# Public-key cryptography

An asymmetric cryptosystem or public-key cryptosystem is a cryptographic method, as opposed to a symmetric cryptosystem need to know no common secret key, the communicating parties in the. A user generates a key pair here, the part from a secret (private key) and a non- secret part (public key) is. The public key allows anyone to encrypt data for the owner of the private key to check the digital signature or authenticate it. The private key enables its holder with the public key to decrypt encrypted data to generate digital signatures or to authenticate themselves.

- 5.1 Literature Used
- 5.2 Further Reading

## Principle

Are the theoretical basis for asymmetric cryptosystems trapdoor functions, ie functions that are easy to calculate, but without a secret (the " trapdoor " ) are practically impossible to invert. The public key is then a description of the function, the private key is the trapdoor. A prerequisite is of course that the private key from the public can not be calculated. So that the cryptographic system can be used, the public key must be known to the communication partner.

The decisive advantage of asymmetric methods is that they reduce the key distribution problem. For symmetric method, a key over a secure, ie tap-proof and tamper-resistant, channel must be replaced prior to use. Because the public key is not secret, need not be tap-proof method for asymmetric channel; it is only important that the public key can be assigned to the holder of the associated private key without any doubt. This can for example issue a digital certificate, which associates the public key the private key ( owner ) a trusted certification authority. Alternatively, can also be built without a central location by mutual certify keys a Web of Trust (Web of Trust).

### Security

For asymmetric security method, it is necessary that the various processes underlying one-way functions are virtually irreversible, since otherwise the secret could be calculated from the public key. The safety of all asymmetric cryptosystems always is therefore based on unproven assumptions, and in particular the assumption that P does not equal NP. In general, however, strongly suspected from these assumptions that they apply. The achievable the symmetrical one- time pad, information-theoretic security can be achieved with no asymmetric process because a correspondingly powerful adversary can always solve the underlying mathematical problem.

### Practical aspects

Asymmetric cryptographic systems have the advantage that they hold the secret to a minimum, because each user has to keep secret only his own private key. In contrast, each user has to keep secret all the keys for a symmetric cryptosystem, which an increasing number of users increases with complexity.

Compared with symmetric algorithms, the asymmetric algorithms work very slowly. In practice, this problem is circumvented in various ways. Encryption hybrid method may be employed in which only one symmetric key is encrypted using the asymmetric method, and the actual message with the symmetric key. For digital signatures only their hash value is signed instead of a rule in the message.

## History

The first step in the development of asymmetric methods made Ralph Merkle in 1974 with the eponymous Merkle's puzzle, which was not published until 1978. Under the influence of this work Whitfield Diffie and Martin Hellman developed the Diffie -Hellman key exchange in 1976. In the summer of 1975, Diffie and Hellman published an idea for asymmetric encryption, but without knowing an accurate method. The first asymmetric encryption method was developed in 1977 by Ronald L. Rivest, Adi Shamir and Leonard Adleman and M. named after them RSA method. After today's terminology, this process is a Falltürpermutation that can be used both for construction of encryption and signature method.

Regardless of the developments in scientific cryptology was in the early 1970s by three employees of the British Government Communications Headquarters, James H. Ellis, Clifford Cocks and Malcolm Williamson, both the later Diffie -Hellman key exchange as well as an RSA cryptosystem similar was developed asymmetric method, which does not however published for confidentiality reasons and also not applied for a patent.

## Application

" Asymmetric cryptosystem " is a generic term for public-key encryption scheme, public key authentication and digital signatures. These methods are used today ( OpenPGP, S / MIME) as well as in cryptographic protocols like SSH or SSL / TLS, for example, in e- mail traffic. Extensively used, for example, the https protocol, for secure communication of a Web browser to a server.

For encryption, the public key is applied to the text to be encrypted. The encrypted text is then decrypted by the key owner with the private key.

Digital signatures are used among other things for the secure processing of transactions on the Internet. Here they make it possible to verify the identity of the parties and the authenticity of the data exchanged (Electronic Signature ). For this purpose, usually a public-key infrastructure is still necessary to confirm the validity of the keys used by certificates.

To create a signature, a hash value of the message to be sent, is formed and signed with the private key. Message and signature are then sent to the receiver, the message itself need not be encrypted because this is a signature ( creation of integrity and authenticity ) and not encryption ( creating confidentiality).

To verify the signature of the received signature of the hash value is checked with the public key. If the verification is successful, it can be assumed that the message originates from the owner of the private key and that the message has not been tampered with during transmission.