1. Chapter 9: Key Management
Session and Interchange Keys
Key Exchange
Cryptographic Key Infrastructure
Storing and Revoking Keys
Digital Signatures
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

2. Overview Key exchange Cryptographic key infrastructure Key storage
Session vs. interchange keys
Classical, public key methods
Cryptographic key infrastructure
Binding identity to a key
Certificates
Key storage
Key revocation
Digital signatures
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

3. Notation Generic form : X  Y : { Z } k message Z enciphered by key k
X  Y : { Z || W } kX,Y
X sends Y the message produced by concatenating Z and W enciphered by key kX,Y, which is shared by users X and Y
A  T : { Z } kA || { W } kA,T
A sends T a message consisting of the concatenation of Z enciphered using kA, A’s key, and W enciphered using kA,T, the key shared by A and T
r1, r2 nonces (nonrepeating random numbers)
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

4. Session, Interchange Keys
Alice wants to send a message m to Bob
Assume public key encryption
Alice generates a random cryptographic key ks and uses it to encipher m
To be used for this message only
Called a session key
She enciphers ks with Bob’s public key kB
kB enciphers all session keys Alice uses to communicate with Bob
Called an interchange key
Could also be a secret key shared by Alice and Bob
Alice sends { m } ks || { ks } kB
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

5. Benefits of Session Keys
Limits amount of traffic enciphered with single key
Standard practice, to decrease the amount of traffic an attacker can obtain
Compared to encrypting all messages with interchange key
Prevents some attacks not others – if the number of possible messages are few, then potential for successful discovery.
Example: Alice will send Bob message that is either “BUY” or “SELL”. Eve computes possible cipher texts { “BUY” } kB and { “SELL” } kB. Eve intercepts enciphered message, compares, and gets plaintext at once
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

6. Key Exchange Algorithms
Goal: Alice, Bob get shared key
Key cannot be sent in clear
Attacker can listen in
Key can be sent enciphered, or derived from exchanged data plus data not known to an eavesdropper
Alice, Bob may trust third party
All cryptosystems, protocols publicly known
Only secret data is the keys, ancillary information known only to Alice and Bob needed to derive keys
Anything transmitted is assumed known to attacker
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

7. Classical Key Exchange
Bootstrap problem: how do Alice, Bob begin?
Alice can’t send it to Bob in the clear!
Assume trusted third party, Cathy
Alice and Cathy share secret key kA
Bob and Cathy share secret key kB
Use this to exchange shared key ks
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

8. Simple Protocol { request for session key to Bob } kA,C Alice Cathy
7:15
Alice
Cathy
{ ks } kA,C || { ks } kB,C
Alice
Cathy
7:20
Okay, Alice. This is your session key ks
And tell Bob I got him a session key ks
{ ks } kB,C
7:25
Alice
Bob
Hey, Bob, Cathy wants me to forward you a session key ks with which we can talk
{ message } ks
7:30
Alice
Bob
Hey, Bob, here’s the message

9. Problems How does Bob know he is talking to Alice?
Replay attack: Eve records message from Alice to Bob, later replays it; Bob may think he’s talking to Alice, but he isn’t
Session key reuse: Eve replays message from Alice to Bob, so Bob re-uses session key
Protocols must provide authentication and defense against replay
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

10. Replay Attack { ks } kB,C 7:35 Eve Bob { message } ks 7:40 Eve Bob
He must be Alice again
Hey, Bob, Cathy wants me to forward you a session key ks with which we can talk
{ message } ks
7:40
Eve
Bob
He must be Alice again
Hey, Bob, here’s the message
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

11. Replay Attack (Cont’d)
Why is replaying (a valid) message a problem?
Think about this scenario
By SOD principle, Alice takes deposit and Bob credits the corresponding account
Alice sends Bob a message “Eve just deposited $50k”
Eve replays it…
Protocols must defend against such replay attack
Adds considerable complexity
Basic idea is “challenge-response”
Eve: “Hey, bob, this is Alice”
Bob: “Hmm, then you must have Alice’s key”
Bob: (Bob generates r1 ) “Now encrypt this!”
Eve: ……

12. Needham-Schroeder Assume Bob and Alice trust Cathy. r1, r2 are random
Needham-Schroeder Assume Bob and Alice trust Cathy. r1, r2 are random. r1, not used before. Nonce.
Alice || Bob || r1
Alice
Cathy
Hey, Cathy, I need to talk to Bob.
Alice
Cathy
{Alice || Bob || r1|| ks ||{Alice|| ks} kB,C } kA,C
Hey, Alice, this is Cathy
And tell Bob I got him a session key ks
this is your key ks
Alice
Bob
{ Alice || ks } kB,C
Hey, Bob, this is Alice. Cathy wants me to forward you a session key ks with which we can talk
Alice
Bob
{ r2 } ks
You’re Alice? So you must have ks. Prove it!
Alice
Bob
{ r2 – 1 } ks
Here’s the proof that I have ks

13. Alice’s Point of View Second message Third message
Encrypted with a key kA,C that only Alice and Cathy know, so only Cathy can create the message
Containing a challenge r1, so the message is not a replay
Third message
Encrypted with a key kB,C that only Bob and Cathy know, so only Bob can read it and extract the session key
{ Alice || Bob || r1|| ks||{ Alice || ks } kB,C } kA,C
Alice
Cathy
Alice
Bob
{Alice|| ks} kB,C

14. Bob’s Point of View Third message Fourth and Fifth messages
Encrypted with a key that only Bob and Cathy know, so the message can only be created by Cathy
The name Alice is in the message, so Cathy says the session key is to be used while talking to Alice
Fourth and Fifth messages
Determine if it is a replay from someone other than Alice
If not, Alice will respond correctly in fifth message
If so, Eve can’t decipher r2 and so can’t respond, or responds incorrectly
Alice
Bob
{ Alice || ks } kB,C
Alice
Bob
{ r2 } ks
Alice
Bob
{ r2 – 1 } ks

15. Denning-Sacco Modification
What if after some time, Eve obtains the session key ks?
More likely to be compromised than kA,C or kBB,C
Eve replays the third message
{ Alice || ks } kB,C
Eve
Bob
Hey, Bob, this is Alice (replay)
{ r2 } ks
Eve
Bob
You’re Alice? So you must have ks. Prove it!
{ r2 – 1 } ks
Eve
Bob
Here’s the proof that I have ks

16. Solution In protocol above, Eve impersonates Alice
Problem: replay in third step
First in previous slide
Solution: use time stamp T to detect replay
Weakness: if clocks not synchronized, may either reject valid messages or accept replays
Parties with either slow or fast clocks vulnerable to replay
Resetting clock does not eliminate vulnerability
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

17. Denning-Sacco Modification (Cont’d)
Solution: use time stamp T to detect replay
Weakness: clocks must be synchronized
Alice || Bob || r1
Alice
Cathy
{ Alice || Bob || r1 || ks || { Alice || T || ks } kB,C } kA,C
7:35
Alice
Cathy
{ Alice || T || ks } kB,C
7:36
Alice
Bob
{ r2 } ks
Alice
Bob
{ r2 – 1 } ks
Alice
Bob

18. Kerberose Chapters 13 and 14 from Kaufmann, Perlman and Speciner
More detailed than the textbook
(With permission of Prof Duminda)

19. What Kerberos Provides
A centralized authentication service
Authenticate users to services
Authenticate services to users
Servers are relieved of the burden of maintaining authentication information
Supports inter-server authentication

20. Properties of Kerberos
Rely exclusively on conventional encryption.
Public key based Kerberos has been considered.
Stateless: Kerberos server doesn’t need to maintain the state information about any entities being authenticated.

21. Kerberos Design Requirements
Secure
A network eavesdropper should not be able to obtain the necessary info to impersonate a user.
Reliable
Kerberos should be highly available and should employ a distributed server architecture.
Transparent
The user shouldn’t be aware that authentication is taking place.
Scalable
The system should be capable of supporting large numbers of clients and servers.

22. Main Components and Interaction ModeAS
TGS
Kerberos
1. Request ticket to talk to Bob
Client: Alice
2. Invents session key Kab,
encrypts with Alice’s master key = EKa(Kab),
encrypts with Bob’s master key = EKb(Kab),
Sends over to Alice
3. Submits EKb(Kab),
Main Component: Key Distribution Center
Shares a master key with each principle
Generates session keys,
encrypts using a remote recipient’s key = Ticket
4. Checks and start using Kab
Server: Bob

23. The Kerberos Protocol
Outline of the introduction to the Kerberos protocol
A simple authentication protocol
A more secure authentication protocol
Kerberos Version 4 authentication protocol

24. A Simple Authentication Protocol
Use an authentication server (AS)
Basic idea: use a ticket to authenticate a user to a server.
Protocol
CAS: IDC || PWC || IDV
AS C: Ticketv = EKV[IDC || IDV]
C V: IDC || Ticketv

25. A Simple Authentication Protocol (Cont’d)
Advantages
A centralized authentication service
Weaknesses
A user needs to enter a password for every different service.
Password is transmitted in plaintext.
Subject to replay attack

26. A More Secure Authentication Protocol
A new server: ticket-granting server (TGS)
The protocol
Once per user logon session
CAS: IDC || IDtgs
AS C: EKC[Tickettgs]
Once per type of service
C TGS: IDC || IDV || Tickettgs
TGS C: TicketV
Once per service session
C V: IDC || TicketV
Tickettgs = EKtgs[IDC || IDtgs || TS1 || lifetime1]
TicketV = EKV[IDC || IDV || TS2 || lifetime2]
TS=time stamp

27. A More Secure Authentication Protocol (Cont’d)
Ticket-granting ticket (TGT): Tickettgs .
Service-granting ticket: TicketV.
Weaknesses
Replay attack: No authentication of the valid ownership of the tickets.
No authentication of the servers.
What are the components in the tickets?
Why do we have them?

28. Kerberos Version 4 Protocol
Basic idea to address the previous weaknesses
Session key
Authentication of the valid ownership of the tickets
Provide authentication of servers.
Assume Authentication Server knows
Each client’s master secret key, which is derived from each client’s password

29. Kerberos Version 4 Protocol (Cont’d)
Authentication Service Exchange: to obtain ticket-granting ticket (TGT)
CAS: IDC || IDtgs || TS1
AS C: EKC[KC,tgs || IDtgs || TS2 || Lifetime2 || Tickettgs]
Tickettgs = EKtgs[KC,tgs || IDC || IDtgs || TS2 || Lifetime2]
KC,tgs is the session key between C and TGS!

30. Kerberos Version 4 Protocol (Cont’d)
Ticket-Granting Service Exchange:
to obtain service-granting ticket (SGT)
C TGS: IDV || Tickettgs || Authenticatorc
TGS C: EKC,tgs[KC,V || IDV || TS4 ||Lifetime4|| TicketV]
Tickettgs = EKtgs[KC,tgs || IDC || IDtgs || TS2 || Lifetime2]
TicketV = EKV[KC,V || IDC || IDV || TS4 || Lifetime4]
Authenticatorc = EKC,tgs[IDC || TS3]

31. Kerberos Version 4 Protocol (Cont’d)
Client/Server Authentication Exchange: to obtain service
CV: TicketV || Authenticatorc
VC: EKC,V[TS5 + 1]
TicketV = EKV[KC,V || IDC || ADC || IDV || TS4 || Lifetime4]
Authenticatorc = EKC,V[IDC || ADC || TS5]

32. The Whole Picture Keberos Server Authentication Server (AS)
1. Request TGT
2. TGT + session key
3. Request SGT
Ticket-Granting
Server (TGS)
4. Ticket + session key
5. Request service
6. Server authenticator
Server

33. Kerberos Deployment
The Kerberos server must have the user ID and hashed password of all participating users in its database.
The Kerberos server must share a secret key with each server.
Kerberi are physically secured
Kerberos libraries are distributed on all nodes with users, applications, and other Kerberos-controlled resources

34. Replicated Kerberos
Multiple replica of Kerberos - availability and performance
Keeping Kerberos databases consistent
Single master Kerberos as the point of direct update to principals’ database entries
Updated database is downloaded from the master to all replica Kerberos
Periodic download or on-demand

35. Kerberos Realms and Multiple Kerberi
A full-service Kerberos environment consisting of a Kerberos server, a number of clients, and a number of application servers
Inter-realm authentication
The Kerberos server in each interoperating realm shares a secret key with the server in the other realm. The two Kerberos servers are registered with each other.

36. Inter-realm AuthenticationAS
TGS
Kerberos
1. Request ticket for local TGS
client
2. Ticket for local TGS
3. Request ticket for remote TGS
4. Ticket for remote TGS
7. Ticket for remote server
8. Remote server authenticator
5. Request ticket for remote server
6. Ticket for remote server AS
TGS
Kerberos
server
Realm B

37. Race Condition in Multiple Kerberi
What happens if some key is updated?
An existing ticket may become obsolete since it was encrypted with old keys!
Alice’s TGT – TGS has updated its master key Ktgs !
Alice’s ticket to Bob – Bob has updated his DES key KBob !
TGS sends Alice her TGT – Alice has updated her password KAlice !
In Kerberos, TGS and all servers maintain several versions of keys
What about Alice? Does she maintain several versions of her keys?
Small time window that Alice could not login by using her recently updated password

38. Kerberos Slides Following Class Text Introduction to Computer Security
November 1, 2004
Introduction to Computer Security
©2004 Matt Bishop

39. Kerberos Authentication system Ticket Authenticator
Based on Needham-Schroeder with Denning-Sacco modification
Central server plays role of trusted third party (“Cathy”)
Ticket
Issuer vouches for identity of requester of service
Authenticator
Identifies sender
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

40. Idea User u authenticates to Kerberos server
Obtains ticket Tu,TGS for ticket granting service (TGS)
User u wants to use service s:
User sends authenticator Au, ticket Tu,TGS to TGS asking for ticket for service
TGS sends ticket Tu,s to user
User sends Au, Tu,s to server as request to use s
Details follow
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

41. Tu,s = s || { u || u’s address || valid time || ku,s } ks
Ticket
Credential saying issuer has identified ticket requester
Example ticket issued to user u for service s
Tu,s = s || { u || u’s address || valid time || ku,s } ks
where:
ku,s is session key for user and service
Valid time is interval for which ticket valid
u’s address may be IP address or something else
Note: more fields, but not relevant here
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

42. Au,s = { u || generation time || kt } ku,s
Authenticator
Credential containing identity of sender of ticket
Used to confirm sender is entity to which ticket was issued
Example: authenticator user u generates for service s
Au,s = { u || generation time || kt } ku,s
where:
kt is alternate session key
Generation time is when authenticator generated
Note: more fields, not relevant here
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

43. Protocol user || TGS user Cathy { ku,TGS } ku || Tu,TGS Cathy user
service || Au,TGS || Tu,TGS
user
TGS
user || { ku,s } ku,TGS || Tu,s
user
TGS
Au,s || Tu,s
user
service
{ t + 1 } ku,s
user
service
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

44. Analysis First two steps get user ticket to use TGS
User u can obtain session key only if u knows key shared with Cathy
Next four steps show how u gets and uses ticket for service s
Service s validates request by checking sender (using Au,s) is same as entity ticket issued to
Step 6 optional; used when u requests confirmation
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

45. Problems Relies on synchronized clocks Tickets have some fixed fields
If not synchronized and old tickets, authenticators not cached, replay is possible
Tickets have some fixed fields
Dictionary attacks possible
Kerberos 4 session keys weak (had much less than 56 bits of randomness); researchers at Purdue found them from tickets in minutes
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

46. Public Key Exchange Here interchange keys known Simple protocol
eA, eB Alice and Bob’s public keys known to all
dA, dB Alice and Bob’s private keys known only to owner
Simple protocol
ks is desired session key
{ ks } eB
Alice
Bob
November 1, 2004
Introduction to Computer Security
©2004 Matt Bishop

47. Problem and Solution Vulnerable to forgery or replay
Because eB known to anyone, Bob has no assurance that Alice sent message
Simple fix uses Alice’s private key
ks is desired session key
{ { ks } dA } eB
Alice
Bob
November 1, 2004
Introduction to Computer Security
©2004 Matt Bishop

48. Notes Can include message enciphered with ks
Assumes Bob has Alice’s public key, and vice versa
If not, each must get it from public server
If keys not bound to identity of owner, attacker Eve can launch a man-in-the-middle attack (next slide; Cathy is public server providing public keys)
Solution to this (binding identity to keys) discussed later as public key infrastructure (PKI)
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

49. Man-in-the-Middle Attack
send Bob’s public key
Eve intercepts request
Alice
Cathy
send Bob’s public key
Eve
Cathy eB
Eve
Cathy eE
Alice
Eve
{ ks } eE
Eve intercepts message
Alice
Bob
{ ks } eB
Eve
Bob
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

50. Cryptographic Key Infrastructure
Goal: bind identity to key
Classical: not possible as all keys are shared
Use protocols to agree on a shared key (see earlier)
Public key: bind identity to public key
Crucial as people will use key to communicate with principal whose identity is bound to key
Erroneous binding means no secrecy between principals
Assume principal identified by an acceptable name
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

51. Certificates Binds an identity to a cryptographic key
Create token (message) containing
Identity of principal (here, Alice)
Corresponding public key
Timestamp (when issued)
Other information (perhaps identity of signer)
signed by trusted authority (here, Cathy)
Alice Certificate--
CA = { eA || Alice || T } dC
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

52. Use Bob wants to communicate with Alice
Bob gets Alice’s certificate
If he knows Cathy’s public key, he can decipher the certificate
When was certificate issued?
Is the principal Alice?
Now Bob has Alice’s public key
Problem: Bob needs Cathy’s public key to validate certificate
Problem pushed “up” a level
Two approaches: Merkle’s tree, signature chains
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

53. Certificate Signature Chains
Create certificate
Generate hash of certificate
Encipher hash with issuer’s private key
Validate
Obtain issuer’s public key
Decipher enciphered hash
Recompute hash from certificate and compare
Problem: getting issuer’s public key
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

54. X.509 Chains Some certificate components in X.509v3: Version
Serial number
Signature algorithm identifier: hash algorithm
Issuer’s name; uniquely identifies issuer
Interval of validity
Subject’s name; uniquely identifies subject
Subject’s public key
Signature: enciphered hash
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

55. X.509 Certificate Validation
Obtain issuer’s public key
The one for the particular signature algorithm
Decipher signature
Gives hash of certificate
Recompute hash from certificate and compare
If they differ, there’s a problem
Check interval of validity
This confirms that certificate is current
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

56. Issuers Certification Authority (CA): entity that issues certificates
Multiple issuers pose validation problem
Alice’s CA is Cathy; Bob’s CA is Don; how can Alice validate Bob’s certificate?
Have Cathy and Don cross-certify
Each issues certificate for the other
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

57. Validation and Cross-Certifying
X<<Y>> X is CA that issued certificate for subject Y
Certificates:
Cathy<<Alice>>
Dan<<Bob>
Cathy<<Dan>>
Dan<<Cathy>>
Alice validates Bob’s certificate
Alice obtains Cathy<<Dan>>
Alice uses (known) public key of Cathy to validate Cathy<<Dan>>
Alice uses Cathy<<Dan>> to validate Dan<<Bob>>
Long signatures are possible – each certificate must be validated by the one before it
Cathy and Dan are cross certified
Each has issued certificate for other
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

58. PGP Chains OpenPGP certificates structured into packets
Packet is a record with a tag describing its purpose
One public key packet
Zero or more signature packets
Public key packet:
Version (3 or 4; 3 compatible with all versions of PGP, 4 not compatible with older versions of PGP)
Creation time
Validity period (not present in version 3)
Public key algorithm, associated parameters
Public key
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

59. OpenPGP Signature Packet
Version 3 signature packet
Version (3)
Signature type (level of trust)
Creation time (when next fields hashed)
Signer’s key identifier (identifies key to encipher hash)
Public key algorithm (used to encipher hash)
Hash algorithm
Part of signed hash (used for quick check)
Signature (enciphered hash)
Version 4 packet more complex
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

60. Signing Single certificate may have multiple signatures
Notion of “trust” embedded in each signature
Range from “untrusted” to “ultimate trust”
Signer defines meaning of trust level (no standards!)
All version 4 keys signed by subject
Called “self-signing”
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

61. Validating Certificates
Arrows show signatures
Self signatures not shown
Alice wants to communicate with Bob
Alice needs to validate Bob’s OpenPGP cert
Does not know Fred, Giselle, or Ellen
Alice gets Giselle’s cert
Knows Henry slightly, but his signature is at “casual” level of trust
Alice gets Ellen’s cert
Knows Jack, so uses his cert to validate Ellen’s, then hers to validate Bob’s
Jack
Henry
Ellen
Irene
Giselle
Fred
Bob
November 1, 2004
Introduction to Computer Security
©2004 Matt Bishop

62. Storing Keys
Multi-user or networked systems: attackers may defeat access control mechanisms
Encipher file containing key
Attacker can monitor keystrokes to decipher files
Key will be resident in memory that attacker may be able to read
Use physical devices like “smart card”
Key never enters system
Card can be stolen, so have 2 devices combine bits to make single key
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

63. Key Revocation Certificates invalidated before expiration Problems
Usually due to compromised key
May be due to change in circumstance (e.g., someone leaving company)
Problems
Entity revoking certificate authorized to do so
Revocation information circulates to everyone fast enough
Network delays, infrastructure problems may delay information
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

64. CRLs Certificate revocation list lists certificates that are revoked
X.509: only certificate issuer can revoke certificate
Added to CRL
PGP: signers can revoke signatures; owners can revoke certificates, or allow others to do so
Revocation message placed in PGP packet and signed
Flag marks it as revocation message
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

65. Digital Signature
Construct that authenticated origin, contents of message in a manner provable to a disinterested third party (“judge”)
Sender cannot deny having sent message (service is “nonrepudiation”)
Limited to technical proofs
Inability to deny one’s cryptographic key was used to sign
One could claim the cryptographic key was stolen or compromised
Legal proofs, etc., probably required; not dealt with here
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

66. This is not a digital signature
Common Error
Classical: Alice, Bob share key k
Alice sends m || { m } k to Bob
This is a digital signature
WRONG
This is not a digital signature
Why? Third party cannot determine whether Alice or Bob generated message – Bob could have sent it to himself!
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

67. Classical Digital Signatures
Require trusted third party
Alice, Bob each share keys with trusted party Cathy
To resolve dispute, judge gets { m } kAlice, { m } kBob, and has Cathy decipher them; if messages matched, contract was signed
{ m }kAlice
Alice
Bob
{ m }kAlice
Cathy
Bob
{ m }kBob
Cathy
Bob
November 1, 2004
Introduction to Computer Security
©2004 Matt Bishop

68. Public Key Digital Signatures
Alice’s keys are dAlice, eAlice
Alice sends Bob
m || { m } dAlice
In case of dispute, judge computes
{ { m } dAlice } eAlice
and if it is m, Alice signed message
She’s the only one who knows dAlice!
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

69. RSA Digital Signatures
Use private key to encipher message
Protocol for use is critical
Key points:
Never sign random documents, and when signing, always sign hash and never document
Mathematical properties can be turned against signer
Sign message first, then encipher
Changing public keys causes forgery
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

70. Attack #1 Example: Alice, Bob communicating
nA = 95, eA = 59, dA = 11
nB = 77, eB = 53, dB = 17
26 contracts, numbered 00 to 25
Alice has Bob sign 05 and 17:
c = mdB mod nB = 0517 mod 77 = 3
c = mdB mod nB = 1717 mod 77 = 19
Alice computes 0517 mod 77 = 08; corresponding signature is 0319 mod 77 = 57; claims Bob signed 08
Judge computes ceB mod nB = 5753 mod 77 = 08
Signature validated; Bob is toast
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

71. Attack #2: Bob’s Revenge
Bob, Alice agree to sign contract 06
Alice enciphers, then signs:
(meB mod 77)dA mod nA = (0653 mod 77)11 mod 95 = 63
Bob now changes his public key
Computes r such that 13r mod 77 = 6; say, r = 59
Computes reB mod (nB) = 5953 mod 60 = 7
Replace public key eB with 7, private key dB = 43
Bob claims contract was 13. Judge computes:
(6359 mod 95)43 mod 77 = 13
Verified; now Alice is toast
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

72. Key Points Key management critical to effective use of cryptosystems
Different levels of keys (session vs. interchange)
Keys need infrastructure to identify holders, allow revoking
Key escrowing complicates infrastructure
Digital signatures provide integrity of origin and content
Much easier with public key cryptosystems than with classical cryptosystems
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004

73. Exercise
5: Needham and Schroeder suggest the following variant of their protocol:
Alice → Bob : Alice
Bob → Alice : { Alice, rand3 } kBob
Alice → Cathy : { Alice, Bob, rand1, { Alice, rand3 } kBob }
Cathy → Alice : { Alice, Bob, rand1, ksession, {Alice, rand3, ksession} kBob } kAlice
Alice → Bob : { Alice, rand3, ksession } kBob
Bob → Alice : { rand2 } ksession
Alice → Bob : { rand2 – 1 }ksession
Show that this protocol solves the problem of replay as a result of stolen session keys.
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Approach: assume that attacker knows the session key ksession , and has intercepted the message at step 5
Two situations –
Attacker does not send an initial message to Bob (steps 1 and 2)
Attacker does.
Introduction to Computer Security
©2004 Matt Bishop
November 1, 2004