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In an asymmetric key algorithm (e.g., RSA), there are two different keys: a public key and a private key. The public key is published, thereby allowing any sender to perform encryption. The private key is kept secret by the receiver, thereby allowing only the receiver to correctly perform decryption.
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. [1] [2] Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions.
RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem, one of the oldest widely used for secure data transmission.The initialism "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977.
The length of the encryption key is an indicator of the strength of the encryption method. [29] For example, the original encryption key, DES (Data Encryption Standard), was 56 bits, meaning it had 2^56 combination possibilities. With today's computing power, a 56-bit key is no longer secure, being vulnerable to brute force attacks. [30]
With public-key systems, one can maintain secrecy without a master key or a large number of keys. [72] But, some algorithms like BitLocker and VeraCrypt are generally not private-public key cryptography. For example, Veracrypt uses a password hash to generate the single private key. However, it can be configured to run in public-private key ...
Thus public key systems require longer key lengths than symmetric systems for an equivalent level of security. 3072 bits is the suggested key length for systems based on factoring and integer discrete logarithms which aim to have security equivalent to a 128 bit symmetric cipher.” [9]
This concern is particularly serious in the case of public key cryptography, where any party can encrypt chosen messages using a public encryption key. In this case, the adversary can build a large "dictionary" of useful plaintext/ciphertext pairs, then observe the encrypted channel for matching ciphertexts.
More specifically, the RSA problem is to efficiently compute P given an RSA public key (N, e) and a ciphertext C ≡ P e (mod N). The structure of the RSA public key requires that N be a large semiprime (i.e., a product of two large prime numbers), that 2 < e < N, that e be coprime to φ(N), and that 0 ≤ C < N.