Cryptography Lecture 1 Welcome! - PowerPoint Presentation

Slide1

Cryptography

Lecture 1

Slide2

Welcome!

Crypto is amazing

Can do things that initially seem impossible

Crypto is important

It impacts each of us every day

Crypto is fun!

Deep theory

Attackers’ mindset

Slide3

Necessary administrative stuff

Course webpage

http://www.cs.umd.edu/~jkatz/crypto/s18

Prerequisites/information posted there

Syllabus posted there

HWs posted there

Announcements posted there

Midterm already scheduled

Slide4

Necessary administrative stuff

Canvas/ELMS

Used only to submit HW electronically

Let me know if unable to access class

Piazza

Useful for discussions/questions

Preferable to email if you think others will have the same question

Slide5

Necessary administrative stuff

Capacity will not be increased beyond 75

Seats are reserved for registered students

Historically, 10-15% of the class drops by end of first full week

If you are trying to get in, do the first HW even if not yet admitted

After that, assume you will not get in

Slide6

TAs

Aaron Hall

Neal Gupta

Slide7

This is a tough class

Mathematical prerequisites

Discrete math, probability, modular arithmetic

Requires mathematical maturity

Proofs, abstraction

Slide8

This is a tough class

CS prerequisites

Binary, hex,

pseudocode

/algorithms, big-O notation

Programming assignments

Hard part should not be the programming, but the thought behind it

Flexibility in choice of language

Slide9

This is new for me…

Never taught so many students before

Never taught in an “interactive classroom” like this before

Try to promote “

a

ctive learning”

MUST read textbook before class

Lecture will move quickly, expect questions and discussion

30-40 minutes/week devoted to problem solving

Slide10

“Active learning”

Read textbook before class

See course syllabus

Can also view my videos on

Coursera

Ask questions in advance on Piazza and/or bring questions to class

Regular quizzes at beginning of class to test understanding

5% of the grade

Slide11

Textbook

Required

textbook: “Introduction to Modern Cryptography, 2

nd

edition,” Katz and

Lindell

Exams will be open book

Physical copies only

Slide12

HWs/exams

Expect HWs every 2-3 lectures

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 on syllabus is fair game

Slide13

Laptops/electronics

No-laptop/no-electronics policy

Distracting to you

Distracting to others

If you feel you need an exception, talk to me

Slide14

How to reach me

Best way to contact me is by email:

jkatz@cs.umd.edu

Please put “CMSC 456” in subject line

Office hours before class

Please email me in advance if you plan to come to office hours

Slide15

Questions?

Please ask questions throughout!

Slide16

Course goals

Understand real-world crypto via a rigorous approach

When you encounter crypto in your career:

Understand the key terms

Understand the security guarantees provided

Know how to use crypto

Understand what goes on “under the hood”

“Crypto mindset”

Slide17

Course non-goals

Designing your own crypto schemes

Implementing your own crypto for

real-world use

Course goal:

realize when

to consult an

expert!

Slide18

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

)

Slide19

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,

cryptocurrencies

)

Slide20

Modern cryptography

Design

, analysis, and implementation of

mathematical techniques

for securing information, systems, and

distributed computations

against adversarial

attack

Slide21

Modern cryptography

Cryptography is ubiquitous

Passwords, password hashing

Secure credit-card transactions over the internet

Encrypted

WiFi

Disk encryption

Digitally signed software updates

Bitcoin

…

Slide22

Cryptography (historically)

“…the art of writing or solving codes…”

Historically

,

cryptography was an

art

Heuristic

, unprincipled

design and analysis

Schemes proposed, broken, repeat…

Slide23

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

Slide24

Rough course outline

Building blocks

Pseudorandom (number) generators

Pseudorandom functions/block ciphers

Hash functions

Number theory

Secrecy

Integrity

Private-key setting

Private-key encryption

Message authentication codes

Public-key setting

Public-key encryption

Digital

signatures

Slide25

Classical Cryptography

Slide26

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

Slide27

Classical cryptography

Until the 1970s, exclusively

concerned with ensuring

secrecy

of communication

I.e.,

encryption

Slide28

Classical cryptography

Until the 1970s, relied exclusively on secret information (a

key

) shared in advance between the communicating parties

Private-key

cryptography

a

ka secret-key / shared-key / symmetric-key cryptography

Slide29

Private-key encryption

k

k

c

key

m

c

:=

Enc

k

(m)

m

essage/plaintext

encryption

ciphertext

m

:= Dec

k

(c)

decryption

key

Slide30

Private-key encryption

k

c

m

c

:=

Enc

k

(m)

m

:= Dec

k

(c)

k

c

c

Slide31

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



Enc

k

(m)

Dec (decryption algorithm): takes key k and

ciphertext

c as input; outputs m or “error”

m := Dec

k

(c)

For all

m



M

and k output by Gen,

Dec

k

(

Enc

k

(m)) = m

Slide32

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

Some 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

P

ublic validation

Slide33

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

Slide34

Modular arithmetic

x

=

y

mod N if and only if N divides x-y

[x mod N] =

t

he

remainder when x is divided by N

I.e., the unique value

y

{0, …, N-1} such that

x =

y

mod N

2

5 = 35 mod 10

25 ≠ [35 mod 10]

5 = [35 mod 10]

Slide35

The shift cipher, formally

M

= {strings over lowercase English alphabet

}

Gen: choose uniform k

{0, …, 25}

Enc

k

(m

1

…

m

t

): output c

1

…

c

t

, where

c

i

:= [m

i

+ k mod 26]

Dec

k

(c

1

…

c

t

): output m

1

…

m

t

, where

m

i

:= [c

i

- k mod 26]

Can verify that correctness holds…

Slide36

Is the shift cipher secure?

No -- only 26 possible keys!

Given a

ciphertext

, try decrypting with every possible key

O

nly one possibility will “make sense”

(What assumptions are we making here?)

Example of a “brute-force” or “exhaustive-search” attack

Slide37

Example

Ciphertext

uryybjbeyq

Try every possible key…

t

qxxaiadxp

s

pwwzhzcwo

…

helloworld