 Asymmetric encryption is a form of cryptosystem in which encryption and decryption are performed using the different keys one a public key and one a private key. It is also known as publickey encryption.
 Asymmetric encryption can be used for confidentiality, authentication, or both.
 The difficulty of attacking RSA is based on the difficulty of finding the prime factors of a composite number.
 In fact, the security of any encryption scheme depends on the length of the key and the computational work involved in breaking a cipher.
 PublicKey encryption techniques suffer from the computational overhead. This supports the need for using PrivateKey encryption.
Principles of PublicKey Cryptosystems

The concept of publickey cryptography evolved from an attempt to attack two of the most difficult problems associated with symmetric encryption:

Key distribution.

That was done using either:
 Two communicants already share a key, which somehow has been distributed to them.
 The use of a key distribution center.


Need for digital signature.
 That is, could a method be devised that would stipulate, to the satisfaction of all parties, that a digital message had been sent by a particular person? (authentication purpose).


Characteristics of publickey cryptosystem:
 It is computationally infeasible to determine the decryption key given only knowledge of the cryptographic algorithm and the encryption key.
 In RSA, either of the two related keys can be used for encryption, with the other used for decryption.
 261Essential steps for the encryption process.
 The disadvantage of this last approach is that the publickey algorithm, which is complex, must be exercised four times rather than two in each communication.

Classification of public key cryptosystem:
 Encryption/Decryption.
 Digital Signature.
 Key Exchange.

Requirements for publickey cryptography:
 It is computationally easy for a party B to generate a pair (public key PU_{b}, private key PR_{b}).
 It is computationally easy for a sender A, knowing the public key and the message to be encrypted, M, to generate the corresponding ciphertext: C = E(PU_{b}, M).
 It is computationally easy for the receiver B to decrypt the resulting ciphertext using the private key to recover the original message: M = D(PR_{b}, C) = D[PR_{b}, E(PU_{b}, M)].
 It is computationally infeasible for an adversary, knowing the public key, PU_{b}, to determine the private key, PR_{b}.
 It is computationally infeasible for an adversary, knowing the public key, PU_{b}, and a ciphertext, C, to recover the original message, M.
 The two keys can be applied in either order: M = D[PU_{b}, E(PR_{b}, M)] = D[PR_{b}, E(PU_{b}, M)].
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