Cryptography (from Greek κρυπτός, kryptos, "hidden, secret"; and γράφω,gráphō, "I write") is the practice and study of hiding information. In other words cryptography is the practice of converting a plaintext to an unreadable string of characters. A cryptographic process uses a cipher (or cypher), which is a pair of algorithms that create the encryption and the reversing decryption. The detailed operation of a cipher is controlled both by the algorithm and in each instance by a key. This is a secret parameter (ideally known only to the communicants) for a specific message exchange context. In modern times cryptography is used broadly in the computer science and electronics areas, especially in financial transfer protocols, ATM’s and secure-transmission communication software.

Modern cryptography is based mostly on the huge computational power, in the binary representation of the data and in complex algorithms that can be processed only by machines. Cryptography can be divided in symmetric key and asymmetric key cryptography. Symmetric cryptography uses the same key for encryption and decryption. In this simple case the receiver must own the key in order to read the encrypted content. Asymmetric key cryptography uses a pair of keys, related to one another by advanced mathematical relations. One of the keys is the private one used to encrypt the data and the other one is called the public one and is used only to decrypt it. Example:

The message “ALGEBRA” has relative character numbers: 00 11 06 04 01 17 00. If we encrypt these numbers with the secret key and the RSA algorithm we would have: 00 11 18 31 01 29 00. The same way if we would own the relative public key for the encrypted message: 13 31 11 11 05 25 08 29 30 09 28 05 18 29 00 09 13 31 29 24 07 we would have the decrypted one: "Hello Cryptographers".

For curiosity: The process in the first case goes something like this, two prime numbers p=3, q=11, n=p*q=33, e=3; =0 (mod33) =11 (mod 33) =18 (mod33), =31 (mod33) =1 (mod33), =29 (mod33), would be encrypted as:  00 11 18 31 01 29 00.

Regarding the electronic signatures technology, cryptography is essential. A message or document goes through an algorithm, outputting its fingerprint (or HASH). After this we can generate the electronic signature by encrypting the HASH with the private key. Then we would have a cryptographic envelope containing: the original document, the electronic signature and qualified certificate which holds the public key. The receiver decrypts the signature with the public key, producing in this case the original HASH, comparing the HASH with another one he himself generates. If the HASH’s are identical the receiver can prove the integrity of the sent document.

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PKI – is the abbreviation for Public Key Infrastructure: a set of hardware, software, people, policies, and procedures needed to create, manage, distribute, use, store, and revoke digital certificates for a certain number of users. Many governments and organizations have built different types of PKI systems, but by infrastructure we must understand the baseline framework used in such cases in the financial transfer systems, server protection and private networks etc....