Applied Cryptography

1
Applied Cryptography

• Secure Hashes and their Uses

2
Hash Functions

• Take an input from a large domain and return an
  output in a smaller range
• Easy to compute

3
Hash Example

• Matrix multiplication

4
Secure Hashes

• One-Way
• Given f(x), hard to find x.
• Collision-Free
• Hard to find x and y so that f(x)f(y)
• Hard to bias output
• Hard to generate a set xi so that we can
  differentiate between f(xi) and f(U) where U is
  a uniformly distributed input.

5
Secure Hashes Example

• No proven secure hashes exist!
• Not even one-way functions are known to exist!
• If a one-way function exists P?NP

6
Practical Secure Hashes

• Standards
• MD5(Message Digest)
• SHA-1(Secure Hash Algorithm)

Diagram of a SHA-1 round.
7
Uses for Secure Hashes

• Message Authentication Checksums
• Prevent an attacker from changing messages
• Faster Digital Signatures
• Faster Bit-Commitment Schemes
• Pseudo-Random Number Generators
• (Not covered in this lecture)

8
Simple Message Authentication

• Send a hash via another channel

10101001010101010101010101101010100010101010010
100011010010101010
Alice
Bob
Bulletin Board
SHA-1
100010010101100011
9
Cryptographic Authentication

• Use a Keyed Hash

10101001010101010101010101101010100010101010010
100011010010101010
Alice
Bob
Shared Secret
SHA-1
100010010101100011
10
Digital Signatures Problem

• Operations on big numbers are slow
• exponentiation
• multiplication
• RSA can only sign messages up to the keysize (a
  few thousand bits)
• To sign long messages using RSA we have divide
  the message and sign many times
• The signature is as long as the message

11
Digital Signatures Solution

• Sign a secure hash of the message instead
• Advantages
• Hashing is fast
• We only have to perform RSA once
• The size of the signature is constant

12
Digital Signatures Diagram
Message
101011101010101010
101011101010101010
SHA-1
010001
101011
101010
101010
RSA
RSA
RSA
RSA
010101
001010
001110
111001
010101001010001110
Signature
13
Bit Commitment - Suggestion1
Commitment
SHA-1
Alice
Bob
01001
1
Unveiling
Alice
Bob
1
14
Bit Commitment - Suggestion2
Commitment
Alice
Bob
Unveiling
101110100
Alice
Bob
1
15
Bit Commitment - Assumptions

• Hash is one way and collision-free
• Alice is computationally bounded
• Hash doesnt leak information
• Example of a leaky hash

SHA-1
101110100
1001
1
1
16
Bit Commitment - Protocol

• Due to Shai Halevi and Silvio Micali
• Requires only collision-free property

Universal Hash
SHA-1
Alice
Bob
01001
1
01001010001
11010101
17
Using Secure Hashes in Java

• Java has a MessageDigest class
• import java.security.
• Implementations for MD5 and SHA-1 are included

18
MessageDigest Class

• getInstance(String)
• Generates a MessageDigest object that implements
  the specified digest algorithm.
• update(byte)
• Updates the digest using the specified byte.
• update(byte)
• Updates the digest using the specified array of
  bytes.
• update(byte, int, int)
• Updates the digest using the specified array of
  bytes, starting at the specified offset.

19

• digest()
• Completes the hash computation by performing
  final operations such as padding.
• digest(byte)
• Performs a final update on the digest using the
  specified array of bytes, then completes the
  digest computation.
• The DigestInputStream and DigestOutputStream can
  also be used to update a MessageDigest object
  while input is being read or written.

20
DigestInputStream
public DigestInputStream(InputStream stream,
MessageDigest digest)
Creates a digest input stream, using the
specified input stream and message digest.
Parameters stream - the input stream.
digest - the message digest to associate
with this stream

• The read method can be used to read bytes from
  the input stream.
• The digest is automatically updated as bytes are
  read.
• The digest can be switched off if necessary.

21
DigestOutputStream

• The DigestOutputStream is the analogous stream
  for updating a digest as you write to an output
  stream, using the write() methods.
• The Documentation for the class is available on
  line at
• http//java.sun.com/products/jdk/1.1/docs/api/java
  .security.DigestOutputStream.html
• For more information on how input and output
  streams work, look at
• http//java.sun.com/docs/books/tutorial/essential/
  io/index.html

22
Available Digests

• SHA-1
• MessageDigest.getInstance(SHA)
• MD5
• MessageDigest.getInstance(MD5)

23
Further Reading

• Bit-Commitment with Secure Hashes
• http//citeseer.nj.nec.com/halevi96practical.html
• SHA-1 Specification
• http//www.itl.nist.gov/fipspubs/fip180-1.htm
• MD5 Specification (rfc1321)
• http//andrew2.andrew.cmu.edu/rfc/rfc1321.html
• Keyed Hashes HMAC
• http//www-cse.ucsd.edu/users/mihir/papers/hmac.ht
  ml