Digital Signatures

Anononymity and the Internet

Potential For Mischief

Microsoft

You

HackerControlled

Website

Signature

• Signature - verifies identity

• What could go wrong?

Signature Bank

• Record of signatures

Physical Signature

• Sign a message by locking with a key you own

Physical Key Back

• Still need a trusted entity to manage keys

Asymmetric Cryptography

• Symmetric cryptography:Key for encoding same as key for decoding– Shift three letters

• Asymmetric cryptography:Key for encoding different than for decoding

Simple Example

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

Decoding

• If x * 6 clock 11 = ythen y * 2 clock 11 = x

Decryption Key

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

Picking Keys

• Pick clock size C– Prime clock sizes work best

• Find x and y such that x * y clock C = 1

Public / Private

• One key is kept private• Other key made public– Give to anyone who wants it

Private Key

• Any message encrypted with a private key MUST have been written by the person who signed it

• Anyone can decryptthe message– Encryption for

authenticationnot secrecy

How Do We Know Public Key Is Good?

Ravi

You

HackerControlled

Website

Authenticating a Key

• Official key bank??

Can't Really Trust a Bank

Key Bank

You

HackerControlled

Website

Authenticating a Key

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

Authenticating a Key

• Browsers come with public keys of known banks called Certification Authorities

2 Part Message

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

Chain Of Trust

• Reality may involve chain of locks

Encrypting With Public Key

• Anyone can use public key to secretly send message to holder of private key

Locked with Private KeyAuthentication

Locked with Public KeySecrecy

Web Security

• HTTPS : Secure web connection– Browser asks server for public key– Browser picks shared secret,

encrypts with public key, sendsto server

RSA

• Multiplication keys too easy to break…

RSA

• Multiplication keys too easy to break… …use exponents

• RSA (Rivest, Shamir, Adelman) invented algorithm in 1977

RSA Math

• Private key : raise to x power, clock size C• Public key : raise to y power, clock size C

Message: 443 clock 22 =64 clock 22 = 20Encrypted: 20207 clock 22 = 4

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

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

Factoring

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

Factoring

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

• Larger keys : 2048 bits (prime numbers with 100's of digits)

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/

Two messages:

• My public key: exponent 3, clock 34encrypted ^ exponent mod clock = message

• Which 1 of these messages is NOT from me?– Three should check out, one should not

Message 5 4 15 8EncryptedVersion

11 30 12 2