Protocols Chapter 2 Protocol: A series of steps, involving two or more parties, designed to accomplish a task. • All parties involved must know the protocol • All parties must agree to follow it • Must be unambiguous • Must be complete
Dec 31, 2015
Protocols Chapter 2
Protocol:A series of steps, involving two or more parties,
designed to accomplish a task.• All parties involved must know the protocol
• All parties must agree to follow it
• Must be unambiguous
• Must be complete
The Playersdramatis personae
Alice First participant
Bob Second
Carol Third
Eve Eavesdropper
Mallory Malicious attacker
Trent Trusted arbitrator
Peggy Prover
Victor Verifier
Types of Protocols
Arbitrated ProtocolsIntermediary trusted by all parties
Lawyer is involved
Adjudicated ProtocolsIn case of a dispute a third party becomes
involved
Judge is involved
Self-Enforcing ProtocolsThe protocol itself guarantees fairness
No third party is involved
Attacks against Protocols
Passive attackPassive eavesdropper e.g. network sniffing
Difficult to detect
Active attackAlter protocol
Pretend to be someone else
CheatersNot following the protocol
Liars
Protocol Building Blocks
Symmetric key cryptography
One-Way Hash functions
Public-key cryptography
Digital signatures
Random sequence generators
Symmetric Key Cryptography
Secure communications
Secure storage
Computationally efficient
Depends on a shared secret
Symmetric Key Cryptography
Alice and Bob want to communicate securely.1. Alice & Bob agree on a crypto algorithm
2. Alice & Bob agree on a key
3. Alice encrypts message with the key
4. Alice sends ciphertext to Bob
5. Bob decrypts with the key and reads the message
Symmetric Key Cryptography
Alice Bob
Key: KMessage: MCiphertext: C = E
K(M)
Key: KCiphertext: CMessage: M = D
K(C) = D
K(E
K(M))
C
Symmetric Key CryptographyAttacks
Passive attack:
Eve can only try a ciphertext only attack
Eve can attempt to determine the key during the key exchange
Active attack:
Intercept Alice's message and substitute his own
Break communication channel
Cheaters:
Alice can give the key to Eve, so Eve can read Bob's message
One-Way Hash functions
One-way functionsNo inverse (known to exist)
Hash functionNo known collisions
Variable length inputs
Fixed length outputs
Message Authentication Code
Uses a secret key
One-way hash of both the pre-image and the secret keyK = symmetric key
M = Message
MAC = H(EncK(M))
Only those who have the key K can calculate H(EncK(M).
Public-Key Cryptography
Public key and private key
Each player has their own key pair
Computationally intensive
Vulnerable to chosen-plaintext attacks
Very difficult to deduce the private key from the public key
Public-Key Cryptography
Let:
Pr = Alice's private key
Pu = Alice's public key
(Pr, Pu) is the key pair, and must go together.
M = Plaintext from Bob
Ciphertext C = EPu
(M) is calculated by Bob with Alice's public
key.
Only Alice has access to her private key. Thus only she can calculate
the plaintext M = DPr
(EPu
(M)).
Public-Key Cryptography
Alice Bob
Message: MCiphertext: C = E
BPu(M)
Key pair: BPu, BPrCiphertext: CMessage: M = D
BPr(C) = D
BPr(E
BPu(M))
C
BPu
Digital Signatures
Authentic
Not forgeable
Not reusable
Unalterable
Cannot be repudiated
Digital Signatures with Symmetric Crypto
Alice wants to sign a digital message and send it to Bob with Trent's help.
1. Alice/Trent key, KA. Bob/Trent key, K
B.
2. Alice encrypts her message to Bob with KA and sends it to Trent.
3. Trent decrypts the message with KA.
4. Trent encrypts Alice's message to Bob along with a message that it is from Alice.
5. Trent sends the encrypted bundle to Bob.
6. Bob decrypts the bundle with KB. Bob can read Alice's message along with
Trent's certification.
Digital SignaturesPublic-Key Crypto
Alice wants to sign a digital message and send it to Bob without Trent's help
1. Alice's public key, KA-pu
, private key, KA-pr
..
2. Alice encrypts her document with her private key, KA-pr
.
3. Alice sends the signed document to Bob.
4. Bob decrypts the document with KA-pu
, thereby verifying the signature.
Digital Signatures Public-Key Crypto & Hash Functions
Alice wants to sign a large digital message and send it to Bob without the public-key's compute hit.
1. Alice's public key, KA-pu
, private key, KA-pr
..
2. Alice produces a one-way hash of her document.
3. Alice encrypts the hash with her private key, KA-pr
.
4. Alice sends the document and the encrypted hash to Bob.
5. Bob decrypts the hash with KA-pu
, calculates the hash of the
document himself and compares them, thereby verifying the signature.
Digital SignaturesVulnerabilities
Alice can cheat.She can sign a document.
She can claim that her private key was compromised.
Time stamps help.
Escrow agents are expensive.
Tamper resistant modules.
Random Sequence Generators
Pseudo-random generatorLooks random:
Passes all of the statistical tests.
Cryptographically Secure
Cryptographically SecureRandom Sequence Generators
It is unpredictable.Computationally infeasible to predict what the
next random bit will be given complete knowledge of the algorithm and all previous bits.
It cannot be reliably reproduced.
Basic Protocols Chapter 3
Protocols• Key Exchange
• Authentication and key exchange
• Secret splitting
• Secret sharing
Key Exchange with Symmetric Crypto
1. Alice/Trent key, KA. Bob/Trent key, K
B.
2. Alice calls Trent and requests a session key to communicate with Bob.
3. Trent generates a random session key.
4. Trent encrypts the session key with KA and encrypts another copy with K
B.
5. Trent sends both copies to Alice.
6. Alice decrypts her copy with KA and sends Bob his copy.
7. Bob decrypts his copy with KB.
8. Alice and Bob can communicate securely with the shared session key.
Key Exchangewith Public-Key Crypto
1. Bob sends Alice his public key, Pu.
2. Alice generates a random session key, K.
3. Alice encrypts K using Bob's public key, EPu
(K).
4. Alice sends EPu
(K) to Bob.
5. Bob decrypts Alice's message using his private key,
DPr
(EPu
(K)) = K.
6. Alice and Bob encrypt their communications using the same session key, K.
Authentication
• Passwords and pass phrases• Dictionary attacks
• Hashed passwords subject to dictionary attacks
• Salted passwords
• Public key encryption• Requires key pairs
• Key management
AuthenticationPublic Key Encryption
1. Host sends Alice a random string.
2. Alice encrypts with her private key and sends it back to the host along with her name.
3. Host looks up Alice's public key and decrypts the messsage.
4. If the message matches the string the host sent Alice then the host permits access to Alice.
Key Exchange with Authentication
• All involve a trust intermediary –Trent
• All subject to man in the middle attack
• Want to be sure you know who you are talking to.
Kerberos
Guarding the Gates of Hell.No one leaves.
Authentication & Key ExchangeKerberos
• Maintained by MIT
• Up to version 5-1.10.3 - Release 1.9.4
• Strong authentication
• Uses symmetric key encryption
• Uses a trusted intermediary
Authentication & Key ExchangeKerberos
Alice Bob
TrentA = Alice's IDB = Bob's IDK
AT = Alice/Trent symmetric key
KBT
= Bob/Trent symmetric key
KAT
KBT
Alice sends message to Trent
Alice Bob
TrentA = Alice's IDB = Bob's ID
A, B
Trent responds to Alicewith info for Alice and Bob
Alice Bob
TrentA = Alice's IDB = Bob's ID
Trent generates:TS = Time stampL = Lifetime for the keyK
AB = Session key
M1 = (TS, L, K
AB, A)
M2 = (TS, L, K
AB, B)
EKAT
(M2)
EKBT
(M1)
Alice gets message from Trent
Alice Bob
TrentA = Alice's IDB = Bob's ID
Trent generates:TS = Time stampL = Lifetime for the keyK
AB = Session key
M1 = (TS, L, K
AB, A)
M2 = (TS, L, K
AB, B)
EKAT
(M2)
EKBT
(M1)
Alice calc's DKAT
(EKAT
(M2)). She now knows
TS, L, KAB
, B and EKBT
(M1) which she cannot decrypt.
Alice also calc's EKAB
(A, TS).
Alice sends message to Bob
Alice Bob
TrentA = Alice's IDB = Bob's ID
Trent generates:TS = Time stampL = Lifetime for the keyK
AB = Session key
M1 = (TS, L, K
AB, A)
M2 = (TS, L, K
AB, B)
EKAT
(M2)
EKBT
(M1)
Alice calc's DKAT
(EKAT
(M2)). She now knows
TS, L, KAB
, B and EKBT
(M1) which she cannot decrypt.
Alice also calc's EKAB
(A, TS).
EKAB
(A, TS), EKBT
(M1)
Bob calc's DKBT
(EKBT
(M1)). He now
knows TS, L, KAB
, A. He can also
calc DKAB
(EKAB
(A, TS)).
Bob gets message from Alice and replies to Alice
Alice Bob
TrentA = Alice's IDB = Bob's ID
Trent generates:TS = Time stampL = Lifetime for the keyK
AB = Session key
M1 = (TS, L, K
AB, A)
M2 = (TS, L, K
AB, B)
EKAT
(M2)
EKBT
(M1)
Alice calc's DKAT
(EKAT
(M2)). She now knows
TS, L, KAB
, B and EKBT
(M1) which she cannot decrypt.
Alice also calc's EKAB
(A, TS).
EKAB
(A, TS), EKBT
(M1)
Bob calc's DKBT
(EKBT
(M1)). He now
knows TS, L, KAB
, A. He can also
calc DKAB
(EKAB
(A, TS)).
EKAB
(A, TS + 1)
Secret Splitting Protocol
Secret splitting• Split a message up into n-pieces
• Give each to a person
• The message can be read only if all n-people put their pieces together
Secret Splitting Protocol
1. Trent wants send a message to Alice and Bob that they can only read together.
2. Trent generates a random bit string R, the same length as the message, M.
3. Trent XOR's M with R to generate S.
M R = S
4. Trent gives R to Alice and S to Bob.
5. Alice and Bob XOR their pieces together to reconstruct the message:
R S = R M R = M
Secret Splitting Protocol n – parties
1. Trent generates random bit strings R1, ... R
n-1 the same length
as the message, M.
2. Trent XOR's M with R1, ... R
n-1 to generate R
n.
M + R1+ ... + R
n-1 = R
n
3. Trent gives Ri to Alice
i.
4. The Alicei's XOR their pieces together to reconstruct the
message:
R1+ ... + R
n = M
Secret Sharing Protocol n – parties
Goal: To share a message among 5 people so that any 3 can reconstruct the message.
Threshold Scheme: (m, n) – threshold scheme.A message is divided into n pieces called shadows or shares so that any m of them can be used to reconstruct the original message.
Intermedate Protocols Chapter 4
• Time Stamping
• Subliminal Channels
• Bit Commitment
Time Stamping
Goals:• The document itself must be time stamped.
• Impossible to change any part of the document without it being apparent.
• Impossible to timestamp the document with a date/time different from the present one.
Time Stamping
Arbitrated Solution:1.Alice transmits a copy of the document to Trent
2.Trent records the date/time he received the document and retains a copy of the document for safekeeping.
Storage problems
Privacy problems
Time Stamping
Improved Arbitrated Solution:1.Alice produces a one-way hash of the document.
2.Alice transmits the hash to Trent
3.Trent appends the date/time he received the hash onto the hash.
H(M) | dtg
4.Trent signs the rersult.E
Tpri (H(M) | dtg)
5.Trent sends the result back to Alice.
Subliminal Channels
• Secret messages sent within other messages
• Often within the digital signature of an innocuous message
• Useful enough for a lot of work to be done in this area
Computing with Encrypted Data
• Alice wants to calculate f(x) on Bob's machine.• Alice does not want Bob to know x.
• You want to know the value of your portfolio without the news service knowing what your portfolio is.
Bit Commitment
• Alice picks a winner for tomorrow's race.
• Alice doesn't want Bob to know.
• Bob doesn't want Alice to be able to change her choice tomorrow.
Bit Commitment
1. Bob generates a random-bit string, R, and sends it to Alice.
2. Alice creates a message of her commitment, b and R.
3. Alice generates a random key, K, and encrypts Rb with it and sends the result to Bob. Result is E
K(R,b)
4. Later Alice sends Bob the key, K.
5. Bob decrypts the message and checks his random string.
Zero-Based KnowledgeProblem
Zero-Knowledge Protocol• Alice knows a secret
• Alice wants to prove to Bob she knows the secret
• Alice does not want to reveal the secret to Bob.
Zero-Knowledge Protocol
Alice claims she knows the secret combination to the door in the back of the cave. She wants to prove so to Bob.
1. Bob stands at point A.
2. Alice goes to point C or D.
3. Bob goes to B and asks Alice come out of the cave either on the left or the right.
4. Alice complies using her secret combination if she has to.
5. Repeat n times until Bob is convinced.
Zero-Knowledge Protocol
A
B
C D