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In cryptography, a zero-knowledge proof is a protocol in which one party (the prover) can convince another party (the verifier) that some given statement is true, without conveying to the verifier any information beyond the mere fact of that statement's truth. [1]
Most non-interactive zero-knowledge proofs are based on mathematical constructs like elliptic curve cryptography or pairing-based cryptography, which allow for the creation of short and easily verifiable proofs of the truth of a statement. Unlike interactive zero-knowledge proofs, which require multiple rounds of interaction between the prover ...
In cryptography, the Fiat–Shamir heuristic is a technique for taking an interactive proof of knowledge and creating a digital signature based on it. This way, some fact (for example, knowledge of a certain secret number) can be publicly proven without revealing underlying information.
The hybrid argument is extensively used in cryptography. Some simple proofs using hybrid arguments are: If one cannot efficiently predict the next bit of the output of some number generator, then this generator is a pseudorandom number generator (PRG). [3] We can securely expand a PRG with 1-bit output into a PRG with n-bit output. [4]
The first mention of Alice and Bob in the context of cryptography was in Rivest, Shamir, and Adleman's 1978 article "A method for obtaining digital signatures and public-key cryptosystems." [ 2 ] They wrote, "For our scenarios we suppose that A and B (also known as Alice and Bob) are two users of a public-key cryptosystem".
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields , such as the RSA cryptosystem and ElGamal cryptosystem .
They are typically used when the proof cannot be carried out using weaker assumptions on the cryptographic hash function. A system that is proven secure when every hash function is replaced by a random oracle is described as being secure in the random oracle model, as opposed to secure in the standard model of cryptography.
In cryptography, a proof of knowledge is an interactive proof in which the prover succeeds in 'convincing' a verifier that the prover knows something. What it means for a machine to 'know something' is defined in terms of computation. A machine 'knows something', if this something can be computed, given the machine as an input.