RSA – Public Key Cryptography Algorithm
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1. Introduction to Cryptography:
In the era of information technology, the possibility that the information stored in a person’s computer or the information that are being transferred through network of computers or internet being read by other people is very high. This causes a major concern for privacy, identity theft, electronic payments, corporate security, military communications and many others. We need an efficient and simple way of securing the electronic documents from being read or used by people other than who are authorized to do it. Cryptography is a standard way of securing the electronic documents.
1.1 Basic idea of Cryptography:
Basic idea of cryptography is to mumble-jumble the original message into something that is unreadable or to something that is readable but makes no sense of what the original message is. To retrieve the original message again, we have to transform the mumble-jumbled message back into the original message again.
1.2 Basic Terminologies used in Cryptography:
Data that can be read and understood without any special measures is called plaintext or cleartext. This is the message or data that has to be secured. The method of disguising plaintext in such a way as to hide its substance is called encryption. Encrypting plaintext results in unreadable gibberish called ciphertext. You use encryption to ensure that information is hidden from anyone for whom it is not intended, even those who can see the encrypted data. The process of reverting ciphertext to its original plaintext is called decryption.
Cryptography is the science of mathematics to “encrypt” and “decrypt” data. Cryptography enables us to store sensitive information or transmit it across insecure networks like Internet so that no one else other the intended recipient can read it. Cryptanalysis is the art of breaking Ciphers that is retrieving the original message without knowing the proper key. Cryptography deals with all aspects of secure messaging, authentication, digital signatures, electronic money, and other applications.
1.3 Cryptographic Algorithms:
Cryptographic algorithms are mathematical functions that are used in the encryption and decryption process. A cryptographic algorithms works in combination with a key (a number, word or phrase), to encrypt the plain text. Same plain text encrypts to different cipher texts for different keys. Strength of a cryptosystems depends on the strength of the algorithm and the secrecy of the key.
1.4 Two Kinds of Cryptography Systems:
There are two kinds of cryptosystems: symmetric and asymmetric. Symmetric cryptosystems use the same key (the secret key) to encrypt and decrypt a message, and asymmetric cryptosystems use one key (the public key) to encrypt a message and a different key (the private key) to decrypt it. Symmetric cryptosystems are also called as private key cryptosystems and asymmetric cryptosystems are also called as public key cryptosystems.
2. Overview of Private Key Cryptography:
In private-key cryptography, the sender and recipient agree beforehand on a secret private key. The plaintext is somehow combined with the key to create the ciphertext. The method of combination is such that, it is hoped, an adversary could not determine the meaning of the message without decrypting the message, for which he needs the key. The following diagram illustrates the encryption process:
The following diagram illustrates the decryption process:
To break a message encrypted with private-key cryptography, an adversary must either exploit a weakness in the encryption algorithm itself, or else try an exhaustive search of all possible keys (brute force method). If the key is large enough (e.g., 128 bits), such a search would take a very long time (few years), even with very powerful computers.
Private-key methods are efficient and difficult to break. However, one major drawback is that the key must be exchanged between the sender and recipient beforehand, raising the issue of how to protect the secrecy of the key. When the President of the United States exchanges launch codes with a nuclear weapons site under his command, the key is accompanied by a team of armed couriers. Banks likewise use high security in transferring their keys between branches. These types of key exchanges are not practical, however, for e-commerce between, say, amazon.com and a casual web surfer.
3. Overview of Public Key Cryptography:
Public Key cryptography uses two keys Private key (known only by the recipient) and a Public key (known to everybody). The public key is used to encrypt the message and then it is sent to the recipient who can decrypt the message using the private key. The message encrypted with the public key cannot be decrypted with any other key except for its corresponding private key. The following Diagram illustrates the encryption process in the public key cryptography
The following diagram illustrates the decryption process in the public key cryptography:
The public-key algorithm uses a one-way function to translate plaintext to ciphertext. Then, without the private key, it is very difficult for anyone (including the sender) to reverse the process (i.e., translate the ciphertext back to plaintext). A one-way function is a function that is easy to apply, but extremely difficult to invert. The most common one-way function used in public-key cryptography involves factoring very large numbers. The idea is that it is relatively easy to multiply numbers, even large ones, with a computer; however, it is very difficult to factor large numbers. The only known algorithms basically have to do a sort of exhaustive search (Does 2 go in to? Does 3? 4? 5? 6? and so on). With numbers 128 bits long, such a search requires performing as many tests as there are particles in the universe.
For instance, someone wishing to receive encrypted messages can multiply two very large numbers together. She keeps the two original numbers a secret, but sends the product to anyone who wishes to send her a message. The encryption/decryption algorithm is based upon combining the public number with the plaintext. Because it is a one-way function, the only way to reverse the process is to use one of the two original numbers. However, assuming the two original numbers are very large, their product is even bigger; it would be impractical for an adversary to try every possibility to determine what the two original numbers were.
4. RSA – Public Key Cryptography Algorithm:
4.1 Introduction to RSA Algorithm:

RSA is one of the most popular and successful public key cryptography algorithms. The algorithm has been implemented in many commercial applications. It is named after its inventor’s Ronald L. Rivest, Adi Shamir, and Leonard Adleman. They invented this algorithm in the year 1977. They utilized the fact that when prime numbers are chosen as a modulus, operations behave “conveniently”. They found that if we use a prime for the modulus, then raising a number to the power (prime 1) is 1.
RSA algorithm simply capitalizes on the fact that there is no efficient way to factor very large integers. The security of the whole algorithm relies on that fact. If someone comes up with an easy way of factoring a large number, then that’s the end of the RSA algorithm. Then any message encrypted with the RSA algorithm is no more secure.
4.2 RSA Algorithm:
The encryption and decryption in the RSA algorithm is done as follows. Before encryption and decryption is done, we have to generate the key pair and then those keys are used for encryption and decryption.
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hi! can I Ask what basic algorithm you would discuss in RSA enryption?
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