Apr 16, 2018 In cryptography a ‘key’ is a piece of information used in combination with an algorithm (a ‘cipher’) to transform plaintext into ciphertext (encryption) and vice versa (decryption). A cipher can be ‘reciprocal’ if it is used for both encryption and decryption, or ‘non-reciprocal’ if a transformation to the key is required when using it in reverse.
Public Key Cryptography
Unlike symmetric key cryptography, we do not find historical use of public-key cryptography. It is a relatively new concept.
Symmetric cryptography was well suited for organizations such as governments, military, and big financial corporations were involved in the classified communication.
With the spread of more unsecure computer networks in last few decades, a genuine need was felt to use cryptography at larger scale. The symmetric key was found to be non-practical due to challenges it faced for key management. This gave rise to the public key cryptosystems.
The process of encryption and decryption is depicted in the following illustration −
The most important properties of public key encryption scheme are − https://skieywelove205.weebly.com/veeam-management-pack-for-veeam-backup-key-generator.html.
There are three types of Public Key Encryption schemes. We discuss them in following sections −
RSA Cryptosystem
This cryptosystem is one the initial system. It remains most employed cryptosystem even today. The system was invented by three scholars Ron Rivest, Adi Shamir, and Len Adleman and hence, it is termed as RSA cryptosystem.
We will see two aspects of the RSA cryptosystem, firstly generation of key pair and secondly encryption-decryption algorithms.
Generation of RSA Key Pair
Microsoft word 2010 activation key generator. Each person or a party who desires to participate in communication using encryption needs to generate a pair of keys, namely public key and private key. The process followed in the generation of keys is described below −
The Extended Euclidean Algorithm takes p, q, and e as input and gives d as output.
Example
An example of generating RSA Key pair is given below. (For ease of understanding, the primes p & q taken here are small values. Practically, these values are very high).
Encryption and Decryption
Once the key pair has been generated, the process of encryption and decryption are relatively straightforward and computationally easy.
Interestingly, RSA does not directly operate on strings of bits as in case of symmetric key encryption. It operates on numbers modulo n. Hence, it is necessary to represent the plaintext as a series of numbers less than n.
RSA Encryption
RSA Decryption
RSA Analysis
The security of RSA depends on the strengths of two separate functions. The RSA cryptosystem is most popular public-key cryptosystem strength of which is based on the practical difficulty of factoring the very large numbers. https://skieywelove205.weebly.com/generate-public-ssh-key-github.html.
If either of these two functions are proved non one-way, then RSA will be broken. In fact, if a technique for factoring efficiently is developed then RSA will no longer be safe.
The strength of RSA encryption drastically goes down against attacks if the number p and q are not large primes and/ or chosen public key e is a small number.
ElGamal Cryptosystem
Along with RSA, there are other public-key cryptosystems proposed. Many of them are based on different versions of the Discrete Logarithm Problem.
ElGamal cryptosystem, called Elliptic Curve Variant, is based on the Discrete Logarithm Problem. It derives the strength from the assumption that the discrete logarithms cannot be found in practical time frame for a given number, while the inverse operation of the power can be computed efficiently.
Let us go through a simple version of ElGamal that works with numbers modulo p. In the case of elliptic curve variants, it is based on quite different number systems.
Generation of ElGamal Key Pair
Each user of ElGamal cryptosystem generates the key pair through as follows −
Encryption and Decryption
The generation of an ElGamal key pair is comparatively simpler than the equivalent process for RSA. But the encryption and decryption are slightly more complex than RSA.
ElGamal Encryption
Suppose sender wishes to send a plaintext to someone whose ElGamal public key is (p, g, y), then −
ElGamal Decryption
ElGamal Analysis
In ElGamal system, each user has a private key x. and has three components of public key − prime modulus p, generator g, and public Y = gx mod p. The strength of the ElGamal is based on the difficulty of discrete logarithm problem.
The secure key size is generally > 1024 bits. Today even 2048 bits long key are used. On the processing speed front, Elgamal is quite slow, it is used mainly for key authentication protocols. Due to higher processing efficiency, Elliptic Curve variants of ElGamal are becoming increasingly popular.
Elliptic Curve Cryptography (ECC)
Elliptic Curve Cryptography (ECC) is a term used to describe a suite of cryptographic tools and protocols whose security is based on special versions of the discrete logarithm problem. It does not use numbers modulo p.
ECC is based on sets of numbers that are associated with mathematical objects called elliptic curves. There are rules for adding and computing multiples of these numbers, just as there are for numbers modulo p.
ECC includes a variants of many cryptographic schemes that were initially designed for modular numbers such as ElGamal encryption and Digital Signature Algorithm.
It is believed that the discrete logarithm problem is much harder when applied to points on an elliptic curve. This prompts switching from numbers modulo p to points on an elliptic curve. Also an equivalent security level can be obtained with shorter keys if we use elliptic curve-based variants.
The shorter keys result in two benefits −
These benefits make elliptic-curve-based variants of encryption scheme highly attractive for application where computing resources are constrained.
RSA and ElGamal Schemes – A Comparison
Let us briefly compare the RSA and ElGamal schemes on the various aspects.
Key generation is the process of generating keys in cryptography. A key is used to encrypt and decrypt whatever data is being encrypted/decrypted.
A device or program used to generate keys is called a key generator or keygen.
Generation in cryptography[edit]
Modern cryptographic systems include symmetric-key algorithms (such as DES and AES) and public-key algorithms (such as RSA). Symmetric-key algorithms use a single shared key; keeping data secret requires keeping this key secret. Public-key algorithms use a public key and a private key. The public key is made available to anyone (often by means of a digital certificate). A sender encrypts data with the receiver's public key; only the holder of the private key can decrypt this data.
Since public-key algorithms tend to be much slower than symmetric-key algorithms, modern systems such as TLS and SSH use a combination of the two: one party receives the other's public key, and encrypts a small piece of data (either a symmetric key or some data used to generate it). The remainder of the conversation uses a (typically faster) symmetric-key algorithm for encryption.
Computer cryptography uses integers for keys. In some cases keys are randomly generated using a random number generator (RNG) or pseudorandom number generator (PRNG). A PRNG is a computeralgorithm that produces data that appears random under analysis. PRNGs that use system entropy to seed data generally produce better results, since this makes the initial conditions of the PRNG much more difficult for an attacker to guess. Another way to generate randomness is to utilize information outside the system. veracrypt (a disk encryption software) utilizes user mouse movements to generate unique seeds, in which users are encouraged to move their mouse sporadically. In other situations, the key is derived deterministically using a passphrase and a key derivation function.
Many modern protocols are designed to have forward secrecy, which requires generating a fresh new shared key for each session.
Classic cryptosystems invariably generate two identical keys at one end of the communication link and somehow transport one of the keys to the other end of the link.However, it simplifies key management to use Diffie–Hellman key exchange instead.
The simplest method to read encrypted data without actually decrypting it is a brute-force attack—simply attempting every number, up to the maximum length of the key. Therefore, it is important to use a sufficiently long key length; longer keys take exponentially longer to attack, rendering a brute-force attack impractical. Currently, key lengths of 128 bits (for symmetric key algorithms) and 2048 bits (for public-key algorithms) are common.
Generation in physical layer[edit]Wireless channels[edit]
A wireless channel is characterized by its two end users. By transmitting pilot signals, these two users can estimate the channel between them and use the channel information to generate a key which is secret only to them.[1] The common secret key for a group of users can be generated based on the channel of each pair of users.[2]
Optical fiber[edit]
A key can also be generated by exploiting the phase fluctuation in a fiber link.[clarification needed]
See also[edit]Key Generation Function Encryption G N K Auto Truck In Metairie
References[edit]
Key Generation Function Encryption G N Karaoke
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