zkp demystify zokrates
pipelinesource filean example, square.zok The keyword private signals that we do not want to reveal this input, but still prove that we know its value. compile after compile, it generates b…
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cryptography
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groth16 demystified
1. IntroductionGoldwasser, Micali and Rackoff [GMR89] introduced zero-knowledge proofs that enable a prover to convince a verifier that a statement is true without revealing anything else. …
Read articlezkp how and why it works
The medium of proof: PolynomialIf a prover claims to know some polynomial (no matter how large its degree is) that the verifier also knows, they can follow a simple protocol to verify the s…
Read articleelliptic curve paring
introductionPairings allow you to check certain kinds of more complicated equations on elliptic curve points — for example, if \(P = G * p\), \(Q = G * q\) and \(R = G * r\), you can check …
Read articlezkp a brief understanding (1)
introductionzk-SNARKs cannot be applied to any computational problem directly; rather, you have to convert the problem into the right “form” for the problem to operate on. The form is calle…
Read articlecryptography (4) digital signature
Elgamal Digital Signature SchemeThe Elgammal signature scheme is based on the difficulty of computing discrete logarithms. Unlike RSA, where encryption and digital signature are almoste ide…
Read articlecryptography (3) elliptic curve
elliptic curve definitionfor cryptographic use, we need to conside the curve not over the real numbers but over a finite field. the most popular fields GF(p), where all arithmetic is perfor…
Read articlecryptography (2) RSA cryptosystem
introductionthe security of RSA relies on the difficulty of factoring a product of two large primes(the integer factorization problem). it is firstly presented in 1978 in [1]. Euclidean Alg…
Read articlecryptography (1) group & field
Groupa group is a set of elements \( G \) together with an operation \( \circ \). a group has the following properties the group operation \( \circ \) is closed. that is, for all \( a,b, \i…
Read articlepaillier encryption
fundamentals fundamental theorem of arighmeticthe fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer …
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