An asymmetric-key cryptosystem was published in 1976 by Whitfield Diffie and Martin Hellman who, influenced by Ralph Merkle's work on public-key distribution, disclosed a method of public-key agreement.

Merkle-Hellman is an asymmetric-key cryptosystem, meaning that for communication, two keys are required: a public key and a private key.

No asymmetric-key algorithms with this property are known ; elliptic curve cryptography comes the closest with an effective security of roughly half its key length.

The goal in finding these " hard " instances is for their use in public key cryptography systems, such as the Merkle-Hellman knapsack cryptosystem.

Key escrow ( also known as a “ fair ” cryptosystem ) is an arrangement in which the keys needed to decrypt encrypted data are held in escrow so that, under certain circumstances, an authorized third party may gain access to those keys.

In 1979, Michael O. Rabin published a related cryptosystem that is provably secure, at least as long as the factorization of the public key remains difficult-it remains an assumption that RSA also enjoys this security.

Most are used in hybrid cryptosystems for reasons of efficiency-in such a cryptosystem, a shared secret key (" session key ") is generated by one party, and this much briefer session key is then encrypted by each recipient's public key.

An example is PGP released as source code, and generally regarded ( when properly used ) as a military-grade cryptosystem.

In cryptography, Kerckhoffs's principle ( also called Kerckhoffs's Desiderata, Kerckhoffs's assumption, axiom, or law ) was stated by Auguste Kerckhoffs in the 19th century: A cryptosystem should be secure even if everything about the system, except the key, is public knowledge.

A backdoor in a computer system ( or cryptosystem or algorithm ) is a method of bypassing normal authentication, securing remote access to a computer, obtaining access to plaintext, and so on, while attempting to remain undetected.

The ElGamal cryptosystem is usually used in a hybrid cryptosystem.

I. e., the message itself is encrypted using a symmetric cryptosystem and ElGamal is then used

The Cramer – Shoup cryptosystem is secure under chosen ciphertext attack assuming DDH holds for.

Malleability is often an undesirable property in a general-purpose cryptosystem, since it allows an attacker to modify the contents of a message.

In the RSA cryptosystem, a plaintext is encrypted as, where is the public key.

In the ElGamal cryptosystem, a plaintext is encrypted as, where is the public key.

For example, the El Gamal cryptosystem is semantically secure under chosen-plaintext attack, but this semantic security can be trivially defeated under a chosen-ciphertext attack.

When a cryptosystem is vulnerable to chosen-ciphertext attack, implementers must be careful to avoid situations in which an adversary might be able to decrypt chosen-ciphertexts ( i. e., avoid providing a decryption oracle ).

A better approach is to use a cryptosystem which is provably secure under chosen-ciphertext attack, including ( among others ) RSA-OAEP, Cramer-Shoup and many forms of authenticated symmetric encryption.

Ciphertext is generally the easiest part of a cryptosystem to obtain and therefore is an important part of cryptanalysis.

In 1985, Elgamal published a paper titled A Public key Cryptosystem and A Signature Scheme based on discrete Logarithms in which he proposed the design of the ElGamal discrete log cryptosystem and of the ElGamal signature scheme.

These names were used by Ron Rivest in the 1978 Communications of the ACM article presenting the RSA cryptosystem, and in A Method for Obtaining Digital Signatures and Public-Key Cryptosystems published April 4, 1977, revised September 1, 1977 as technical Memo LCS / TM82.

In 2008, Bernstein, Lange and Peters described a practical attack on the original McEliece cryptosystem, based on finding low-weight code words using an algorithm published by Jacques Stern in 1989.

In cryptography, Merkle's Puzzles is an early construction for a public-key cryptosystem, a protocol devised by Ralph Merkle in 1974 and published in 1978.

Note that any published ( or otherwise accessible ) random data table is unsuitable for cryptographic purposes since the accessibility of the numbers makes them effectively predictable, and hence their effect on a cryptosystem is also predictable.

The ElGamal cryptosystem, invented by Taher ElGamal.

The Merkle – Hellman knapsack cryptosystem was one of the earliest public key cryptosystems invented by Ralph Merkle and Martin Hellman in 1978.

The Paillier cryptosystem, named after and invented by Pascal Paillier in 1999, is a probabilistic asymmetric algorithm for public key cryptography.

In cryptography, a timing attack is a side channel attack in which the attacker attempts to compromise a cryptosystem by analyzing the time taken to execute cryptographic algorithms.

Attempts to break a cryptosystem by deceiving or coercing people with legitimate access are not typically called side-channel attacks: see social engineering and rubber-hose cryptanalysis.

In all cases, the underlying principle is that physical effects caused by the operation of a cryptosystem ( on the side ) can provide useful extra information about secrets in the system, for example, the cryptographic key, partial state information, full or partial plaintexts and so forth.

In cryptography, the McEliece cryptosystem is an asymmetric encryption algorithm developed in 1978 by Robert McEliece.

Instead, cryptosystem engineers must ensure that devices ' power variations do not reveal information usable by adversaries.

The notion of security of a cryptosystem is meaningful only with respect to particular attacks ( usually presumed to be carried out by particular sorts of adversaries ).

The underlying cryptosystem is IND-CPA ( and thus semantically secure under chosen plaintext attack ) if the adversary cannot determine which of the two messages was chosen by the oracle, with probability significantly greater than ( the success rate of random guessing ).

It has been largely superseded by the Miller – Rabin primality test, but has great historical importance in showing the practical feasibility of the RSA cryptosystem.

The Kushilevitz and Ostrovsky protocol is based on the Goldwasser – Micali cryptosystem while the protocol by Lipmaa is based on the Damgård – Jurik cryptosystem.

Developed by Ronald Cramer and Victor Shoup in 1998, it is an extension of the Elgamal cryptosystem.

Kleptographic attacks can be constructed as a cryptotrojan that infects a cryptosystem and opens a backdoor for the attacker, or can be implemented by the manufacturer of a cryptosystem.

Knapsack problems appear in real-world decision-making processes in a wide variety of fields, such as finding the least wasteful way to cut raw materials, selection of capital investments and financial portfolios, selection of assets for asset-backed securitization, and generating keys for the Merkle – Hellman knapsack cryptosystem.

* Merkle – Hellman knapsack cryptosystem

He co-invented the Merkle – Hellman knapsack cryptosystem, Merkle – Damgård construction, and invented Merkle trees.

* Merkle – Hellman knapsack cryptosystem