cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adv ...

the standard model is the model of computation in which the

adversary An adversary is generally considered to be a person, group, or force that opposes and/or attacks. Adversary may also refer to: * Satan ("adversary" in Hebrew), in Judeo-Christian religion Entertainment Fiction * Adversary (comics), villain fro ...

is only limited by the amount of time and computational power available. Other names used are bare model and plain model. Cryptographic schemes are usually based on complexity assumptions, which state that some problems, such as

factorization In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several ''factors'', usually smaller or simpler objects of the same kind ...

, cannot be solved in

polynomial time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...

. Schemes that can be proven secure using only complexity assumptions are said to be secure in the standard model. Security proofs are notoriously difficult to achieve in the standard model, so in many proofs, cryptographic primitives are replaced by idealized versions. The most common example of this technique, known as the random oracle model, involves replacing a

cryptographic hash function A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output ...

with a genuinely random function. Another example is the generic group model, where the adversary is given access to a randomly chosen encoding of a

group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic ide ...

, instead of the

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...

or elliptic curve groups used in practice. Other models used invoke trusted third parties to perform some task without cheating; for example, the

public key infrastructure A public key infrastructure (PKI) is a set of roles, policies, hardware, software and procedures needed to create, manage, distribute, use, store and revoke digital certificates and manage public-key encryption. The purpose of a PKI is to facili ...

(PKI) model requires a

certificate authority In cryptography, a certificate authority or certification authority (CA) is an entity that stores, signs, and issues digital certificates. A digital certificate certifies the ownership of a public key by the named subject of the certificate. Thi ...

, which if it were dishonest, could produce fake certificates and use them to forge signatures, or mount a

man in the middle attack In cryptography and computer security, a man-in-the-middle, monster-in-the-middle, machine-in-the-middle, monkey-in-the-middle, meddler-in-the-middle, manipulator-in-the-middle (MITM), person-in-the-middle (PITM) or adversary-in-the-middle (AiTM) ...

to read encrypted messages. Other examples of this type are the

common random string model Common may refer to: Places * Common, a townland in County Tyrone, Northern Ireland * Boston Common, a central public park in Boston, Massachusetts * Cambridge Common, common land area in Cambridge, Massachusetts * Clapham Common, originally co ...

, where it is assumed that all parties have access to some string chosen uniformly at random, and its generalization, the

common reference string model Common may refer to: Places * Common, a townland in County Tyrone, Northern Ireland * Boston Common, a central public park in Boston, Massachusetts * Cambridge Common, common land area in Cambridge, Massachusetts * Clapham Common, originally co ...

, where a string is chosen according to some other probability distribution. These models are often used for

non-interactive zero-knowledge proof Non-interactive zero-knowledge proofs are zero-knowledge proofs where information between a prover and a verifier can be authenticated by the prover, without revealing any of the specific information beyond the validity of the transaction itself. T ...

s (NIZK). In some applications, such as the Dolev–Dwork–Naor encryption scheme, it makes sense for a particular party to generate the common reference string, while in other applications, the common reference string must be generated by a trusted third party. Collectively, these models are referred to as models with special setup assumptions.

References

Theory of cryptography {{crypto-stub