March R. Smith - University of St Thomas - Minnesota QMCS Class Today Homework backHomework back Take-home exam will be on Blackboard after classTake-home exam will be on Blackboard after class Public Key Crypto – ExamplesPublic Key Crypto – Examples Public key applicationsPublic key applications

March R. Smith - University of St Thomas - Minnesota Homework back We worked on it in class last timeWe worked on it in class last time

March R. Smith - University of St Thomas - Minnesota Uses a pair of keys: the Private Key and the Public KeyUses a pair of keys: the Private Key and the Public Key Usually, one key of the pair decrypts what the other key encrypts, and vice versaUsually, one key of the pair decrypts what the other key encrypts, and vice versa “Asymmetric Encryption”“Asymmetric Encryption” Encryption Procedure Clear Text Clear Text Public Key Encryption Cipher Text Public Key Decryption Procedure Private Key

March R. Smith - University of St Thomas - Minnesota Public Key cryptography Diffie HellmanDiffie Hellman ‘Distributive property’ of exponents‘Distributive property’ of exponents Modulus operationModulus operation

March R. Smith - University of St Thomas - Minnesota RSA Weird variantWeird variant Multiply two primesMultiply two primes –Product is part of the key –2 other numbers form rest of the key “Public” number (often 3 or 65537)“Public” number (often 3 or 65537) “Private” number (the modular inverse)“Private” number (the modular inverse) Works in both directions – encrypt and decryptWorks in both directions – encrypt and decrypt

March R. Smith - University of St Thomas - Minnesota Applications Sharing a keySharing a key –Diffie Hellman approach –RSA approach Digital signaturesDigital signatures –Creating one, RSA –Checking one, RSA

March R. Smith - University of St Thomas - Minnesota Digital Signature Concept Honest Abe must possess the private key in order to produce the digital signatureHonest Abe must possess the private key in order to produce the digital signature Honest Abe’s Private Key Document Signed Document Signed: Honest Abe ‘I certify that this is really true and Signature Procedure Honest Abe ‘I certify that this is really true and

March R. Smith - University of St Thomas - Minnesota Signature Procedure Digital Signature Validation Alice trusts Honest AbeAlice trusts Honest Abe Alice needs proof that Abe wrote the documentAlice needs proof that Abe wrote the document Abe’s public key shows that Abe signed the document with his private keyAbe’s public key shows that Abe signed the document with his private key Honest Abe’s Public Key Valid Signature Valid Document Alice Digital Signature ‘I certify that this is really true and

March R. Smith - University of St Thomas - Minnesota Decryption Procedure Secret Key Secret Key (temporary) Random Number Generator Encryption Procedure Cipher Text RSA Encrypting Secret Keys First send the secret key, then send the dataFirst send the secret key, then send the data Encryption Procedure { } Public Key Clear Text John J. Jones Clear Text John J. Jones Decryption Procedure Private Key

March R. Smith - University of St Thomas - Minnesota Hash Digital Signatures Signature is the hash value, encrypted with the private keySignature is the hash value, encrypted with the private key Associates the document’s contents with the signerAssociates the document’s contents with the signer Detects changes to documentDetects changes to document Encryption Procedure Private Key ‘I certify that this is really true and Signed Document Digital Signature ‘I certify that this is really true and

March R. Smith - University of St Thomas - Minnesota Valid? = Digital Signature Validation Decrypt the hash with the public keyDecrypt the hash with the public key Compare with the document’s hashCompare with the document’s hash Hash Public Key Signed Document Digital Signature Hash Decryption Engine

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