Public KeyCryptosystems

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ElGamal Encryption:Based on Diffie Hellman Key Exchange

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Security of Diffie Hellman key exchange not based on integer factoring (like RSA and Rabin)but on the discrete logarithm problem (DLP).

Discrete Logarithm

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Diffie Hellman Key Exchange

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Diffie Hellman Key Exchange

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Choose order g at least 2^160 to prevent Pohlig Hellman.

ElGamal Key Generation

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ElGamal Key Encryption

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ElGamal Key Decryption

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ElGamal

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ElGamal and Diffie Hellman

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Hash functions

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Hash Function

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Compression Function

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One-way Function

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One-way Function

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Collisions

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Collisions

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Collisions

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Compression function from encryption functions

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Compression function from encryption functions

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Hash functions fromcompression functions

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SHA-1

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

SHA-1

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SHA-1

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SHA-1

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Message Authentication Codes

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Message Authentication Codes

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Message Authentication Codes

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Message Authentication Codes

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Digital Signatures & Identification

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Digital Signatures

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RSA Signatures

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Key Generation:

RSA Signatures

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Signature Generation:

RSA Signatures

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Signature Verification:

RSA Signatures

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RSA Signatures with Hash Functions

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Other Public Key Digital Signatures

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ElGamal Signatures

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Key Generation:

ElGamal Signatures

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Signature Generation:

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Signature Verification:

ElGamal Signatures

ElGamal Signatures

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Identification

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Identification

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One can use for example• Passwords • Challenge-Response identification based on

• symmetric encryption• public key encryption

• Zero-knowledge proofs

Multimedia: crypto is not enough

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