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The security of RSA relies on the practical difficulty of factoring the product of two large prime numbers, the "factoring problem". Breaking RSA encryption is known as the RSA problem. Whether it is as difficult as the factoring problem is an open question. [3] There are no published methods to defeat the system if a large enough key is used.
In a key transport scheme, encrypted keying material that is chosen by the sender is transported to the receiver. Either symmetric key or asymmetric key techniques can be used in both schemes. [11] The Diffie–Hellman key exchange and Rivest-Shamir-Adleman (RSA) are the most two widely used key exchange algorithms. [12]
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 .
In cryptography, Optimal Asymmetric Encryption Padding (OAEP) is a padding scheme often used together with RSA encryption. OAEP was introduced by Bellare and Rogaway , [ 1 ] and subsequently standardized in PKCS#1 v2 and RFC 2437.
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] Examples of asymmetric systems include Diffie–Hellman key exchange, RSA (Rivest–Shamir–Adleman), ECC (Elliptic Curve Cryptography), and Post-quantum cryptography.
For example, the security available with a 1024-bit key using asymmetric RSA is considered approximately equal in security to an 80-bit key in a symmetric algorithm. [ 2 ] The actual degree of security achieved over time varies, as more computational power and more powerful mathematical analytic methods become available.
If they use a code, both will require a copy of the same codebook. If they use a cipher, they will need appropriate keys. If the cipher is a symmetric key cipher, both will need a copy of the same key. If it is an asymmetric key cipher with the public/private key property, both will need the other's public key.
Asymmetric keys differ from symmetric keys in that the algorithms use separate keys for encryption and decryption, while a symmetric key’s algorithm uses a single key for both processes. Because multiple keys are used with an asymmetric algorithm, the process takes longer to produce than a symmetric key algorithm would.