1. Overview of Cryptography
Rajesh Palit, Ph.D.
Assistant Professor
Department of Electrical and Computer Engineering

2. Pinpoint of the discussion
Cryptography
Cryptology = Cryptography + Cryptanalysis
Computer Network Security
Computer Security (also Privacy)
Cyber Crimes
Digital Forensics
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Cryptosystems
Steganography
(hidden)
Code
(replace words)
Secret
Writing
Substitution
Cryptography
(scrambled)
Cipher
(replace letters)
Transposition
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Steganography
is the art or practice of concealing a message, image, or file within another message, image, or file 
The advantage is that the intended secret message does not attract attention to itself as an object of scrutiny. Plainly visible encrypted messages—no matter how unbreakable—will arouse interest.
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5. Definition of Cryptography
The science of “secret” writing (communication)
cipher is a function which transforms a plaintext message into a ciphertext (cryptogram) by the process of encipherment
plaintext is recovered from the ciphertext by the process of deciphering
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Terminologies
Plaintext
The initial unencrypted (unscrambled) data to be communicated.
Example: “dr partha pratim das”
Ciphertext
Plaintext is encrypted (scrambled) into something unintelligible – ciphertext for communication
Example: “es qbsuib qsbujn ebt”
Encryption
The process of converting ordinary information (plaintext) into ciphertext.
Decryption
The reverse process of moving from unintelligible ciphertext to plaintext.
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Crypto Communicators
Crypto literature frequently illustrates secret communication scenarios in terms of some fictitious characters:
Alice and Bob
The common communicating parties.
Carol and Dave
If there is a third or fourth party to the communication
Mallory
The malicious party
Eve
An eavesdropper
Trent
A trusted third party.
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8. Goals of Crypto Systems
Confidentiality: Ability to keep information communicated between (among) authorized parties private. In a stronger sense, an observer cannot determine the parties involved or whether a communication session occurred
Message Authentication (Data Integrity): Ability to ascertain that information exchanged has not been subject to additions, deletions, modifications or undue delay
User Authentication: Ability of the authorized parties in a communication session to ascertain the identity of other authorized parties
Non-Repudiation: Ability to prevent an authorized party from denying the existence or contents of a communication session
Access Control and Availability
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Cryptographic Tools
Encryption/Decryption
Message Authentication Codes (Hashing)
Digital Signatures
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10. Encryption/Decryption
Encryption is the process of transforming a plaintext message M into ciphertext C using an a unique key K
C = EK(M)
Decryption is just the reverse operation; transforming ciphertext C into plaintext M under control of key K
M = DK(C)
It should be (computationally) infeasible for an observer of C to recover either M or K (in a reasonable time) – security requirement
Security depends on the secrecy of the key, not the secrecy of the algorithm.
Plaintext, Encryption algorithm, Secret Key, Ciphertext, Decryption algorithm
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11. Classification of Secure Systems
Unconditionally Secure
Cannot be broken regardless of attackers computational abilities
One time pad (used once and then discarded)
Computationally Secure
Secure against attacker with “reasonable” resources
Takes one thousand year to break
Computationally Insecure
Easily breakable
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Perfect Secrecy
To achieve perfect secrecy, we wish to make C and M statistically independent I(M;C) = 0, that is, the cryptanalyst can do no better than guess
This implies H(M) ≤ H(K), for binary transmissions, # of key bits ≥ # of message bits
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13. Message Authentication/Hashing
This function allows the detection of any modification of the plaintext message
It is usually a digest of the message created in such a way that as little as one bit change in the message will produce an unpredictable change in approximately 50% of the bits or characters of the digest
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14. Hashing
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Digital Signatures
Ability to prove to an independent third party at a later date the author and contents of a message
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16. Properties of Encryption process
Confusion
Process of substituting characters or symbols to make relationship between ciphertext and key as complex as possible
Attacker’s uncertainty as to the contents of a message or the key used for encryption/decryption
Diffusion
Process of spreading effect of plaintext or key as widely as possible over ciphertext
Dispersion of the effect of individual key or message bits over the ciphertext
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Types of Ciphers
Block Ciphers
Stream Ciphers
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Transposition Cipher
Transposition Ciphers rely on rearranging the order of letters according to some predetermined pattern
Common method is Columnar
Transposition - Write message in a matrix then rearrange columns
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Transposition Cipher
“Key” is the order in which columns are read
choose
Ciphertext is now
– IUSTATSERSITCEESIEMGHQAES
“Looks” complex, but…..
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Substitution Ciphers
Message symbols are mapped into permuted set of symbols
We observe that Transposition introduces Diffusion while Substitution introduces Confusion to the cipher
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Modern Ciphers
Secret-Key (Symmetric) Cryptography
Uses a single key for both encryption and decryption
Public-Key (Asymmetric) Cryptography
Uses one key for encryption and another for decryption
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22. Secret-Key Cryptography
Single key used for both encryption & decryption.
Sender uses the key (or some set of rules) to encrypt the plaintext and sends the ciphertext to the receiver.
Receiver applies the same key (or ruleset) to decrypt the message and recover the plaintext.
Also called symmetric encryption.
The key must be known to sender & receiver both.
Popular:
Data Encryption Standard (DES) 
Advanced Encryption Standard (AES)
Drawback
Distribution of the key.
Advantage
Very fast in encryption / decryption
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DES
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Breaking DES
In June 1997 a DES encrypted challenge message, sponsored by RSA Data Security Inc., was broken using a distributed brute force attack involving 10,000 computers - the key was recovered in 96 days.
Several more DES Challenges have been broken, the most recent in Jan This attack involved 100,000 computers and some special hardware and required only 22 hours to recover the key
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27. Public-Key Cryptography
A crypto system for secure communication over a non-secure communications channel without having to share a secret key.
Usually, a two-key system
Public Key
Private Key
One key (public / private) is used to encrypt while the other (public / private) is used to decrypt.
The most significant new development in cryptography in the last years.
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28. Public-Key Cryptography
Applications:
Encryption
Digital Signature
Key Distribution for Symmetric Algorithm
Popular:
RSA public-key cryptosystem
Diffie-Hellman public-key cryptosystem
In modern cryptosystem designs, both asymmetric (public key) and symmetric algorithms are used to take advantage of the
virtues of both.
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29. Key Generation: Public-Key
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30. Encryption: Public-Key
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31. Signature: Public-Key
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32. Public-Key Cryptography
Based upon one-way trapdoor functions
Mathematical functions that are easy to compute whereas their inverse function is relatively difficult to compute.
Multiplication vs. factorization
Exponentiation vs. logarithms
Has a trap door in the one-way function so that the inverse calculation becomes easy given knowledge of some item of information.
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33. PKC: Multiplication vs Factorization
It is easy to multiply two primes:
3 * 5 = 15
17 * 23 = 391
101 * 223 = 22523
It is difficult to factorize into two primes:
35 = 5 * 7
551 = 19 * 29
24503 = 107 * 229
Heart of RSA
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34. PKC: Exponentiation vs Logarithm
It is easy to raise a prime to another:
3 ^ 2 = 9
5 ^ 3 = 125
11 ^ 7 =
It is difficult to find base-exponent pair:
8 = 2 ^ 3
243 = 3 ^ 5
= 7 ^ 11
Heart of Diffie-Hellman
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