The document discusses cryptography, highlighting its definitions, goals, and applications while tracing its historical evolution from ancient Greek techniques to modern encryption methods. It covers key concepts like encryption, decryption, and ciphers, as well as challenges and advancements in the field, particularly in relation to computer science and mathematics. The work also emphasizes the practical importance of cryptography in ensuring data security across various platforms.

1. What is Cryptography?
Pratik Poddar
Senior Undergraduate
Computer Science and Engineering
IIT Bombay
23th February 2010

2. What is Cryptology?
Greek: “krypto” meaning hide
Study of: 1) Hiding data
2) Reading Hidden data
3) Signing data
Goals: 1) Authentication
2) Integrity
3) Non-repudiation
4) Confidentiality

3. Applications of Cryptography
1) ATM
2) Email - Passwords
3) E-payment
4) Electronic Voting
5) Securing Data

4. Basic Terminology
Encryption -> Plaintext to Ciphertext
Decryption -> Ciphertext to Plaintext

5. History of Cryptography
Greeks used Transposition Cipher
“hello world” becomes
“ehlol owrdl”

6. “Asimplese
ntenceoft
ransposit
ioncipher”
becomes
“Anri stao ienn mnsc pcpi leop eosh sfie ettr”

7. History of Cryptography
Greeks used Substitution Cipher
“hello world” becomes “uryyb jbeyq”
26! (~ 30 digit number) keys possible

8. Caesar Cipher
Caesar Substitution Cipher with key 3
“hello world” becomes “khoor zruog”
26 keys possible

9. th
Statistical Attacks (9 century)
Frequency Analysis in 9th century
Armed with statistical knowledge about the
plaintext, one can easily break a monoalphabetic
substitution cipher:
Most frequent characters: e, t, o, a, n, i
Most frequent diagrams: th, in, er, re, an
Most frequent trigrams: the, ing, and, ion

11. Take the following example cipher text
BPMZM WVKM EIA IV COTG LCKSTQVO EQBP NMIBPMZA ITT
ABCJJG IVL JZWEV IVL BPM WBPMZ JQZLA AIQL QV AW UIVG
EWZLA OMB WCB WN BWEV OMB WCB, OMB WCB, OMB WCB
WN BWEV IVL PM EMVB EQBP I YCIKS IVL I EILLTM IVL I YCIKS
QV I NTCZZG WN MQLMZLWEV BPIB XWWZ TQBBTM COTG
LCKSTQVO EMVB EIVLMZQVO NIZ IVL VMIZ JCB IB MDMZG
XTIKM BPMG AIQL BW PQA NIKM VWE OMB WCB, OMB WCB,
OMB WCB WN PMZM IVL PM EMVB EQBP I YCIKS IVL I EILLTM
IVL I YCIKS IVL I DMZG CVPIXXG BMIZ
We need to compare the frequency distribution of this text with
standard English

13. Hence the key is probably equal to 8
We can now decrypt the cipher text to reveal:
There once was an ugly duckling With feathers all stubby and brown
And the other birds said in so many words Get out of town Get out,
get out, get out of town And he went with a quack and a waddle and
a quack In a flurry of eiderdown That poor little ugly duckling Went
wandering far and near But at every place they said to his face Now
get out, get out, get out of here And he went with a quack and a
waddle and a quack And a very unhappy tear

14. Poly-alphabetic Cipher (1467)
Use different ciphers (i.e., substitution alphabets)
for various parts of a message
The first automatic cipher device
Frequency analysis fails

15. KILL HIM TONIGHT
with key PRATIK
KILL HIM TONIGHT
PRAT IKP RATIKPR
------------------------------
ZZLE PSB KOGQQWK

16. Attack on Poly-Alphabetic Cipher
If period is known, individual frequency analysis

17. Kerchoff's Principle (1800s)
Cryptography always involves:
Transformation and Secret
Security of the key used should alone be
sufficient for a good cipher to maintain
confidentiality under an attack
The enemy knows the system

18. Cryptography Machines (1900s)
Mechanical
encryption/decryption
devices
Rotor machines (electro-
mechanical)
Enigma machine was used
by the German government
and military from the late 20s
and during World War II

19. Post WW2 Cryptography
1) Cryptography now on bits instead of letters
2) Academic Research began in 1970s
3) Computers helped Cryptography?
4) No more linguistic and lexicographic patterns,
but aspects of information theory, computational
complexity, statistics, combinatorics, abstract
algebra, number theory, and finite mathematics

20. “Modern cryptography is a remarkable discipline. It is a cornerstone
of computer and communications security, with end products that
are imminently practical. Yet its study touches on branches
of mathematics that may have been considered esoteric, and it
brings together fields like number theory, computational-complexity
theory, and probability theory”

21. Block vs Stream
Block Cipher
Message is broken into blocks, each of which is
then encrypted
Stream Cipher
Process the message bit by bit ( as a stream )

22. Symmetric Key Cryptosystem

23. Symmetric Key Algorithm - DES

24. Asymmetric Key Cryptosystem

26. Asymmetric Key Cryptosystem -
Idea
Some modern cryptographic techniques can only
keep their keys secret if certain mathematical
problems are intractable, such as the integer
factorization or the discrete logarithm problems

27. Designing Cipher
-- Little Secrets Hide Bigger Secrets
-- Open Algorithms and value of Peer-Review
-- Mathematical Background
-- Unbroken is Not Necessarily Unbreakable
What is a good encryption scheme?

28. 1) Complexity of encrypting or decrypting
2) Unbreakable
3) Size of cipher-text relative to plaintext
4) Key exchange should be easy

29. Breaking Cipher
Weakness:
Length of the key Quality of Random Source
Statistical Leaking Faulty Implementation
Inadequate Peer-Review Social Engineering and Coercion
Attacks:
Brute-Force Attack Frequency Analysis
Index of Coincidence Linear Cryptanalysis
Differential Cryptanalysis Meet in the Middle Attack

30. Research and Education
-- Encryption Decryption Algorithms
-- Cryptanalysis
-- Mathematics
-- Proofs of cryptosystem
-- Key Exchange Protocols
-- Certificates

31. Work being done at IIT Bombay
Prof. Bernard Menezes and his 5-6 students
Contact:
Pratik Poddar
pratik.poddar@iitb.ac.in
pratik@cse.iitb.ac.in
(Topic: IBE and Elliptic-Curve Cryptography)

32. Thank You!