number theory
2
INTRODUCTION TO
CRYPTOGRAPHY
2.1 WHAT IS CRYPTOGRAPHY?
The word cryptography comes from the Greek words κρυπτο (hidden or secret) and γραφη
(writing). Oddly enough, cryptography is the art of secret writing. More generally, people think of cryptography as the art of mangling information into apparent unintelligibility in a manner allowing a secret method of unmangling. The basic service provided by cryptography is the ability to send information between participants in a way that prevents others from reading it. In this book we will concentrate on the kind of cryptography that is based on representing information as numbers and mathematically manipulating those numbers. This kind of cryptography can provide other services, such as
•
integrity checking—reassuring the recipient of a message that the message has not been altered since it was generated by a legitimate source
•
authentication—verifying someone’s (or something’s) identity
But back to the traditional use of cryptography. A message in its original form is known as plaintext or cleartext. The mangled information is known as ciphertext. The process for producing ciphertext from plaintext is known as encryption. The reverse of encryption is called decryption.
plaintext
encryption
ciphertext
decryption
plaintext
While cryptographers invent clever secret codes, cryptanalysts attempt to break these codes.
These two disciplines constantly try to keep ahead of each other. Ultimately, the success of the cryptographers rests on the
39
40
INTRODUCTION TO CRYPTOGRAPHY
2.1.1
Fundamental Tenet of Cryptography
If lots of smart people have failed to solve a problem, then it probably won’t be solved (soon).
Cryptographic systems tend to involve both an algorithm and a secret value. The secret value is known as the key. The reason for having a key in addition to an algorithm is that it is difficult to keep devising new algorithms that will allow
INTRODUCTION TO
CRYPTOGRAPHY
2.1 WHAT IS CRYPTOGRAPHY?
The word cryptography comes from the Greek words κρυπτο (hidden or secret) and γραφη
(writing). Oddly enough, cryptography is the art of secret writing. More generally, people think of cryptography as the art of mangling information into apparent unintelligibility in a manner allowing a secret method of unmangling. The basic service provided by cryptography is the ability to send information between participants in a way that prevents others from reading it. In this book we will concentrate on the kind of cryptography that is based on representing information as numbers and mathematically manipulating those numbers. This kind of cryptography can provide other services, such as
•
integrity checking—reassuring the recipient of a message that the message has not been altered since it was generated by a legitimate source
•
authentication—verifying someone’s (or something’s) identity
But back to the traditional use of cryptography. A message in its original form is known as plaintext or cleartext. The mangled information is known as ciphertext. The process for producing ciphertext from plaintext is known as encryption. The reverse of encryption is called decryption.
plaintext
encryption
ciphertext
decryption
plaintext
While cryptographers invent clever secret codes, cryptanalysts attempt to break these codes.
These two disciplines constantly try to keep ahead of each other. Ultimately, the success of the cryptographers rests on the
39
40
INTRODUCTION TO CRYPTOGRAPHY
2.1.1
Fundamental Tenet of Cryptography
If lots of smart people have failed to solve a problem, then it probably won’t be solved (soon).
Cryptographic systems tend to involve both an algorithm and a secret value. The secret value is known as the key. The reason for having a key in addition to an algorithm is that it is difficult to keep devising new algorithms that will allow