compression function from encryption functions

  21. Compression function from encryption functions

  22. Hash functions fromcompression functions

  23. SHA-1 3. The original length of x is written as a 64-bit number. 4. Append 3. to x from 2.

  24. SHA-1

  25. SHA-1

  26. SHA-1

  27. Message Authentication Codes

  28. Message Authentication Codes

  29. Message Authentication Codes

  30. Message Authentication Codes

  31. Digital Signatures & Identification

  32. Digital Signatures

  33. RSA Signatures Key Generation:

  34. RSA Signatures Signature Generation:

  35. RSA Signatures Signature Verification:

  36. RSA Signatures

  37. RSA Signatures with Hash Functions

  38. Other Public Key Digital Signatures

  39. ElGamal Signatures Key Generation:

  40. ElGamal Signatures Signature Generation:

  41. ElGamal Signatures Signature Verification:

  42. ElGamal Signatures

  43. Identification

  44. Identification • One can use for example • Passwords • Challenge-Response identification based on • symmetric encryption • public key encryption • Zero-knowledge proofs

  45. Multimedia: crypto is not enough

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