The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively.
Public-key cryptography, or asymmetric cryptography, is a cryptographic system which uses pairs of keys: public keys, and private keys. The generation of such key pairs depends on cryptographic algorithms which are based on mathematical problems termed one-way functions. Effective security requires keeping the private key private; the public key can be openly distributed without compromising security.
Adi Shamir is an Israeli cryptographer. He is a co-inventor of the Rivest–Shamir–Adleman (RSA) algorithm, a co-inventor of the Feige–Fiat–Shamir identification scheme, one of the inventors of differential cryptanalysis and has made numerous contributions to the fields of cryptography and computer science.
The Merkle–Hellman knapsack cryptosystem was one of the earliest public key cryptosystems. It was published by Ralph Merkle and Martin Hellman in 1978. A polynomial time attack was published by Adi Shamir in 1984. As a result, the cryptosystem is now considered insecure.
In cryptography, the RSA problem summarizes the task of performing an RSA private-key operation given only the public key. The RSA algorithm raises a message to an exponent, modulo a composite number N whose factors are not known. Thus, the task can be neatly described as finding the eth roots of an arbitrary number, modulo N. For large RSA key sizes, no efficient method for solving this problem is known; if an efficient method is ever developed, it would threaten the current or eventual security of RSA-based cryptosystems—both for public-key encryption and digital signatures.
Kleptography is the study of stealing information securely and subliminally. The term was introduced by Adam Young and Moti Yung in the Proceedings of Advances in Cryptology—Crypto '96. Kleptography is a subfield of cryptovirology and is a natural extension of the theory of subliminal channels that was pioneered by Gus Simmons while at Sandia National Laboratory. A kleptographic backdoor is synonymously referred to as an asymmetric backdoor. Kleptography encompasses secure and covert communications through cryptosystems and cryptographic protocols. This is reminiscent of, but not the same as steganography that studies covert communications through graphics, video, digital audio data, and so forth.
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete. In his 1972 paper, "Reducibility Among Combinatorial Problems", Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete to show that there is a polynomial time many-one reduction from the boolean satisfiability problem to each of 21 combinatorial and graph theoretical computational problems, thereby showing that they are all NP-complete. This was one of the first demonstrations that many natural computational problems occurring throughout computer science are computationally intractable, and it drove interest in the study of NP-completeness and the P versus NP problem.
Merkle and Merckle are surnames of German origin. They may refer to:
The Goldwasser–Micali (GM) cryptosystem is an asymmetric key encryption algorithm developed by Shafi Goldwasser and Silvio Micali in 1982. GM has the distinction of being the first probabilistic public-key encryption scheme which is provably secure under standard cryptographic assumptions. However, it is not an efficient cryptosystem, as ciphertexts may be several hundred times larger than the initial plaintext. To prove the security properties of the cryptosystem, Goldwasser and Micali proposed the widely used definition of semantic security.
The Naccache–Stern Knapsack cryptosystem is an atypical public-key cryptosystem developed by David Naccache and Jacques Stern in 1997. This cryptosystem is deterministic, and hence is not semantically secure. While unbroken to date, this system also lacks provable security.
Rabin is a Hebrew surname. It originates from the Hebrew word rav meaning Rabbi, or from the name of the specific Rabbi Abin. The most well known bearer of the name was Yitzhak Rabin, prime minister of Israel and Nobel Peace prize Laureate.
Jacques Stern is a cryptographer, currently a professor at the École Normale Supérieure, where he is Director of the Computer Science Laboratory. He received the 2006 CNRS Gold medal. His notable work includes the cryptanalysis of numerous encryption and signature schemes, the design of the Pointcheval–Stern signature algorithm, the Naccache–Stern cryptosystem and Naccache–Stern knapsack cryptosystem, and the block ciphers CS-Cipher, DFC, and xmx. He also contributed to the cryptanalysis of the SFLASH signature scheme.
David Naccache is a cryptographer, currently a professor at the École normale supérieure and a member of its Computer Laboratory. He was previously a professor at Panthéon-Assas University. He received his Ph.D. in 1995 from the École nationale supérieure des télécommunications. Naccache's most notable work is in public-key cryptography, including the cryptanalysis of digital signature schemes. Together with Jacques Stern he designed the similarly named but very distinct Naccache-Stern cryptosystem and Naccache-Stern knapsack cryptosystem.
Knapsack is a locality of Hürth, Rhine-Erft district, North Rhine-Westphalia, Germany.
Cryptography, or cryptology, is the practice and study of techniques for secure communication in the presence of third parties called adversaries. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages; various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics. Applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
In cryptography, the Niederreiter cryptosystem is a variation of the McEliece cryptosystem developed in 1986 by Harald Niederreiter. It applies the same idea to the parity check matrix, H, of a linear code. Niederreiter is equivalent to McEliece from a security point of view. It uses a syndrome as ciphertext and the message is an error pattern. The encryption of Niederreiter is about ten times faster than the encryption of McEliece. Niederreiter can be used to construct a digital signature scheme.
The following outline is provided as an overview of and topical guide to cryptography:
Knapsack Cryptosystems are cryptosystems which security is based on the hardness of solving the knapsack problem. They remain quite unpopular because simple versions of these algorithms have been broken for several decades. However that type of cryptosystem is a good candidate for post-quantum cryptography.
