In cryptography, GMR is a digital signature algorithm named after its inventors Shafi Goldwasser, Silvio Micali and Ron Rivest.
As with RSA the security of the system is related to the difficulty of factoring very large numbers. But, in contrast to RSA, GMR is secure against adaptive chosen-message attacks , which is the currently accepted security definition for signature schemes— even when an attacker receives signatures for messages of his choice, this does not allow them to forge a signature for a single additional message.
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security.
RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem, one of the oldest, that is widely used for secure data transmission. The acronym "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government Communications Headquarters (GCHQ) by the English mathematician Clifford Cocks. That system was declassified in 1997.
A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature on a message gives a recipient confidence that the message came from a sender known to the recipient.
Ronald Linn Rivest is a cryptographer and computer scientist whose work has spanned the fields of algorithms and combinatorics, cryptography, machine learning, and election integrity. He is an Institute Professor at the Massachusetts Institute of Technology (MIT), and a member of MIT's Department of Electrical Engineering and Computer Science and its Computer Science and Artificial Intelligence Laboratory.
A chosen-ciphertext attack (CCA) is an attack model for cryptanalysis where the cryptanalyst can gather information by obtaining the decryptions of chosen ciphertexts. From these pieces of information the adversary can attempt to recover the hidden secret key used for decryption.
Articles related to cryptography include:
An adaptive chosen-ciphertext attack is an interactive form of chosen-ciphertext attack in which an attacker first sends a number of ciphertexts to be decrypted chosen adaptively, and then uses the results to distinguish a target ciphertext without consulting the oracle on the challenge ciphertext. In an adaptive attack, the attacker is further allowed adaptive queries to be asked after the target is revealed. It is extending the indifferent (non-adaptive) chosen-ciphertext attack (CCA1) where the second stage of adaptive queries is not allowed. Charles Rackoff and Dan Simon defined CCA2 and suggested a system building on the non-adaptive CCA1 definition and system of Moni Naor and Moti Yung.
The Rabin cryptosystem is a family of public-key encryption schemes based on a trapdoor function whose security, like that of RSA, is related to the difficulty of integer factorization.
Shafrira Goldwasser is an Israeli-American computer scientist and winner of the Turing Award in 2012. She is the RSA Professor of Electrical Engineering and Computer Science at Massachusetts Institute of Technology; a professor of mathematical sciences at the Weizmann Institute of Science, Israel; the director of the Simons Institute for the Theory of Computing at the University of California, Berkeley; and co-founder and chief scientist of Duality Technologies.
In cryptography, a semantically secure cryptosystem is one where only negligible information about the plaintext can be feasibly extracted from the ciphertext. Specifically, any probabilistic, polynomial-time algorithm (PPTA) that is given the ciphertext of a certain message , and the message's length, cannot determine any partial information on the message with probability non-negligibly higher than all other PPTA's that only have access to the message length. This concept is the computational complexity analogue to Shannon's concept of perfect secrecy. Perfect secrecy means that the ciphertext reveals no information at all about the plaintext, whereas semantic security implies that any information revealed cannot be feasibly extracted.
Probabilistic encryption is the use of randomness in an encryption algorithm, so that when encrypting the same message several times it will, in general, yield different ciphertexts. The term "probabilistic encryption" is typically used in reference to public key encryption algorithms; however various symmetric key encryption algorithms achieve a similar property, and stream ciphers such as Freestyle which are inherently random. To be semantically secure, that is, to hide even partial information about the plaintext, an encryption algorithm must be probabilistic.
Silvio Micali is an Italian computer scientist, professor at the Massachusetts Institute of Technology and the founder of Algorand, a proof-of-stake blockchain cryptocurrency protocol. Micali's research at the MIT Computer Science and Artificial Intelligence Laboratory centers on cryptography and information security.
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.
In cryptography, the Full Domain Hash (FDH) is an RSA-based signature scheme that follows the hash-and-sign paradigm. It is provably secure in the random oracle model. FDH involves hashing a message using a function whose image size equals the size of the RSA modulus, and then raising the result to the secret RSA exponent.
In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: no efficient algorithm can distinguish between a function chosen randomly from the PRF family and a random oracle. Pseudorandom functions are vital tools in the construction of cryptographic primitives, especially secure encryption schemes.
In the mathematical and computer science field of cryptography, a group of three numbers (x,y,z) is said to be a claw of two permutations f0 and f1 if
In a cryptographic digital signature or MAC system, digital signature forgery is the ability to create a pair consisting of a message, , and a signature, , that is valid for , but has not been created in the past by the legitimate signer. There are different types of forgery.
Cryptography, or cryptology, is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
