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Digital Signatures

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Anononymity and the Internet

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Potential For Mischief Microsoft You Hacker Controlled Website

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Signature Signature - verifies identity What could go wrong?

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Signature Bank Record of signatures

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Physical Signature Sign a message by locking with a key you own

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Physical Key Back Still need a trusted entity to manage keys

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Asymmetric Cryptography Symmetric cryptography: Key for encoding same as key for decoding – Shift three letters Asymmetric cryptography: Key for encoding different than for decoding

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Simple Example Encryption Key : – Multiply by 6, clock size 11 – Encode 5 = 5 * 6 clock 11 = 30 clock 11 = 8

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Decoding If x * 6 clock 11 = y then y * 2 clock 11 = x

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Decryption Key 2 is the decryption Key for encryption key 6 and clock size 11

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Picking Keys Pick clock size C – Prime clock sizes work best Find x and y such that x * y clock C = 1

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Public / Private One key is kept private Other key made public – Give to anyone who wants it

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Private Key Any message encrypted with a private key MUST have been written by the person who signed it Anyone can decrypt the message – Encryption for authentication not secrecy

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How Do We Know Public Key Is Good? Ravi You Hacker Controlled Website

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Authenticating a Key Official key bank??

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Can't Really Trust a Bank Key Bank You Hacker Controlled Website

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Authenticating a Key Key bank "signs" people's public keys by encrypting them

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Authenticating a Key Browsers come with public keys of known banks called Certification Authorities

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2 Part Message Send two things: – Message encrypted with private key – Public key encrypted by trusted authority

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Chain Of Trust Reality may involve chain of locks

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Encrypting With Public Key Anyone can use public key to secretly send message to holder of private key Locked with Private Key Authentication Locked with Public Key Secrecy

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Web Security HTTPS : Secure web connection – Browser asks server for public key – Browser picks shared secret, encrypts with public key, sends to server

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RSA Multiplication keys too easy to break…

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RSA Multiplication keys too easy to break… …use exponents RSA (Rivest, Shamir, Adelman) invented algorithm in 1977

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RSA Math Private key : raise to x power, clock size C Public key : raise to y power, clock size C Message: 4 4 3 clock 22 = 64 clock 22 = 20 Encrypted: 20 20 7 clock 22 = 4

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Picking Keys Start with two prime numbers p, q – multiply to make clock size Pick private key, calculate public key from private, p and q using multiplication trick

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Picking Keys Start with two prime numbers p, q – multiply to make clock size Pick private key, calculate public key from private, p and q using multiplication trick If anyone figures out p and q they can figure out your private key

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Factoring Factoring large numbers is hard – But we are getting faster

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Factoring Factoring large numbers is hard – But we are getting faster Larger keys : 2048 bits (prime numbers with 100's of digits)

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Factoring Factoring large numbers is hard – But we are getting faster Larger keys : 2048 bits (prime numbers with 100's of digits) May need to move to different kinds of math: http://arstechnica.com/security/2013/10/a- relatively-easy-to-understand-primer-on- elliptic-curve-cryptography/2/ http://arstechnica.com/security/2013/10/a- relatively-easy-to-understand-primer-on- elliptic-curve-cryptography/2/

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Two messages: My public key: exponent 3, clock 34 encrypted ^ exponent mod clock = message Which 1 of these messages is NOT from me? – Three should check out, one should not Message 54158 Encrypted Version 1130122

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