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## Key Exchange Protocols

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Next few lectures

- Today 1/17
- Brief cryptography background
- Key exchange protocols and properties
- Thursday 1/19
- Wireless security: 802.11i
- Choose your project partner
- Next Tues 1/24
- Password authentication protocols
- Next Thurs 1/26
- Contract-signing protocols
- Project presentation #1 2/2

Talk about protocols for a while before looking at more tools

Basic Concepts in Cryptography

- Encryption scheme:
- functions to encrypt, decrypt data
- key generation algorithm
- Secret key vs. public key
- Public key: publishing key does not reveal key-1
- Secret key: more efficient, generally key = key-1
- Hash function, MAC
- Map input to short hash; ideally, no collisions
- MAC (keyed hash) used for message integrity
- Signature scheme
- Functions to sign data, verify signature

Cryptosystem

- A cryptosystem consists of five parts
- A set P of plaintexts
- A set C of ciphertexts
- A set K of keys
- A pair of functions

encrypt: K P C

decrypt: K C P

such that for every key kK and plaintextpP

decrypt(k, encrypt(k, p)) = p

What is a “secure” cryptosystem?

- One idea
- If enemy intercepts ciphertext, cannot recover plaintext
- Issues in making this precise
- What else might your enemy know?
- The kind of encryption function you are using
- Some plaintext-ciphertext pairs from last year
- Some information about how you choose keys
- What do we mean by “cannot recover plaintext” ?
- Ciphertext contains no information about plaintext
- No efficient computation could make a reasonable guess
- Cannot use ciphertext for any nontrivial purpose

Public-key Cryptosystem

- Different keys to encrypt and decrypt
- encrypt(key, message)
- decrypt(key -1, encrypt(key, message)) = message
- Encryption key does not help decrypt
- Cannot compute m from encrypt(key, m) and key, unless you have key-1

key pair

Example: RSA

- Arithmetic modulo pq
- Generate secret primes p, q
- Generate secret numbers a, b with xab x mod pq
- Public encryption key n, a
- Encrypt(n, a, x) = xa mod n
- Private decryption key n, b
- Decrypt(n, b, y) = yb mod n
- Main properties
- This works
- Cannot compute b from n,a
- Apparently, need to factor n = pq

n

Cryptographic hash functions

- Length-reducing function h
- Map arbitrary strings to strings of fixed length
- One way (“preimage resistance”)
- Given y, hard to find x with h(x)=y
- Collision resistant
- Hard to find any distinct m, m’ with h(m)=h(m’)
- Also useful: 2nd preimage resistance
- Given x and y=h(x) hard to find x’x with h(x’)=h(x)
- Collision resistance 2nd preimage resistance

Iterated hash functions

- Repeat use of block cipher or custom function
- Pad input to some multiple of block length
- Iterate a length-reducing function f
- f : 22k -> 2k reduces bits by 2
- Repeat h0= some seed

hi+1 = f(hi, xi)

- Some final function g

completes calculation

x

Pad to x=x1x2 …xk

xi

f(xi-1)

f

g

Applications of one-way hash

- Password files (one way)
- Digital signatures (collision resistant)
- Sign hash of message instead of entire message
- Data integrity
- Compute and store hash of some data
- Check later by recomputing hash and comparing
- Keyed hash for message authentication
- MAC – Message Authentication Code

Digital Signatures

- Public-key encryption
- Alice publishes encryption key
- Anyone can send encrypted message
- Only Alice can decrypt messages with this key
- Digital signature scheme
- Alice publishes key for verifying signatures
- Anyone can check a message signed by Alice
- Only Alice can send signed messages

Properties of signatures

- Functions to sign and verify
- Sign(Key-1, message)
- Verify(Key, x, m) =
- Resists forgery
- Cannot compute Sign(Key-1, m) from m and Key
- Resists existential forgery:

given Key, cannot produce Sign(Key-1, m)

for any random or otherwise arbitrary m

- true if x = Sign(Key-1, m)
- false otherwise

Basic Concepts in Cryptography

- Encryption scheme:
- functions to encrypt, decrypt data
- key generation algorithm
- Secret key vs. public key
- Public key: publishing key does not reveal key-1
- Secret key: more efficient, generally key = key-1
- Hash function, MAC
- Map input to short hash; ideally, no collisions
- MAC (keyed hash) used for message integrity
- Signature scheme
- Functions to sign data, verify signature

Key Management

- Out of band
- Can set up some keys this way (Kerberos)
- Public-key infrastructure (PKI)
- Leverage small # of public signing keys
- Protocols for session keys
- Generate short-lived session key
- Avoid extended use of important secret
- Don’t use same key for encryption and signing
- Forward secrecy

Cryptography reduces many problems to key management

Key Distribution: Kerberos Idea

Shared symmetric key Kc

KeyCenter

{Kcs, {Kcs}Ks}Kc

Shared symmetric key Ks

Client

{Kcs}Ks { msg }Kcs

Server

Key Center generates session key Kcs and distributes using shared long-term keys

Public-Key Infrastructure

Known public signature verification key Ka

Certificate Authority

Certificate

Sign(Ka, Ks)

Ks

Sign(Ka, Ks), Sign(Ks, msg)

Client

Server

Server certificate can be verified by any client that has CA key Ka

Certificate authority is “off line”

Key Exchange

- Parties may have initial information
- Generate and agree on session key
- Authentication – know ID of other party
- Secrecy – key not known to any others
- Avoid replay attack
- Forward secrecy
- Avoid denial of service
- Identity protection – disclosure to others
- Other properties you can think of???

Diffie-Hellman Key Exchange

- Assume finite group G = S,
- Generator g so every xS is x = gn
- Example: integers modulo prime p
- Protocol

ga mod p

gb mod p

A

B

Alice, Bob share gab mod p not known to anyone else

Diffie-Hellman Key Exchange

ga mod p

gb mod p

A

B

- Authentication?
- Secrecy?
- Replay attack
- Forward secrecy?
- Denial of service?
- Identity protection?

m2

IKE subprotocol from IPSECA, (ga mod p)

B, (gb mod p)

, signB(m1,m2)

signA(m1,m2)

A

B

Result: A and B share secret gab mod p

Signatures provide authentication, as long as signature verification keys are known

IPSec: Network Layer Security

- Authentication Header (AH)
- Access control and authenticate data origins
- replay protection
- No confidentiality
- Encapsulated Secure Payload (ESP)
- Encryption and/or authentication
- Internet Key management (IKE)
- Determine and distribute secret keys
- Oakley + ISAKMP
- Algorithm independent
- Security policy database (SPD)
- discarded, or bypass

IKE: Many modes

- Main mode
- Authentication by pre-shared keys
- Auth with digital signatures
- Auth with public-key encryption
- Auth with revised public-key encryption
- Quick mode
- Compress number of messages
- Also four authentication options

Aug 2001 Position Statement

- In the several years since the standardization of the IPSEC protocols (ESP, AH, and ISAKMP/IKE), … several security problems…, most notably IKE.
- Formal and semi-formal analyses by Meadows, Schneier et al, and Simpson, have shown … security problems in IKE stem directly from its complexity.
- It seems … only a matter of time before serious *implementation* problems become apparent, again due to the complex nature of the protocol, and the complex implementation that must surely follow.
- The Security Area Directors have asked the IPSEC working group to come up with a replacement for IKE.

General Problem in Security

- Divide-and-conquer is fundamental
- Decompose system requirements into parts
- Develop independent software modules
- Combine modules to produce required system
- Common belief:
- Security properties do not compose

Difficult system development problem

Example protocol

Protocol P1

A B : {message}KB

A B : KA-1

- This satisfies basic requirements
- Message is transmitted under encryption
- Revealing secret key KA-1does not reveal message

Similar protocol

Protocol P2

B A : {message’}KA

B A : KB-1

- Transmits msg securely from B to A
- Message is transmitted under encryption
- Revealing secret key KB-1does not reveal message

Composition P1; P2

- Sequential composition of two protocols

A B : {message}KB

A B : KA-1

B A : {message’}KA

B B : KB-1

- Definitely not secure
- Eavesdropper learns both keys, decrypts messages

STS family

STS0H

STS0

cookie

distribute

certificates

open

responder

STSa

JFK0

STSaH

m=gx, n=gy

k=gxy

STS

STSH

JFK1

protect

identities

STSPH

JFK

STSP

symmetric

hash

RFK

Example

- Construct protocol with properties:
- Shared secret
- Authenticated
- Identity Protection
- DoS Protection
- Design requirements for IKE, JFK, IKEv2 (IPSec key exchange protocol)

Component 1

- Diffie-Hellman

A B: ga

B A: gb

- Shared secret (with someone)
- A deduces:

Knows(Y, gab) (Y = A) ۷ Knows(Y,b)

- Authenticated
- Identity Protection
- DoS Protection

Component 2

- Challenge Response:

A B: m, A

B A: n, sigB {m, n, A}

A B: sigA {m, n, B}

- Shared secret (with someone)
- Authenticated
- A deduces: Received (B, msg1) Λ Sent (B, msg2)
- Identity Protection
- DoS Protection

n := gb

Composition- ISO 9798-3 protocol:

A B: ga, A

B A: gb, sigB {ga, gb, A}

A B: sigA {ga, gb, B}

- Shared secret: gab
- Authenticated
- Identity Protection
- DoS Protection

Refinement

- Encrypt signatures:

A B: ga, A

B A: gb, EK {sigB {ga, gb, A}}

A B: EK {sigA {ga, gb, B}}

- Shared secret: gab
- Authenticated
- Identity Protection
- DoS Protection

Transformation

- Use cookie: JFK core protocol

A B: ga, A

B A: gb, hashKB {gb, ga}

A B: ga, gb, hashKB {gb, ga}

EK {sigA {ga, gb, B}}

B A: gb, EK {sigB {ga, gb, A}}

- Shared secret: gab
- Authenticated
- Identity Protection
- DoS Protection

- (Here B must store b in step 2, but we’ll fix this later…)

Cookie transformation

- Typical protocol
- Client sends request to server
- Server sets up connection, responds
- Client may complete session or not (DOS)
- Cookie version
- Client sends request to server
- Server sends hashed data back
- Send message #2 later after client confirms
- Client confirms by returning hashed data
- Need extra step to send postponed message

Cookie in JFK

- Protocol susceptible to DOS

A B: ga, A

B A: gb, EK {sigB {ga, gb, A}}

A B: EK {sigA {ga, gb, B}}

- Use cookie: JFK core protocol

A B: ga, A

B A: gb, hashKB {gb, ga}

A B: ga, gb, hashKB {gb, ga}, eh2

B A: gb, eh1

eh1

eh2

Efficiency: Reuse D-H key

- Costly to compute ga, gb, gab
- Solution
- Keep medium-term ga, gb (change ~10 min)
- Replace ga by pair ga, nonce
- JFKi, JFKr protocols (except cert or grpinfo, …)

A B: Na, ga, A

B A: Nb, gb, hashKB {Nb,Na, gb, ga}

A B: Na,Nb, ga, gb, hashKB {Nb,Na, gb, ga},

EK {sigA {Na,Nb, ga, gb, B}}

B A: gb, EK {sigB {Na,Nb, ga, gb, A}}

- Note: B does not need to store any short-term data in step 2

Conclusion

- Many protocol properties
- Authentication Secrecy
- Prevent replay Forward secrecy
- Denial of service Identity protection
- Systematic understanding is possible
- But be careful; easy to make mistakes
- State of the art:

need to analyze complete protocol

Block cipher modes (for DES, AES, …)

- ECB – Electronic Code Book mode
- Divide plaintext into blocks
- Encrypt each block independently, with same key
- CBC – Cipher Block Chaining
- XOR each block with encryption of previous block
- Use initialization vector IV for first block
- OFB – Output Feedback Mode
- Iterate encryption of IV to produce stream cipher
- CFB – Cipher Feedback Mode
- Output block yi = input xi encyrptK(yi-1)

Electronic Code Book (ECB)

Plain

Text

Plain

Text

Block Cipher

Block Cipher

Block Cipher

Block Cipher

Ciphe

rTex

tCip

herT

Problem: Identical blocks encrypted identically

No integrity check

Block Cipher

Cipher Block Chaining (CBC)Plain

Text

Plain

Text

IV

Block Cipher

Block Cipher

Ciphe

rTex

tCip

herT

Advantages: Identical blocks encrypted differently

Last ciphertext block depends on entire input

Comparison (for AES, by Bart Preneel)

Similar plaintext blocks produce similar ciphertext (see outline of head)

No apparent pattern

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