Principles of public key cryptosystems

The principles of public key cryptosystems are based on the concept of asymmetric cryptography, where two mathematically related keys are used: a public key and a private key. Here are the key principles of public key cryptosystems:

1. Key Pair Generation: A user generates a pair of mathematically related keys: a public key and a private key. The private key is kept secret, while the public key is freely distributed to others.
2. Encryption: The public key is used to encrypt plaintext into ciphertext. Anyone with access to the public key can perform this encryption. The ciphertext can only be decrypted using the corresponding private key.
3. Decryption: Decryption is performed using the private key associated with the public key used for encryption. Only the holder of the private key can decrypt the ciphertext and retrieve the original plaintext.
4. Key Distribution: Public keys are distributed widely, while private keys are kept secret. Public keys can be shared openly, posted on public key servers, or exchanged through secure channels.
5. Security through Mathematical Complexity: The security of public key cryptosystems relies on the mathematical complexity of certain algorithms, making it computationally infeasible to derive the private key from the public key. For example, in RSA, the difficulty of factoring large prime numbers forms the basis of its security.
6. Digital Signatures: Public key cryptosystems enable the creation and verification of digital signatures. The sender signs a message using their private key, and the recipient can verify the signature using the sender’s public key. This provides authenticity, integrity, and non-repudiation of the message.
7. Key Exchange: Public key cryptosystems facilitate secure key exchange between parties that have not previously shared a secret key. Methods like Diffie-Hellman key exchange allow two parties to agree on a shared secret key over an insecure channel.
8. Certificate Authorities (CAs): Public key infrastructures often involve Certificate Authorities, trusted entities that issue digital certificates. These certificates bind public keys to the identity of individuals or organizations, providing trust and authentication.
9. Hybrid Cryptosystems: Public key cryptosystems are often used in combination with symmetric key encryption for efficiency and performance. In a hybrid cryptosystem, a symmetric session key is generated for encrypting the data, and the session key is then encrypted using the recipient’s public key. This combines the security of public key encryption with the speed of symmetric key encryption.

Public key cryptosystems provide secure communication, data protection, authentication, and digital signatures in various applications. They play a vital role in secure internet communication, secure email, secure transactions, secure file transfer, and many other cryptographic protocols.

Public key cryptography has become an essential means of providing confidentiality, especially through its need of key distribution, where users seeking private connection exchange encryption keys. It also features digital signatures which enable users to sign keys to check their identities.

The approach of public key cryptography derivative from an attempt to attack two of the most complex problems related to symmetric encryption. The first issue is that key distribution. Key distribution under symmetric encryption needed such as −

• that two communicants already shared a key, which somehow has been shared to them.
• the need of a key distribution center.

Public key Cryptosystem − Asymmetric algorithms depends on one key for encryption and a distinct but related key for decryption. These algorithms have the following characteristics which are as follows −

• It is computationally infeasible to decide the decryption key given only information of the cryptographic algorithm and the encryption key.
• There are two related keys such as one can be used for encryption, with the other used for decryption.

A public key encryption scheme has the following ingredients which are as follows −

• Plaintext − This is the readable message or information that is informer into the algorithm as input.
• Encryption algorithm − The encryption algorithm performs several conversion on the plaintext.
• Public and Private keys − This is a set of keys that have been selected so that if one can be used for encryption, and the other can be used for decryption.
• Ciphertext − This is scrambled message generated as output. It based on the plaintext and the key. For a given message, there are two specific keys will create two different ciphertexts.
• Decryption Algorithm − This algorithm get the ciphertext and the matching key and create the original plaintext.

The keys generated in public key cryptography are too large including 512, 1024, 2048 and so on bits. These keys are not simply to learn. Thus, they are maintained in the devices including USB tokens or hardware security modules.

The major issue in public key cryptosystems is that an attacker can masquerade as a legal user. It can substitutes the public key with a fake key in the public directory. Moreover, it can intercepts the connection or alters those keys.

Public key cryptography plays an essential role in online payment services and ecommerce etc. These online services are ensure only when the authenticity of public key and signature of the user are ensure.

The asymmetric cryptosystem should manage the security services including confidentiality, authentication, integrity and non-repudiation. The public key should support the security services including non-repudiation and authentication. The security services of confidentiality and integrity considered as an element of encryption process completed by private key of the user.