1. Network Tools Cryptography Basics
CPS 290 Computer Security
Network Tools
Cryptography Basics
CPS 290

2. Discovering My Laptop’s IPv4 Address
On Windows, use program ipconfig. On Mac or Linux, use ifconfig or ip. Only my wired ethernet interface has an IP address ( )
CPS 290

3. Resolving the name www.cs.duke.edu to an IP address
On Windows, use nslookup. On Mac or Linux, use dig. The answer is provided by the authoritative name server duke.cs.duke.edu ( ) is an alias for the canonical name (CNAME) sibyl.cs.duke.edu The address for sibyl.cs.duke.edu is
CPS 290

4. Capturing and Examining Packets
I begin to capture packets on my wired ethernet interface using the program called wireshark (for Windows, Mac, or Linux). I make a request to through my browser. I enter the filter (ip.src == || ip.dst == ) && (ip.dst == || ip.src == ) to examine only packets between my machine and
CPS 290

5. TCP Three-Way Handshake
SYN
SYN-ACK
ACK
First three packets show the TCP three-way handshake, SYN, SYN-ACK, ACK, which is used to establish a TCP connection. Note: The handshake makes it difficult to establish a TCP connection with a spoofed (forged) browser source address in the SYN packet: Server will send SYN-ACK to the spoofed address, which won’t reply with an ACK. Sender of spoofed SYN packet doesn’t receive the SYN-ACK, doesn’t know the correct sequence number to ACK. Egress filtering: drop packets with non-local source addresses as they leave a network

6. Browser Sends HTTP GET Request
CPS 290

7. Server Responds with HTTP 301 Code
The server didn’t like my request for It wanted me to enter
Criminy!
CPS 290

8. Basic Cryptography Definitions
Encryption
Decryption
Key1
Key2
Cyphertext C
C = Ekey1(M)
M = Dkey2(C)
Original Plaintext M
Plaintext M
Symmetric: Key1 = Key2
Asymmetric: Key1  Key2
Key1 or Key2 may be public depending on the protocol

9. Private Key Cryptosystems
Encryption
Decryption
Key1
Cyphertext C
C =EKey1(M)
M = DKey1(C)
Original Plaintext M
Plaintext M
Example: two parties share Key1 in advance, use it for both encryption and decryption.

10. Public Key Cryptosystems
Introduced by Diffie and Hellman in 1976.
Plaintext M
Public Key systems
K1 = public key
K2 = private key K1
Encryption
C=EK1(M)
Cyphertext C
Digital signatures
K1 = private key
K2 = public key K2
Decryption
M=DK2(C)
Original Plaintext M
Typically used as part of a more complicated protocol.

11. What does it mean to be secure?
Unconditionally Secure: Encrypted message cannot be decoded without the key
Shannon showed in 1943 that key must be as long as the message to be unconditionally secure – this is based on information theory
A one time pad – xor a random key with a message (Used in 2nd world war)
Security based on computational cost: it is computationally “infeasible” to decode a message without the key.
E.g., there is no (probabilistic) polynomial time algorithm can decode the message.
CPS 290

12. Primitives: One-Way Functions
(Informally): A function y = f(x) is one-way if it is easy, given x, to compute f(x), but hard, given y, to find any x such that f(x)=y
Note that f may not be strictly invertible, i.e., there may be more than one x such that f(x)=y
Example: SHA-256 hash function*
The security of most protocols rely on the existence of one-way functions.
*Unfortunately, one-way functions have not been proved to exist, even if we assume P  NP.
CPS 290

13. One-way functions: possible definition
f(x) is polynomial time
f-1(y) is NP-hard
What is wrong with this definition?
“f-1(y) is NP-hard” is a statement only about worst-case complexity
f-1(y) may be NP-hard, but still easy to solve for most y
Efforts to base cryptosystems on NP-hard problems have all failed. We don’t know how to generate difficult to solve instances.
CPS 290

14. One-way functions: better definition
For almost all y no single PPT (probabilistic polynomial time) algorithm can compute x
Roughly: at most a fraction 1/|x|k instances x are easy for any k and as |x| -> 
This definition can be used to make the probability of hitting an easy instance arbitrarily small.
CPS 290

15. Some examples (conjectures)
Factoring: x = (u,v) y = f(u,v) = u*v
If u and v are prime it is hard to generate them from y.
Discrete Log: y = gx mod p
where p is prime and g is a “generator” (i.e., g1, g2, g3, … generates all values < p).
Factoring can be reduced to discrete log and vice versa.
CPS 290

16. One-way functions in private-key protocols
y = ciphertext m = plaintext k = key
y = Ek(m)
Given y, it should be hard to find m (Ek should be one-way)
Rewrite the function: y = Ek(m) = E(k,m) = Em(k)
Given y and m, it better also be hard to find k! I.e., Em should also be a one-way function.
In a known-plaintext attack we know one or more (y,m) pairs, and try to extract the key k.
CPS 290

17. Cryptanalytic Attacks
C = ciphertext messages
M = plaintext messages
Ciphertext Only:Attacker has multiple Cs but does not know the corresponding Ms
Known Plaintext: Attacker knows some number of (C,M) pairs.
Chosen Plaintext: Attacker chooses M and is given C.
Chosen Ciphertext: Attacker chooses C and is given M.
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18. The Cast Alice – initiates a message or protocol
Bob - second participant
Trent – trusted middleman
Eve – eavesdropper
Mallory – malicious active attacker
Mallory
Trent
Alice
Bob
Eve

19. One-way functions in public-key protocols
y = ciphertext m = plaintext k = public key
Consider: y = Ek(m) (i.e., f = Ek)
We know k and thus f
Ek(m) needs to be easy
Ek-1(y) should be hard
Otherwise we could decrypt y.
But what about the intended recipient, who should be able to decrypt y?
CPS 290

20. One-Way Trapdoor Functions
A one-way function with a “trapdoor”
The trapdoor is a key that makes it easy to invert the function y = f(x)
Example: RSA (conjectured to be hard to invert without trapdoor)
y = xe mod n
Where n = pq (p, q are prime)
p or q or d (where ed = 1 mod (p-1)(q-1)) can be used as trapdoors
In public-key algorithms
f(x) = public key (e.g., e and n in RSA)
Trapdoor = private key (e.g., d in RSA)
CPS 290

21. One-way Hash Functions
Y = h(x) where
y is a fixed length independent of the size of x. In general this means h is not invertible since it is many to one.
Calculating y from x is easy
Calculating any x such that y = h(x) give y is hard
Used in digital signatures and other protocols.
CPS 290

22. Protocols: Digital Signatures
Goals:
Convince recipient that message was actually sent by a trusted source
Do not allow tampering with the message without invalidating the signature
CPS 290

23. Using Public Keys Alice Bob Dk1(m)+m K1 = Alice’s private key
Bob decrypts it with her public key
More Efficiently
Dk1(h(m)) + m
Alice
Bob
h(m) is a one-way hash of m
CPS 290