In the last days I started to look at the Cryptography's Theory again. I guess it's an interesting subject for anyone involved in the IT world: for developers and security specialists understand some key concepts is essential to manage particular scenarios. Yesterday there was the Google's announce about the first SHA-1 collision : hash functions will be in one of the articles I currently have in mind. I'll try to write about Cryptographic pills in episodes and I hope you'll appreciate the subject. Let's start!In the beginning
Until the late 20th century Cryptography was considered an art form. Constructing good codes, breaking existing ones and be able to understand the algorithm behind a code relies on creativity and personal skill. There wasn't so much theory around the subject. With the Cryptography's spread in areas different from Military and Defense the whole picture radically changed: a rich theory and rigorous study made the Cryptography an applied Science. Today Cryptography is everywhere.Private-key Encryption
Cryptography was historically concerned with secret communications. In the past we were talking about ciphers, today we talk about encryption schemes: the concepts are the same. Two parts want to communicate in a secret manner and they decide to use a particular encryption scheme. An assumption in this scenario is that the communicating parties must have a way to initially sharing a key in a secret manner.A private-key Encryption scheme is based on three algorithms : A Key-generation algorithm Gen is a probabilistic algorithm that outputs a key k chosen according to some distribution that is determined by the scheme. The Encryption Algorithm Enc takes as input a key k and a plaintext message m and outputs a cyphertext c . We denote by the encryption of the plaintext m using the key k
in the following way
$$Enc_k(m)$$The Decryption Algorithm Dec takes as input a key k and a cyphertext message c and outputs a plaintext m . We denote by the decryption of the cyphertext c using the key k
in the following way
$$Dec_k(c)$$The set of all possible keys generated by the Gen algorithm is denoted as K and it is called the Key Space. The set of all "legal" messages (supported by the Encryption Algorithm Enc ) is denoted as M and it is called the Message Space. Since any Cyphertext is obtained by encrypting some plaintext under some key, the sets K and M together define a set of all possible Cyphertexts denoted with C . Kerckhoffs's principle
From the definitions above it's clear that if an eavesdropping adversary knows the Dec algorithm and the chosen key k , he will be able to decrypt the messages exchanged between the two communicating parts. The key must be secret and this is a fundamental point, but do we need to maintain secret the Encryption and Decryption algorithms too? In the late 19th century August Kerckhoffs gave his opinion:The cipher method must not be required to be secret, and it must be able to fall in the hands of the enemy without incovenience
It's something related to Open Source and Open Standards too. Today any Encryption Scheme is usually demanded to be made public. The main reasons for this can be summarized in the following points:The public scrutiny make the design stronger. If flaws exist it can be found by someone hacking on the scheme Public design enables the establishment of standards.
The Kerckhoffs' principle is obvious, but in same cases it was ignored with disastrous results. Only publicly tried and tested algorithm should be used by organizations. Kerchoffs was one of the first person with an Open vision about these things.What's next
In the next articles I would like to talk about the theory behind the Cryptographic schemes strenght. How we can say a scheme is secure? What are the attack scenarios? What is the definition of a secure scheme? Introduction to Modern Cryptography, Chapman & Hall/Crc, Jonathan Katz, Yehuda Lindell, Chapter 1.