Public Key Infrastructure
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1 Public Key Infrastructure Yan Huang Credit: David Evans (UVA)
2 Using RSA to Encrypt Use 2048-bit modulus (recommended) Encrypt 1MB file bit messages Each M e requires log 2 (e) 1024-bit number modular multiplications (unless e is fixed to some small numbers) Why does not one use RSA like this? About times slower than DES Need to be careful not to encrypt particular Ms Can speed up encryption by choosing e that is an easy number to multiply by (e.g., 3 or ) But, decryption must use non-easy d (~2048 bits) 2
3 Hybrid Encryption Use RSA to establish a shared secret key for symmetric cipher (e.g., AES) Encrypt the secret key with OAEP padding Sign (encrypt with private key) a hash of the message A short block that is associated with the message 3
4 RSA Paper The need for a courier between every pair of users has thus been replaced by the requirement for a single secure meeting between each user and the public file manager when the user joins the system. 4
5 Key Management Public keys only useful if you know: 1. The public key matches the entity you think it does (and no one else). 2. The entity is trustworthy. 5
6 Approach 1: Public Announcement Publish public keys in a public forum USENET groups Append to messages New York Time classifieds Easy for rogue to pretend to be someone else 6
7 Approach 2: Public Directory Trusted authority maintains directory mapping names to public keys Entities register public keys with authority in some secure way Authority publishes directory Print using watermarked paper, special fonts, etc. Allow secure electronic access 7
8 Can we avoid needing an on-line directory? 8
9 Certificates Loren Kohnfelder, MIT 4 th year thesis project, 1978: Towards a Practical Public-key Cryptosystem Public-key communication works best when the encryption functions can reliably be shared among the communicants (by direct contact if possible). Yet when such a reliable exchange of functions is impossible the next best thing is to trust a third party. Diffie and Hellman introduce a central authority known as the Public File Each individual has a name in the system by which he is referenced in the Public File. Once two communicants have gotten each other s keys from the Public File then can securely communicate. The Public File digitally signs all of its transmission so that enemy impersonation of the Public File is precluded. 9
10 Certificates { alice@alice.org, KU A } TrustMe.com { bob@bob.com, KU B } C A = E KRTrustMe [ alice@alice.org, KU A ] C B = E KRTrustMe [ bob@bob.com, KU B ] C A Alice Bob C B KU Public Key KR Private Key 10
11 Data encrypted using secret key exchanged using some public key associated with some certificate.
12 12
13 SSL (Secure Sockets Layer) Simplified TLS Handshake Protocol Client Hello Server Check Certificate using KU CA Pick random K KR CA [Server Identity, KU S ] KU S [K] Find K using KR S Secure channel using K 13
14 Certificates { alice@alice.org, KU A } VarySign { bob@bob.com, KU B } C A = E KRTrustMe [ alice@alice.org, KU A ] C B = E KRTrustMe [ bob@bob.com, KU B ] C A Alice Bob C B How does TrustMe.com decide whether to provide Certificate?
15 Verifying Identities $$$$ { alice@alice.org, KU A } VarySign { bob@bob.com, KU B } C A = E KRTrustMe [ alice@alice.org, KU A ] C B = E KRTrustMe [ bob@bob.com, KU B ] C A Alice Bob C B CS588 Spring
16 With over half a million businesses authenticated, VeriSign follows a rigorous and independently audited authentication process. All involved VeriSign employees pass stringent background checks, and each authentication is split between multiple individuals. We maintain physically secure facilities, including biometric screening on entry. CS588 Spring
17 VeriSign s Certificate Classes Secure Site SSL Certificate Supports 40-bit session key Proves: you are communicating with someone willing to pay VeriSign $598 (or with ~$1000 to break a 40-bit key) Except they have a free 14-day trial (but it uses a different Trial CA key) 17
18 18
19 Secure Site Pro Certificate $995 per year true 128-bit key 128-bit encryption offers 2 88 times as many possible combinations as 40-bit encryption. That s over a trillion times a trillion times stronger. trillion = trillion * trillion = Verisign s marketing claim could be: trillion times a trillion times a trillion times a trillion times a trillion times a trillion times a trillion times ten thousand (in Britain it is a trillions time a trillion times a trillion times a trillion times a billion times a thousand) times stronger (but that would sound even sillier!) Businesses authentication: out-of-band communication, records 19
20 20
21 Limiting The Damage { alice@alice.org, KU A } VarySign.com C A = E KRTrustMe [ alice@alice.org, cert id, expiration time, KU A ] C A Alice Bob Checks expiration time > now
22 22
23 Revoking Certificates { alice@alice.org, KU A } VarySign.com C A E KRTrustMe [CRL] Send me the CRL C A Alice <certid, Date Revoked> <certid, Date Revoked> <certid, Date Revoked> Bob 23
24 Certificate Questions How do participants acquire the authority s public key? If authority s private key is compromised, everything is vulnerable! Keep the key locked up well 24
25 Problems with Certificates Depends on a certificate authority Needs to be a big, trusted entity Needs to make money (or be publicly funded) Need to acquire a certificate Makes anonymity difficult Requires handshaking 25
26 PGP (Pretty Good Privacy) Keyring: list of public keys, signed by owner s private key Alice s keyring: E KR Alice (< bob@bob.com, KU Bob >, < cathy@sharky.com, KU Cathy >) Exchanging Keyrings (Web of Trust) Complete Trust: I trust Alice s keyring (add the public key pairings to my own keyring) Partial Trust: I sort of trust Alice, but require confirmation from someone else too (I need to get E KR Cathy (< bob@bob.com, KU Bob >) before trusting KU Bob 26
27 Charge Look at the certificate chains when you browse the web Find a certificate with a trust chain more than two levels deep Update your browser CRLs: when were they last updated? 27
28 Avoiding Certificates What if your identity (e.g., your address) is your public key? Is it possible to do this with RSA? Do you want your address to be a 200-digit random number? 28
29 Identity Based Encryption [Shamir 1984], [Boneh & Franklin 2003] public-key = identity private-key = F(master-key, identity) The owner of the master-key is the new authority. Must be careful who it gives private keys to. 29
30 Key-Generating Service Holds master-key Participants request private keys from KGS Sends s to KGS, requests corresponding private key KGS authenticates requestor If valid, computes F(master-key, s) and sends over secure channel How does the trust given to the KGS compare to that given to CA in SSL? KGS can decrypt all messages! With certificates, certificate owner still has her own private key. But, CA can impersonate anyone by generating a certificate with a choosen public-key. 30
31 Shamir s IBE Signature Scheme Setup: done by KGS Select p, q large primes N = pq Choose e relatively prime to ϕ (N) = (p-1)(q-1) Choose d satisfying ed 1 mod ϕ (N) Choose h a cryptographic hash function Publish N, e and h to all participants Keep d secret master-key 31
32 Shamir s Signatures Generating a private key privatekey(id) = ID d mod N Can only be done by KGS (d is master secret) Signing a message M with identity ID Obtain g = privatekey(id) from KGS Choose random r less than N Compute signature (s, t): t = r e mod N s = g r h(t M) mod N Warning: book typesetting is off and wrong range for h! 32
33 Verifying a Signature KGS produced g = ID d mod N Recipient knows ID and M, system parameters e and N t = r e mod N s = g r h(t M) mod N Verify (ID, s, t, M) s e = ID t h(t M) mod N (ID d r h(t M) ) e mod N ID de r h(t M)e mod N ID r eh(t M) mod N ID t h(t M) mod N What does non-forgibility of a Shamir IBE signature rely on? 33
34 Identity-Based Encryption Shamir s scheme signatures only, not encryption Boneh & Franklin, 2001 First practical, provably secure IBE scheme Builds on elliptic curves 34
35 Issues in IBE Complete trust in KGS With Boneh & Franklin s system can use secret sharing techniques to divide this trust among multiple entities Could you do this with Shamir s IBE signatures? Revocation Can include expiration times in identities But no way to revoke granted private keys 35
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