CS/COE 1501 Recitation Extended Euclidean Algorithm + Digital Signatures.

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Presentation transcript:

CS/COE 1501 Recitation Extended Euclidean Algorithm + Digital Signatures

Extended Euclidean Algorithm

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN

Extended Euclidean Algorithm

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst NaN 310

Hash Functions

For Crypto Hash Functions, Output Should Appear Random

Digital Signatures – Public Key Cryptography

Creating a Digital Signature

Digital Signatures Often Use Commutative Operations

Plaintext sent by sender

Digital Signatures Often Use Commutative Operations Plaintext sent by sender Cryptotext sent by sender using sender’s private key

Digital Signatures Often Use Commutative Operations Plaintext sent by sender Cryptotext sent by sender using sender’s private key Sender’s public key

Digital Signatures Often Use Commutative Operations Plaintext sent by sender Cryptotext sent by sender using sender’s private key Sender’s public key =

Digital Signatures Often Use Commutative Operations Plaintext sent by sender Cryptotext sent by sender using sender’s private key Sender’s public key = Plaintext recovered matches

Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes

Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM

Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM

Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM Compute

Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM Compute =

Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM Compute = Match. Signature Verified.

Adam J. Lee’s slides from CS Acknowledgements