EECS 395-0-21 Introduction to Cryptography

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EECS 395-0-21Introduction to Cryptography

• Lance Fortnow

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Basic Info

• Webpage Off http//lance.fortnow.com
• Text Intro to Cryptography with Coding Theory by
  Trappe and Washington
• Topics Crypto past, current and future
• Grading on mostly weekly assignments and take-off
  exams.
• Math Background A little probability, a little
  more number theory. Will teach.

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The Players
Bob
Alice
Eve
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Lock and Key
Safe Impossible to open or view inside without
key Cheap and easy to transport
Key Can be used to open safe Easily copied
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Puzzle 1
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Puzzle 1 Solution
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Puzzle 2
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Puzzle 2 Solution
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Flipping a coin
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Flipping a coin
If coins same declare Heads If coins differ
declare Tails
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Poker
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Sudoku
I cant solve it.
I know solution.
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Sudoku
I cant solve it.
I know solution.
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Sudoku
I cant solve it.
I know solution.
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Sudoku
I cant solve it.

• Choose either
• Row
• Column
• 3x3 square
• Original

I know solution.
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Sudoku
I cant solve it.
4th Row
I know solution.
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Sudoku
I cant solve it.
Left Center Box
I know solution.
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Sudoku
I cant solve it.
Original
I know solution.
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Other Cryptography Uses

• Identification
• Digital Signatures
• Secret Sharing
• Electronic Voting
• Electronic Cash

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Data Encryption Standard

• DES approved by NBS (now NIST) in 1977.
• Uses key of 56 bits to encrypt and decrypt.
• Very efficient in time and memory.

Plaintext
DES Encoder
Key
Codeword
Codeword
DES Decoder
Plaintext
Key
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DES
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Data Encryption Standard

• DES approved by NBS (now NIST) in 1977.
• Uses key of 56 bits to encrypt and decrypt.
• Very efficient in time and memory.
• Problem 56 bits not very big by todays
  standards
• Idea Use DES multiple times
• 2 times doesnt help Meet in the middle attack
• 3 times gives 112 bits of security (Triple DES)

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Meet in the Middle
Plaintext
DES Encoder
Key1
Codeword1
Key2
DES Encoder
Final Codeword
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Advanced Encryption Standard

• Also known as Rijndael
• Approved in 1997 by NIST
• Allows key lengths of 128, 192 or 256 bits.

Plaintext
AES Encoder
Key
Codeword
Codeword
AES Decoder
Plaintext
Key
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Safe and Key

• In AES, key k describes function fk(x) that is
  hard to invert without k.
• fk(x)
• k
• Same key to encrypt and decrypt

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Password System

• System has secret key k
• Password file has (users, fk(pass))
• Can check password
• Making password file public is safe
• Dictionary attack/Salt

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Public-Key Cryptography

• Diffie-Hellman

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Public-Key Cryptography

• Diffie-Hellman

Public Key e Private Key d
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Public-Key Cryptography

• Diffie-Hellman

Public Key e Private Key d
Use key e to encrypt and key d to decrypt.
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Public-Key Cryptography

• Diffie-Hellman

Public Key e Private Key d
Key e
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Public-Key Cryptography

• Diffie-Hellman

e
Public Key e Private Key d
Key e
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Public-Key Cryptography

• Diffie-Hellman

Public Key e Private Key d
Key e
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Public-Key Cryptography

• Diffie-Hellman

d
Public Key e Private Key d
Key e
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RSA Algorithm

• Rivest-Shamir-Adelman
• Bob chooses secret primes p and q
• Bob chooses random e, gcd(e,(p-1)(q-1)) 1
• Bob computes d with de ? 1 (mod (p-1)(q-1))
• Public Key n,e
• Private Key p,q,d
• Encoding message m cme (mod n)
• Decoding code c mcd (mod n)