1. Cryptography
Lecture 1

2. Welcome! Crypto is amazing! Crypto is important and pervasive
Can do things that seem impossible…
Crypto is important and pervasive
It impacts each of us every day
Crypto is fun!
Deep theory
Attackers’ mindset, fun assignments

3. Necessary administrative stuff
Course webpage
Prerequisites/information posted there
Syllabus/readings posted there
Midterm already scheduled
Slides posted there
HWs posted there (and on Canvas)
Announcements posted there

4. Necessary administrative stuff
Canvas
HWs will be posted on webpage and Canvas
Use Canvas to submit HWs electronically
Can type solutions using latex (preferred)
Can also scan handwritten solutions
Can also use Word
Piazza
Useful for discussions/questions
Piazza is better than if others will have the same question, or if other students can help answer

5. TAs Erica Blum Makana Castillo-Martin Elijah Grubb Corbin McNeill
Ben Sela
Office hours listed on webpage
May change as semester progresses

6. This is a tough class Mathematical prerequisites
Discrete math, probability, modular arithmetic
Requires mathematical maturity
Definitions, theorems, proofs, abstraction

7. This is a tough class CS prerequisites Programming assignments
Pseudocode/algorithms, big-O notation
Programming assignments
Hard part should not be the programming, but the thought behind it
Some flexibility in choice of language, but will be required to read code I provide

8. Textbook
Required textbook: “Introduction to Modern Cryptography, 2nd edition,” Katz and Lindell
Exams will be open book
Physical copies only

9. Tips for doing well
Expected to read relevant sections of textbook before class
Lecture will move quickly; I expect questions and discussion
If you fall behind on the reading it will be hard to catch up!
Watch my videos on Coursera
“Clicker quizzes” given based on the reading (as well as throughout class)
5% of the grade

10. This is a test Are you able to use the clicker to respond? A: Yes
B: No

11. HWs/exams Expect HWs every 1.5-2 weeks In-class midterm and final
Optional HWs (ungraded) focusing on theory
Solutions given
Graded HWs involving implementation
Meant to reinforce the abstract concepts
Meant to highlight practical applications
In-class midterm and final
Questions similar to optional HWs and in-class exercises; may also be based on programming assignments
Anything covered in class or listed in readings on syllabus is fair game

12. Laptops/electronics No-laptop/no-electronics policy
Distracting to you
Distracting to others
If you feel you need an exception to take notes, talk to me

13. How to reach me
Best way to contact me is by
Please put “CMSC 456” in subject line
Please me in advance if you plan to come to office hours

14. Questions?
Please ask questions throughout!

15. Course goals Understand the theoretical basis for real-world crypto
When you encounter crypto in your career:
Understand the key terms
Understand the security guarantees needed/provided
Know how to use crypto
Understand what goes on “under the hood”
“Crypto mindset”

16. Course non-goals Designing your own crypto schemes
This is hard!
Implementing crypto for real-world use
Course goal: realize when to consult an expert!

17. Cryptography (historically)
“…the art of writing or solving codes…”
Historically, cryptography focused exclusively on ensuring private communication between two parties sharing secret information in advance using “codes” (aka private-key encryption)

18. Modern cryptography Much broader scope!
Data integrity, authentication, protocols, …
The public-key setting
Group communication
More-complicated trust models
Foundations (e.g., number theory, quantum-resistance) to systems (e.g., electronic voting, blockchain, cryptocurrencies)

19. Modern cryptography
Design, analysis, and implementation of mathematical techniques for securing information, systems, and distributed computations against adversarial attack

20. Cryptography (historically)
“…the art of writing or solving codes…”
Historically, cryptography was an art
Heuristic, unprincipled design and analysis
Schemes proposed, broken, repeat…

21. Modern cryptography Cryptography is now much more of a science
Rigorous analysis, firm foundations, deeper understanding, rich theory
The “crypto mindset” has permeated other areas of computer security
Threat modeling
Proofs of security

22. Cryptography (historically)
Used primarily for military/government applications, plus a few niche applications in industry (e.g., banking)

23. Modern cryptography Cryptography is ubiquitous!
Password-based authentication, password hashing
Secure credit-card transactions over the internet
Encrypted WiFi
Disk encryption
Digitally signed software updates
Bitcoin …

24. Rough course outline Building blocks Pseudorandom (number) generators
Secrecy
Integrity
Private-key setting
Private-key encryption
Message authentication codes
Public-key setting
Public-key encryption
Digital signatures
Building blocks
Pseudorandom (number) generators
Pseudorandom functions/block ciphers
Hash functions
Number theory

25. Classical Cryptography

26. Motivation Allows us to “ease into things…,” introduce notation
Shows why unprincipled approaches are dangerous
Illustrates why things are more difficult than they may appear

27. Classical cryptography
Until the 1970s, exclusively concerned with ensuring secrecy of communication
I.e., encryption

28. Classical cryptography
Until the 1970s, relied exclusively on secret information (a key) shared in advance between the communicating parties
Private-key cryptography
aka secret-key / shared-key / symmetric-key cryptography

29. Private-key encryption
ciphertext c k k m
c  Enck(m)
m := Deck(c)
message/plaintext
decryption
encryption

30. Private-key encryptionm
c := Enck(m) c c k
m := Deck(c)

31. Private-key encryption
A private-key encryption scheme is defined by a message space M and algorithms (Gen, Enc, Dec):
Gen (key-generation algorithm): outputs kK
Enc (encryption algorithm): takes key k and message mM as input; outputs ciphertext c c  Enck(m)
Dec (decryption algorithm): takes key k and ciphertext c as input; outputs m or “error” m := Deck(c)
For all mM and k output by Gen, Deck(Enck(m)) = m

32. Kerckhoffs’s principle
The encryption scheme is not secret
The attacker knows the encryption scheme
The only secret is the key
The key must be chosen at random; kept secret
Arguments in favor of this principle
Easier to keep key secret than algorithm
Easier to change key than to change algorithm
Standardization
Ease of deployment
Public scrutiny

33. ccccccccccc jgnnqyqtnfb
The shift cipher
Consider encrypting English text
Associate ‘a’ with 0; ‘b’ with 1; …; ‘z’ with 25
k  K = {0, …, 25}
To encrypt using key k, shift every letter of the plaintext by k positions (with wraparound)
Decryption just does the reverse
helloworldz
ccccccccccc jgnnqyqtnfb

34. Modular arithmetic x = y mod N if and only if N divides x-y
[x mod N] = the remainder when x is divided by N
I.e., the unique value y{0, …, N-1} such that x = y mod N
25 = 35 mod 10
25 ≠ [35 mod 10]
5 = [35 mod 10]

35. The shift cipher, formally
M = {strings over lowercase English alphabet}
Gen: choose uniform k{0, …, 25}
Enck(m1…mt): output c1…ct, where ci := [mi + k mod 26]
Deck(c1…ct): output m1…mt, where mi := [ci - k mod 26]
Can verify that correctness holds…

36. Is the shift cipher secure?
No -- only 26 possible keys!
Given a ciphertext, try decrypting with every possible key
Only one possibility will “make sense”
(What assumptions are we making here?)
Example of a “brute-force” or “exhaustive-search” attack

37. Example Ciphertext uryybjbeyq Try every possible key… tqxxaiadxp
spwwzhzcwo …
helloworld

38. Byte-wise shift cipher
Work with an alphabet of bytes rather than (English, lowercase) letters
Works natively for arbitrary data!
Use XOR instead of modular addition
Essential properties still hold

39. Hexadecimal (base 16) Hex Bits (“nibble”) Decimal 0000 1 0001 2 0010 3
0000 1
0001 2
0010 3
0011 4
0100 5
0101 6
0110 7
0111
Hex
Bits (“nibble”)
Decimal 8
1000 9
1001 A
1010 10 B
1011 11 C
1100 12 D
1101 13 E
1110 14 F
1111 15

40. Hexadecimal (base 16) 0x10 0xAF 0x10 = 16*1 + 0 = 16 0x10 = 0001 0000
0xAF = 16*A + F = 16* = 175
0xAF =