CS G254/U645                                                                             Lecturer: Ravi Sundaram

11/13/07                                                                       

 

 

Recap:

           

Diffie-Hellman(El Gamal): exponentiation is easy, discrete log is hard

            Encryption – Bob picks a a large prime, p, and generator, g, and  a private key <b>        

                                  Bob's public key <  g^b mod p, g, p>   

                                  Bob's private key <b>

                                  Alice wants to send a message to bob.

                                   She picks <a > (Could be Alice's private key or  a new                                                          number she picked randomly for sending message m)

                                  Alice sends <g^a mod p, m * g^(ab) mod p>

                                  

            Decryption – Bob takes Alices m*g(ab) and divides it by g(ab)

 

El Gamal signature:

           

            Bob wants to sign m, generate Sm randomly

            Sends m, g^(Sm) mod p, Sm + m*b mod (p-1)

 

            y = Sm + m*b mod (p-1)

 

            Verification: g^y = (gsm )(gb)^m

 

<m,                signature>

           

            Take messsage, attach signature, encrypt the whole thing

 

RSA:

            Bob picks two large primes p & q and computes n = p*q

            He also computes d,e such that d*e = 1 mod Ψ(n)

 

            Bob's public key <e, n>

            Bob's private key <d>

 

            Encryption:

                        Alice wants to send a message to Bob.

                        She sends me mod n

                       

            Decryption:

                        Bob decrypts by raising it to the d  (me )d = M(ed) = m mod n

(Theorem: For all a such that (a,n) = 1, a^Φ(n) = 1 mod n.)

            Signature:

 

                        Bob signs by sending m, m^d mod n

 

                        Alice verifies by (md)e = m

 

 

Public Key Cryptography & Infrastructure

 

Certificate – Signed (public key + common name)

           

A certificate contains: <common name, public key, signature>

           

They are signed by a CA (Certificate Authority)

 

Certificate Authorities:        

–    “Trust anchors”

–    entities whose public keys are embedded in browsers.

–    VeriSign is trusted by Microsoft, and pays them money to have its key in browser

 

Registration Authorities

                        -- Physically Verify Identity

                        -- Once RA has verified identity, person presents public key, CA signs                                               (public key + common name) and

                                   it and hands it back

Weaknesses :

–    Certificates embedded in browser can be changed, so be wary of public computers

–     You have to pay for certs from VeriSign

–    Certs expire

–    Single point of failure. If Verisign's private keys gets stolen, sites could be easily “signed” be Verisign.

–    Physical identification process needs strengthening

                                              

Certificate Chains:

–    You can obtain certificate issuing certificates from CA for extra $$

–    Such certs have a bit set that allow the owner of the cert to sign the public key of other users in their domain.

–    During verification the verifier starts at the public key of the trusted anchor and goes down the chain verifying signatures.

 

Certificate Revocation:

–    Cancellation of a certificate

–    No revocation today -  no way for browser to check currently

–    Online certificate status protocol (OCSP)

–   Requires bowser to check in real time with VeriSign when authorizing a certificate

–   Basically a black list check.

 

 

SSL/TLS (Secure Socket Layer/Transport Layer Security)

–    SSL v2 – released by Netscape

–    SSL v3 – released by Microsoft

–    TLS – IETF committee (Internet Engineering Taskforce)

–    SSL/TLS – https

 

HTTP

SSL/TLS

TCP

IP

LINK

PHY

 

Application level security

 

 

 

Browser:

Picks session and cipher key
 

Website:

Has certificate and private key

 
 
 

 


                                           -------------------> hi ----------->

                                       <----- Cert, Suit of ciphers <----

                                       >------Epub(session key) cipher ---->

                                       <------ talk using session key ------>