1. CIT 380: Securing Computer Systems
Cryptography Basics
CIT 380: Securing Computer Systems

2. CIT 380: Securing Computer Systems
Topics
Cryptographic Concepts
History of Cryptography
Symmetric Encryption
Public Key Encryption
Digital Signatures
Message Authentication Codes
CIT 380: Securing Computer Systems

3. Cryptographic Concepts
Encryption: a means to allow two parties to establish confidential communication over an insecure channel that is subject to eavesdropping.
Alice
Bob
Eve

4. Encryption and Decryption
The message M is called the plaintext. Alice will convert plaintext M to an encrypted form using an encryption algorithm E that outputs a ciphertext C for M.
encrypt
decrypt
ciphertext
plaintext
shared
secret
key
Communication channel
Sender
Recipient
Attacker
(eavesdropping)

5. Encryption and Decryption
As equations: C = E(M) M = D(C) The encryption and decryption algorithms are chosen so that it is infeasible for someone other than Alice and Bob to determine plaintext M from ciphertext C. Thus, ciphertext C can be transmitted over an insecure channel that can be eavesdropped by an adversary.

6. Cryptosystem The set of possible plaintexts
The set of possible ciphertexts
The set of encryption keys
The set of decryption keys
The correspondence between encryption keys and decryption keys
The encryption algorithm to use
The decryption algorithm to use

7. Caesar Cipher
Replace each letter with the one “three over” in the alphabet.
Public domain image from

8. Kerckhoff’s Principle
Security of cryptosystem should only depend on
Quality of shared encryption algorithm E
Secrecy of key K
Security through obscurity tends to fail
ex: DVD Content Scrambling System

9. Early Cryptography Egyptian hieroglyphics ~ 2000 B.C.E.
Cryptic tomb enscriptions for regality.
Spartan skytale cipher ~ 500 B.C.E.
Wrapped thin sheet of papyrus around staff.
Messages written down length of staff.
Decrypted by wrapped around = diameter staff.
Cæsar cipher ~ 50 B.C.E.
Simple alphabetic substitution cipher.
al-Kindi ~ 850 C.E.
Cryptanalysis using letter frequencies.
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10. Vigènere Cipher (1553) Use phrase instead of letter as key. Example
Message THE BOY HAS THE BALL
Key VIG
Encipher using Cæsar cipher for each letter:
key VIGVIGVIGVIGVIGV
plain THEBOYHASTHEBALL
cipher OPKWWECIYOPKWIRG

11. The World Wars Decryption of Zimmerman telegram 1917
Leads US into World War I
Japanese Purple Machine cracked 1937
US breaks rotor machine for highest secrets.
German Enigma machine cracked
Initially broken by Polish mathematician
Variants broken at Bletchley Park in UK
Colossus, world’s 1st electronic computer.

12. Symmetric Cryptosystems
Alice and Bob share a secret key, which is used for both encryption and decryption.
encrypt
decrypt
ciphertext
plaintext
shared
secret
key
Communication channel
Sender
Recipient
Attacker
(eavesdropping)

13. Symmetric Key Distribution
Requires each pair of communicating parties to share a (separate) secret key.
shared
secret
shared
secret
shared
secret
shared
secret
shared
secret
n (n-1)/2 keys
shared
secret

14. Public-Key Cryptography
Bob has two keys: a private key, SB, which Bob keeps secret, and a public key, PB, which Bob broadcasts widely.
In order for Alice to send an encrypted message to Bob, she need only obtain his public key, PB, use that to encrypt her message, M, and send the result, C = EPB (M), to Bob. Bob then uses his secret key to decrypt the message as M = DSB (C).

15. Public-Key Cryptography
Separate keys for encryption and decryption.
encrypt
decrypt
ciphertext
plaintext
public
key
private
Communication channel
Sender
Recipient
Attacker
(eavesdropping)

16. Public Key Distribution
Only one key is needed for each recipient
n key pairs
private
public

17. Why Johnny Can’t Encrypt
Usability evaluation of PGP 5.0
Pretty Good Privacy
Encrypts data
Plugins for clients
Results of study of 12 users
3 users sent without encryption (2 of 3 realized)
7 users used public key instead of private key to encrypt
Only 2 users could decrypt without problems

18. Digital Signatures
Public-key encryption provides a method for doing digital signatures
To sign a message, M, Alice just encrypts it with her private key, SA, creating C = ESA(M).
Anyone can decrypt this message using Alice’s public key, as M’ = DPA(C), and compare that to the message M.

19. Secure Hash Functions
A secure hash function or message authentication code (MAC) is a checksum on a message, M, with the following properties:
One-way: it should be easy to compute Y=H(M), but hard to find M given only Y.
Collision-resistant: it should be hard to find two messages, M and N, such that H(M)=H(N).
Examples: MD5, SHA-1, SHA-256.
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20. Message Authentication Codes
Allows for Alice and Bob to have data integrity, if they share a secret key.
Given a message M, Alice computes H(K||M) and sends M and this hash to Bob.
(attack detected) =?
MAC h
shared
secret
key
Communication channel
Sender
Recipient
Attacker
(modifying)
6B34339
4C66809
message M’
87F9024
received MAC
computed MAC
message M

21. CIT 380: Securing Computer Systems
References
Anderson, Security Engineering 2nd Edition, Wiley, 2008.
Bishop, Computer Security: Art and Science, Addison-Wesley, 2002.
Goodrich and Tammasia, Introduction to Computer Security, Pearson, 2011.
CIT 380: Securing Computer Systems