Cryptography Intro Notes

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21 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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1

Network Security

Chapter 2


Introduction to
Cryptography

George Hamer
-

CSc 492/592
-

Fall 2008

2

1.
Defintion


process data into unintelligible form,
reversibly, without data loss


typically
digitally


usually one
-
to
-
one in size

compression


analog cryptography: voice changers, shredder


other services:


integrity checking: no tampering


authentication: not an impostor






George Hamer
-

CSc 492/592
-

Fall 2008

This is IMPORTANT!!!!


Fundamental Tenet of Cryptography


If lots of smart people have failed to
solve a problem, then it probably will not
be solved (soon).

George Hamer
-

CSc 492/592
-

Fall
2008

3

Cryptography Caveats


Cannot
prove that code is secure


assume until otherwise

but: can prove (some)
systems/protocols secure (assuming
secure code)


Difficult to explain algorithm securely


Cryptographic system =
algorithm(published or secret) + secret
value (
key)


Assume Trudy has algorithm






George Hamer
-

CSc 492/592
-

Fall
2008

4

Computational Difficulty


algorithm needs to be efficient


may
use inefficient for short key


brute
-
force cryptanalysis: try all keys
until “looks like” plaintext


any scheme can be broken


depends on $ = f(time)


Longer key


more secure


Encryption = O(n+1)


Decryption = O(2
n+1
) twice as hard



George Hamer
-

CSc 492/592
-

Fall
2008

5

Computational Difficulty cont.


cryptanalysis tools:




special
-
purpose hardware




parallel machines




Internet coarse
-
grain
parallelism




. . .


George Hamer
-

CSc 492/592
-

Fall
2008

6

Secret Key vs. Secret Algorithm


Secret algorithm


another hurdle


hard to keep secret if widely used:
reverse engineering, social
engineering


commercial: published


wide
review, trust


military: avoid giving enemy good
ideas (not just messages)



George Hamer
-

CSc 492/592
-

Fall
2008

7

Trivial Codes


Caesar cipher: substitution cipher: A
-
> B, B
-
> C, etc


Captain Midnight secret Decoder ring:
shift by variable n, IBM
-
> HAL


Only 26 possibilities


monoalphabetic

cipher:
generalization, arbitrary mapping
letter to letter, only 2
26

possibilities


Can be broken with statistical analysis




George Hamer
-

CSc 492/592
-

Fall
2008

8

Cryptanalysis


Cipher text only: requires exhaustive
search until it “look like” recognizable
text. Requires much cipher text


Known plain text: requires
<plaintext, ciphertext> pairs. May
not remain secret forever!


Chosen plain text: requires that I can
get text encrypted

George Hamer
-

CSc 492/592
-

Fall
2008

9

Some large numbers


Time to next ice age


14,000 yrs


DES 56 bit keys



7*10
16

keys


Probability of MD5 collision 1/3*10
38



Age of planet



10
9

years


Time until sun goes nova

10
14

years


Age of universe



10
10

years


Number of atoms in universe 10
77

George Hamer
-

CSc 492/592
-

Fall
2008

10

Brute Force Attacks


Number of encryptions/sec: 1 million to 1 billion bits/sec


1999: 56
-
bit key broken in 22.5 h with 1,800 chips
($250,000) (245 * 10
9

keys/sec see eff.org)



1995: 56
-
bit key broken in 1 week with 120,000
processors ($6.7M)


56
-
bit key broken in 1 month with 28,000 processors
($1.6M)


64
-
bit key broken in 1 week with 3.1*10
7

processors
($1.7 billion)


128
-
bit key broken in 1 week with 5.6*10
26

processors


Chinese Lottery: With machines that test at the rate of a
million keys every second, take 64 seconds to break DES
with a billion such machines running in parallel.




George Hamer
-

CSc 492/592
-

Fall
2008

11

Types of Cryptography


Hash function: no key needed


Secret key: one key used


Public key: two keys used, one public
and one private

George Hamer
-

CSc 492/592
-

Fall
2008

12

Secret Key Cryptography

George Hamer
-

CSc 492/592
-

Fall
2008

13

Secret Key Cryptography cont.


Cipher text ≈ same length as plain
text


symmetric cryptography


substitution codes, DES, IDEA


Message transmission: agree on key
(how?), communicate over insecure
channel



George Hamer
-

CSc 492/592
-

Fall
2008

14

Strong Authentication

George Hamer
-

CSc 492/592
-

Fall
2008

15

Strong Authentication cont.


= prove knowledge of key without
revealing it


Notice that Fred can obtain <plain,
cipher> text pairs


Not completely secure!


Integrity check = fixed
-
length checksum
for message CRC not sufficient


easy
to pick
newmessage

with same CRC


encrypt MIC (
message integrity check)


George Hamer
-

CSc 492/592
-

Fall
2008

16

Public Key Cryptography


asymmetric cryptography


publicly invented in 1975


two keys: private (d) and public (e)


much slower than secret key
cryptography


George Hamer
-

CSc 492/592
-

Fall
2008

17

Public Key Cryptography cont.

George Hamer
-

CSc 492/592
-

Fall
2008

18

Public Key Cryptography cont.

George Hamer
-

CSc 492/592
-

Fall
2008

19

Digital Signatures


Encrypt
hash(m)

with private key




Doesn’t reveal text


Authorship


Integrity


non
-
repudiation: can’t do with secret
-
key cryptography



George Hamer
-

CSc 492/592
-

Fall
2008

20

Hash Algorithm


= message digest, one
-
way
transformation h(m)


Length(h(m)) << Length(message)


usually fixed lengths: 48


128 bits


Easy to compute
h(m)


Given
h(m
), but not m, there is no
way to compute m


Computationally infeasible to find m
1

and
m
2

where h(m
1
)= h(m
2
)

George Hamer
-

CSc 492/592
-

Fall
2008

21

22

George Hamer
-

CSc 492/592
-

Fall
2008