Theoretical Background on Cryptographic Primitives

This material intends to be a brief introduction to symmetric and asymmetric cryptographic primitives, pointing out some relevant design principles and security properties. Nonetheless, we call attention to the correct practical use and current standards. This material is intended in part to serve as theoretical background for practical laboratory works were you will get accustomed with the use of cryptographic functions in a more practical way, e.g., by using cryptographic libraries in some programming environment or by analysing protocols. 4 1. Theoretical background on cryptographic primitives 1 Theoretical background on cryptographic primitives We begin with symmetric cryptographic constructions, i.e., functions that rely on the same key for both en-cryption and decryption. The fact that the same key is used for both operations should not be interpreted in a strict way, the keys can actually be distinct but it is mandatory that one can be easily computed from the other (in contrast to assymetric primitives). We also group in this sections a class of primitives that do not require a key: hash functions. The reason for this is that they rely more or less on the same design principles and more, they form the basis of the keyed primitive called Message Authentication Code (MAC). A final subject that we encounter is the construction of some pseudo-random number generators, we stay here to a very shallow approach that exemplifies some basic constructions. Subsequently, we address asymmetric functions, that is, functions that rely on two distinct keys for encryption and decryption (or signing and verification). Since one of the keys (the decryption or signing key) is always kept secret this is also referred as the private key, while its counterpart is made publicly available, hence the name public key. Moreover, computing the private part of the key from the public part must be infeasible. A symmetric key cryptosystem, also referred to as symmetric encryption scheme, requires the existence of three algorithms: the encryption and decryption algorithms which are an immediate need, but also a key generation algorithm. While the key generation algorithm may do nothing more but picking at random a key, it is core to the security of the scheme and cannot be neglected in the definition (some key generation algorithms do more than picking keys at random as keys need to have a predefined format, this is more prominent in the case of public key primitives). Briefly, the symmetric encryption algorithm …