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The definition of security achieved by Cramer–Shoup is formally termed "indistinguishability under adaptive chosen ciphertext attack" (IND-CCA2).This security definition is currently the strongest definition known for a public key cryptosystem: it assumes that the attacker has access to a decryption oracle which will decrypt any ciphertext using the scheme's secret decryption key.
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.
Mathematically, a cryptosystem or encryption scheme can be defined as a tuple (,,,,) with the following properties.. is a set called the "plaintext space". Its elements are called plaintexts.; is a set called the "ciphertext space". Its elements are called ciphertexts.; is a set called the "key space". Its elements are called keys.; = {:} is a set of functions :. Its elements are called ...
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]
The advantage of asymmetric systems is that the public key can be freely published, allowing parties to establish secure communication without having a shared secret key. In practice, asymmetric systems are used to first exchange a secret key, and then secure communication proceeds via a more efficient symmetric system using that key. [14]
In cryptography, a known-key distinguishing attack is an attack model against symmetric ciphers, whereby an attacker who knows the key can find a structural property in cipher, where the transformation from plaintext to ciphertext is not random. There is no common formal definition for what such a transformation may be.
which takes as input a key K, of bit length k (called the key size), and a bit string P, of length n (called the block size), and returns a string C of n bits. P is called the plaintext, and C is termed the ciphertext. For each K, the function E K (P) is required to be an invertible mapping on {0,1} n. The inverse for E is defined as a function
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]