# Part 2 D(E(M, K),K ) E(M, K) E(M, K) Plaintext M. Plaintext M. Decrypt with private key. Encrypt with public key. Ciphertext

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1 Part 2 Plaintext M Encrypt with public key E(M, K) Ciphertext Plaintext M D(E(M, K),K ) Decrypt with private key E(M, K) Public and private key related mathematically Public key can be published; private is a secret Very Hard to deduce private key from public key 2 1

2 !" " Plaintext Plaintext Encrypt with PRIVATE key Ciphertext Decrypt with PUBLIC key Notice that we reversed the role of the keys (and the math just works out) so only one party can send the message but anyone can check it s authenticity 3 # \$%& ' \$ Bob receives the message HELLO encrypted with Alice s private key Bob decrypts the msg using Alice s public key and sees the word HELLO Bob concludes that Alice sent the message to Bob. The protocol defines: The messages that go back and forth. The way the messages are manipulated. The conclusions that can be drawn from the dialog. Three ways to attack a protocol: 1. Break the key. 2. Lead one or both parties to the wrong conclusions. 3. Infect the implementation to thwart, spoof, or circumvent. Bob has drawn the wrong conclusion. 4 2

3 "()((*+, "*-(.)/' Algorithms let you encode the bits Protocols tell you how to decide if the bits are valid Looks pretty easy But in practice, it s pretty hard The Protocols Must Be Correctly Implemented They Achieve What They are Intended to Achieve They Can Not Be Bypassed Most failures come from NOT from attacks on the the algorithm BUT Attacks on the protocol Attacks on the (protocol) implementation Attacks on some other aspects of the target implementation thereby circumventing the protocol itself Can happen when a system is strongly, but not broadly secured. In other words, why work hard to break DES when it s so easy to break IE. 5 )0 1 2 * 6 3

4 7 8 4

5 ! "" For how to break keys, take a crypto class. For how to infect a target, take an OS class and read the literature 30 0" 0 * 0) What does this protocol achieve? Does this protocol need more assumptions than another one? Does this protocol do anything unnecessary that could be left out without weakening it? Does this protocol encrypt something that could be sent in the clear? 5

6 Three-way handshake for mutual authentication Client and server share secrets, e.g., login password Client Server SHK=CHK Client authenticates server here Session key exchanged ClientId, E(x, CHK) E(x + 1, SHK), E(y, SHK) E(y + 1, CHK) E(SK, SHK) Server authenticates client here Weaknesses? 11 \$% Needham-Schroeder Protocol Forms the basis of Kerberos & MS Auth Protocols Key Server 1:A,B,Na 2:{Na,B,Kab,{Kab,A}Kbs}Kas Alice 3:{Kab,A}Kbs 4:{Nb}Kab 5:{Nb-1}Kab Bob What s the weakness in the protocol? 6

7 \$%\$% * 02 Bob assumes that the key it is being given by Alice is fresh. With this assumption, Bob believes that Alice is in fact Alice, and will provide Alice with whatever Alice wants. No protection against replay This doesn t mean the protocol is broken, only that it makes certain assumptions. % Key Server 1:A,B,Na 2:{Na,B,Kab,{Kab,A}Kbs}Kas Alice 3:{Kab,A}Kbs 4:{Nb}Kab 5:{Nb-1}Kab Bob Sniffing Sam several days later... 3:{Kab,A}Kbs 4:{Nb}Kab 5:{Nb-1}Kab Bob 7

8 2 00 %4 Eyeball verification is not very effective Assumptions are often not explicit eg, the key is fresh An attacker will leverage these assumptions to break the protocol What s needed is a way to reason about authentication Stay tuned for part 3 *"5 Seminal paper published in 1991 SOSP by Burrows, Abadi and Needham BAN Logic Simple idea make explicit assumptions in an authentication protocol describe protocol by formal algebra make explicit initial states derive belief relationships through state transitions final state tells us what we can know 8

9 # \$%6 What does this protocol achieve? Does this protocol need more assumptions than another one? Does this protocol do anything unnecessary that could be left out without weakening it? Does this protocol encrypt something that could be sent in the clear ' % Freshness if you ve sent Joe a number (nonce) you ve never sent him before, and if you receive back from Joe something that depends on the number, then you ought to believe that Joe s message is fresher than yours Private key validity if you believe that you and Joe know K, then you ought to believe that anything you receive encrypted with K comes from Joe. 9

10 '% Public validity ifyoubelievethatkisjoe spublic key,thanyoushouldbelieve that any message you can decrypt with K comes from that any message you can decrypt with K comes from Joe. Shared secrets if you believe that only you and Joe know X, then you ought to believe that any encrypted message you receive containing X originally comes from Joe % \$ 5 Joe could reveal his secret to someone. A bad guy could deduce a public/private key. A nonce may not actually be so fresh or random. 10

11 )%% Describe the messages sent in a protocol 2: A->B: {A, Kab}Kbs A sends to B a message containing {A, Kab} encrypted with the private key Kbs, where Kab is a key suggested by some server S. Transform each message into a idealized message that can lead to beliefs 2: A->B: {A <-Kab-> B}Kbs A says to B that Kab is a good key for communicating between A and B according to S. Generally omit cleartext components since they can be forged and can not lead to new beliefs, Beliefs yield assertions about the system B believes that S once said that Kab is a good key for communication between A and B. &51 0 Parties only say what they believe. Present begins with the start of the protocol Past anything before the present If you believe something in the present, then you believe it for the run of the protocol. A belief held in the past (before the current run of the protocol) is not necessarily valid in the present. beware of old beliefs 11

12 %0' " An encrypted message is a logical state concealed by an encryption key (A <-K->B)Kbs K is a good key for use between A and B An encrypted message can not be understood by a principal who does not have the key )*" A,B,S denote principles Kab, Kas, Kbs denote shared (secret) keys Ka, Kb, Ks denote public keys 1/Ka, 1/Kb, 1/Ks denote matching private keys Na, Nb, Ns denote specific statements eg, nonces, which can be used to establish freshness Conjunction (,) is only propositional connective 12

13 \$ P = X P believes X P may act as though X were true P < X P sees X someone has sent P a message containing X. P may repeat X in other messages P ~ X P once said X P at one time sent a message containing the statement X. No one knows how long ago. P => X P has jurisdiction over X P is an authority on X and should be trusted on this matter. Used for delegation, eg, servers that generate keys. #(X) The formula X is fresh never been sent before this run of the protocol P <-K->Q P and Q may use the shared key K to communicate K will never be discovered by any principal except P or Q. K:->P P has K as a public key 1/K (matching private key) will never be discovered by any party but P P=X=Q The formula X is a secret known only to P and Q, and possibly to parties trusted by them Only P and Q may use X to prove their identities to one another (eg, a password) {X}K X encrypted with the key K <X>Y X combined with Y intent is that Y is a secret, eg passwd Y proves the origin of X. ' "' " How to derive beliefs from the origins of messages P = Q <- K -> P, P < {X}K P = Q ~ X SHARED KEYS: If P believes that K is a good key for P and Q, and P sees X encrypted with K, then P believes that Q once said X. P = K:->Q, P< {X}1/K P = Q ~ X PUBLIC KEYS:If P believes that K is Q s public key, and P sees X encrypted with K s private key, then P believes that Q once said X. P = Q =Y= P, P < <X>Y P = Q ~ X SHARED SECRETS: If P believes that Y is a secret shared between Q and P, and P see s <X>Y, then P believes that Q once said X. 13

14 75 Decryption of a message only says that it was uttered at some point, possibly in the past. does not say if the sender still believes it eg, could be result of a replay P = #(X), P = Q ~ X P = Q = X If P believes that X was said recently, and that Q said X, then P believes that Q believes X This is the only formula that promotes ~ to =. It reflects essence of challenge/response protocols. Fresh statement is challenge. Any message containing challenge is also fresh. 80 If P believes that Q has jurisdiction over X, then P trusts Q on the truth of X P = Q => X, P = Q = X P = X This rule gets used a lot when thinking about key servers. 14

15 \$( P believes a set of statements iff P believes each individual statement. P = X, P = Y P = (X,Y) P = (X,Y) P = X P = Q = (X,Y) P = X If a principal sees a formula, then he can see its components (provided keys are known). P < (X,Y) P < X P < <X>Y P < X P = Q<-K->P, P< {X}K P < X If a part of a formula is known to be fresh, the entire formula is fresh (freshness distributes) P = #(X) P = #(X,Y).0 90 Transform a message step into an idealized protocol step include only information that contributes to the beliefs of the recipient eliminate hints make explicit beliefs Example Protocol Step A->B : {A, Kab}Kbs intended to tell B, who knows Kbs, that Kab is a good key for communicating with A. Idealized Protocol Step A ->B : {A <-Kab-> B} Kbs Allows us to deduce B < {A <-Kab->B}Kbs If B = B<-Kbs->S and S=>Kab, then B = S ~ {A<-Kab->B} if B believes that Kbs is a good key for B and S, and S has jurisdiction over Kab, then B believes that S once said that Kab is a good key for use between A and B. is it still a good key?» who knows?? 15

16 / % Derive idealized protocol from original one Write assumptions about initial system state Attach logical formulas to the statements of the protocol Attach assertions to the statements of the protocol Apply postulates to assumptions and assertions to derive new beliefs first assertion contains assumptions last assertion contains the conclusions. Repeat until convinced. \$ - 5 Initial assumptions state what keys are shared between principles, which principles are trusted, and which statements are fresh Authentication then means A = A<-K->B B = A<-K->B Could also mean in addition A = B = A <-K->B B = A = A<-K->B 16

17 0 \$ Alice 1:A,B,Na Key Server 2:{Na,B,Kab,{Kab,A}Kbs}Kas 3:{Kab,A}Kbs 4:{Nb}Kab 5:{Nb-1}Kab Bob 1: A->S: A, B, Na 2: S->A: {Na, B, Kab}, {Kab, A}Kbs}}Kbs 3: A->B:{Kab, A}Kbs 4: B->A: {Nb}Kab 5: A->B: {Nb-1}Kab ) : A->S: A, B, Na 2: S->A: {Na, B, Kab}, {Kab, A}Kbs}}Kbs 3: A->B:{Kab, A}Kbs 4: B->A: {Nb}Kab 5: A->B: {Nb-1}Kab The actual protocol (messages sent) 1:!! Contributes nothing!! 2: S->A: { Na, (A<-Kab->B), #(A<-Kab->B), {A<-Kab->B}Kbs }Kas 3:A->B: {A<-Kab->B}Kbs 4:B->A: {Nb, (A<-Kab->B)}Kab 5:A->B: {Nb, (A<-Kab->B)}Kab The idealized protocol (statements made) 17

18 9"%:. \$% A = A<-Kas->S S = A <-Kas->S S = A <-Kab->B A = (S => A<-K-> B) A = (S => #(A<-K->B)) A = #(Na) S = #(A <-Kab-> B) B = B<-Kbs->S S = B <-Kbs->S B = (S => A<-K-> B) B = #(Nb) B = #(A<-K->B) Initial keys Key server Freshness This is that hidden initial assumption % 2: S->A: {Na, (A<-Kab->B), #(A<-Kab->B), {A<-Kab>B}Kbs}Kas First, A < {Na, (A<-Kab->B), #(A<-Kab->B), {A<-Kab>B}Kbs}Kas which A decrypts using Kas. Since A knows Na to be fresh, we can apply: P = #(X), P = Q ~ X P = Q = X (nonce verification) Leading to A = S = A <-Kab-> B A = S = #(A <-Kab -> B) (good key) (fresh key) Applying Gives P = Q => X, P = Q = X P = X A = A <-Kab-> B A = #(A <-Kab -> B) (jurisdiction) 18

19 % A < {A<-Kab->B}Kbs 3:A->B: {A<-Kab->B}Kbs We apply the message meaning postulate: P = Q <- K -> P, P < {X}K P = Q ~ X SHARED KEYS: If P believes that K is a good key for P and Q, and P sees X encrypted with K, then P believes that Q once said X. To obtain B = S ~ A <-Kab-> B In order to obtain B = A<-Kab->B, we need to rely on nonce verification (recall, only N.V. promotes ~ to =) " \$% #% Since we assumed initially that B = #(A<-K->B) We can promote B = S ~ A <-Kab-> B to B = A <-Kab->B using P = #(X), P = Q ~ X P = Q = X (nonce verification) 19

20 -"+ & 0 4:B->A: {Nb, (A<-Kab->B)}Kab Since A < {Nb, (A<-Kab->B)}Kab} and A = A <-Kab->B then A = B = (A <-Kab->B) (since B said it, B believes it) )5 % 5:A->B: {Nb, (A<-Kab->B)}Kab Allows B = A ~ {Nb, (A<-Kab->B)} Freshness distributes, so we can apply P = #(X), P = Q ~ X P = Q = X nonce verification to get B = A = A <-Kab->B 20

21 0 + A = A <-Kab->B B = A <-Kab->B A = B = A <-Kab> B B = A = A <-Kab> B which is the goal of an authentication protocol. Had we not made the freshness assumption, we would have been stuck and could not have gotten here. We need to make an awful lot of assumptions in designing authentication protocols. The assumptions are there, whether you state them or not. Only by stating them explicitly can we enter into a final acceptable state of mutual authentication. 21

22 0." Sometimes we care about knowing messages authentic, but don t care about privacy. If only sender and receiver knew the keys we would be done but that s often not the case A pair of keys for each pair of communicating parties? In public key (RSA) systems the encryption key is potentially known by everyone anyone could have sent us a confidential message by encrypting with our public key 43 ;" < Encryption can be expensive, e.g., RSA 1Kbps To speed up, let s sign just the checksum instead! Check that the encrypted bit is a signature of the checksum Problem: Easy to alter data without altering checksum Answer: Cryptographically strong checksums called message digests where it s computationally difficult to choose data with a given checksum But they still run much more quickly than encryption MD5 (128 bits) is the most common example 44 22

23 ' "!"'!=1/ Act as a cryptographic checksum or hash Typically small compared to message (MD5 128 bits) One-way : infeasible to find two messages with same digest Initial digest Transform Message (padded) 512 bits 512 bits 512 bits Transform Transform Message digest 45 %" % These techniques can be applied at different levels: IP packets (IPSEC) Web transfers or other transports (SSL/TLS, Secure HTTP) (PGP) Next time

24 % Privacy, integrity, and authenticity Cryptographic mechanisms are used to support these properties: private key, public key and digests 47 24

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