Cryptography

Science of secret (hidden) writing
* kryptos – hidden
* graphen – to write
* Encrypt / encipher
* Convert plaintext into ciphertext
* Decrypt / decipher
* Convert ciphertext into plaintext










Symmetric Key Cryptography

Computationally fast
* Data Encryption Standard (DES)
* Block Cipher, 56 bit key
* Triple DES 112 bit key
* Advanced Encryption Standard (AES)
* Rijndael Algorithm
* Belgian cryptographers, Joan Daemen and Vincent Rijmen.
* 128, 192, 256 bit keys






Asymmetric Key Cryptography

Two mathematically related keys:
* Unable to derive one from the other
* Based upon hard problem
* RSA ‐ Integer Factorization (large primes)
* Diffie‐Hellman ‐ Discrete Logarithms
* ECES ‐ Elliptic Curve Discrete Logarithm
* Public Key Cryptography
* One public key published for all to see
* Other is private key kept secret by owner

Brute Force Against Symmetric Cryptography

It is always possible to break an algorithm by trying every possible key.
* This is independent of the algorithm.
* Brute force cryptanalysis is ideal for parallel processors & distributed computing.
* The only defense is a long key.
* Average time to break an algorithm with given key length using a custom
machine costing $1 million:
- 40 bits 0.2 seconds
- 56 bits 3.6 hours
- 64 bits 38 days
- 80 bits 7,000 years
- 112 bits 10**13 years
- 128 bits 10**18 years
- For every 5 years in the future, assume the attack is 10 times faster or cheaper
- Techniques of differential cryptanalysis proposed by Biham and Shamir and
linear cryptanalysis proposed by Matsui do not represent a threath for the use
of cryptography, as they are chosen palintext attacks wich require large
amounts of plaintext‐chipertext pairs.

From March 2007, dedicated machines such as Copacobana can break DES in an average time of Brute Force Against Symmetric Cryptography 6.4 Days‐ FPGA‐based machine
(http://www.copacobana.org/).
* Also, the Deep Crack machine from Electronic Frontier Foundation (EFF) is capable of testing more than 90 billions DES keys per second, which means that the entire key space can be exhausted in about 9 days, the average time for finding a key will be 4.5 days (http://w2.eff.org).

* The EFF's US$250,000 DES cracking machine contained over 1,800 custom chips and could brute force a DES key in a matter of days — the photo shows a DES Cracker circuit board fitted with 32 Deep Crack chips.

Brute Force and Public‐Key Cryptography

Public‐key crypto gets its power from the difficulty of factoring large
numbers
* 512 bits 30,000 mips‐years
* 768 bits 200,000,000 mips‐years
* 1,024 bits 10**11 mips‐years
* 2,048 bits 10**20 mips‐years
- Pentium‐based PC: 50‐100 mips
- 1600‐node Paragon: 50,000 mips
A recent effort which factored a 200‐digit number (RSA‐200) took eighteen
months and used over half a century of computer time.

What Can You Do With Cryptography?

* Key exchange
* Secret sharing
* Encryption
* Digital signatures
* Authentication
* Proof of identity
* Anonymous key
* Key escrow
* Zero‐knowledge proofs
* Simultaneous contract signing
* Digital certified mail distribution
* Blind signatures
* Voting
* Digital cash

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