Special Topics in Cryptography Mohammad Mahmoody Last time How to - - PowerPoint PPT Presentation

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Oct 18, 2022 202 likes •360 views

Special Topics in Cryptography Mohammad Mahmoody Last time How to combine CPA security + MACS: Security against active attacks CCA secure private-key encryption Today Public-key encryption and key-agreement RSA (PKE) and

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Special Topics in Cryptography

Mohammad Mahmoody

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Last time

How to combine CPA security + MACS:
Security against active attacks
CCA secure private-key encryption
Public-key encryption and key-agreement
RSA (PKE) and Diffie Hellman (KA)

Today

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Public Key Encryption

Secure communication even without shared secret keys!

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Main challenge: starting from zero

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http://www.merkle.com/1974/

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Defining Public Key Encryption

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Security of Public Key Encryption

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A related problem: key agreement

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Security of Key Agreement

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Number Theory 101: Modular Computation

𝑎 : integers, can be added (+), subtracted (−) and multiplied (∗)
𝑎𝑂 : integers “mod 𝑂” : again we can do + , − , ∗
Interesting cases for us:

𝑂 = 𝑟 for prime 𝑟 𝑂 = 𝑞. 𝑟 for primes 𝑞, 𝑟

𝑕 is a (multiplicative) generator if: 𝑕0, 𝑕1, … , 𝑕𝑂−1 = {1,2, … 𝑂 − 1}

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Diffie Hellman Key Agreement

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