Number of Keys Required- To use public key cryptography, Each individual requires two keys- one public key and one private key. 2 Requirements for public key cryptography . It is slower than symmetric key cryptography. 2. 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=EKU b (M). There are legitimate interoperability requirements for these. Public-key cryptography, or asymmetric cryptography, is an encryption scheme that uses two mathematically related, but not identical, keys - a public key and a private key. There are legitimate interoperability requirements for these. If you have 5 users, there are 5 Private keys and 5 Public keys. The key parameters given to the vendor or which will get into the POS are those in the public part of the RSA key: $(N,e)$. Requirements for Public-Key Cryptography  1. It is easy for a sender A, knowing the public key and message to be encrypt. •Requirements -It must be computationally easy to encipher or decipher a message given the appropriate key -It must be computationally infeasible to derive the private key from the public key -It must be computationally infeasible to determine the private key from a chosen plaintext attack Asymmetric Encryption Algorithms- Diffie and Hellman postulated this system without demonstrating that such algorithms exist. For n individuals to communicate, number of keys required = 2 x n = 2n keys. it establishes a communication which is one way where the center which is a public key user can encrypt the data in a message and can also check the authenticity of the digital signature where is on the second hand the recipient who is a private key user can decrypt the message. Requirement of Public key Cryptography 1. Secrecy of private keys. It is computationally easy for a party B to generate a pair of key (public key PUb, private key PRb). There are two specific requirements of key management for public key cryptography. Unlike symmetric key algorithms that rely on one key to both encrypt and decrypt, each key performs a unique function. 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 (PUb, M)  3. It is computationally easy for a party B to generate a pair [KU b, KR b].  2. To implement public-key encryption on a large scale, such as a secure Web server might need, requires a different approach. This is how asymmetric encryption or public-key cryptography works. These keys are mathematically linked. For every user, there is 1 Private key and 1 Public key. The Private key is used to decrypt messages from other users. It involves high computational requirements. This is where digital certificates come in. 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