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Introduction to Cryptography

 

Cryptography is used in most digital money schemes in many different ways. Here are a few examples:

• Authenticate the user to the bank.
• Money can be generated by banks, represented by a long number.
• Nobody except the bank can alter the number representing the value, without the ``bill'' losing its value.
• Send data safely over a public phone line or the Internet. An eavesdropper can not use, read or understand that data.
• Digital signatures.

This section introduces the basic concepts and underlying principles of cryptography. Sections 4.1 up to section 4.3 are taken from [Bla96]. Unfortunately, a profound mathematical knowledge is required to understand section 4.2 up to section 4.3. In case you would like to skip this part, the important concepts introduced are:

• RSA is a public key cryptographic algorithm. This means that everybody on the planet can encrypt a message to Alice with Alice's public key, but only Alice will be capable of decrypting the message, by using its secret key. It is important to note that there are 2 different keys that form a pair, one is public and is used to encrypt a message and the private key is kept secret, so only the receiver can decrypt the message. Every person has a unique keypair.
• DES is a private key algorithm. If Bob and Alice want to exchange encrypted information, they both need to possess one private key, which is kept secretly between them. This key is needed for both encryption and decryption of the message.
• Digital Signatures can be used to uniquely sign an electronic document. Similar to the RSA public key algorithm, but this time using the private key, Alice will compute a number representing the signature of the document, which depends on the document content as well as Alice's private key. Everybody can now verify, by using Alice's public key, that really Alice wrote the document and that the document was not altered by anybody after the computation of the signature.

• Encryption Systems
• Introduction to Number Theory
  • Congruences
  • The Greatest Common Divisor
  • Powers modulo a prime
  • Primitive roots
• Encryption based on powers and congruences
  • The Diffie-Hellman key exchange procedure
  • The Rivest-Shamir-Adleman public key system
  • A public key system as hard as factoring
• Product Ciphers
  • DES
• Message Digest and Digital Signatures
• Methods Of Attack
  • Differential Cryptanalysis