0/ What are Non-Interactive Zero-Knowledge Proofs (NIZKPs)? ๐งโโ๏ธโจ
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1/ First of all, what are zero knowledge proofs (ZKPs) in general?
ZKPs are a #cryptographic technique that allow individuals or entities to prove to another that a statement is true, without revealing any information beyond the validity of the statement.
2/ One variant of ZKPs are non-interactive zero-knowledge proofs (NIZKPs), which don't require interaction between the certifier and verifier.
3/ They rely on a common reference string (CRS), which is generated in a trusted setup ceremony that is publicly verifiable.
4/ The CRS serves as the basis for the NIZKPs and allows for the verification of statements without any interaction.
5/ However, the reliance on a CRS for NIZKPs raises concerns about the security of the system, as the CRS must be generated in a trusted setup ceremony to ensure the integrity of the system.
6/ The trusted setup ceremony involves generating a CRS that consists of cryptographic parameters used to generate the NIZKPs used in the system.
7/ One challenge in the design of NIZKPs is finding the balance between security, efficiency, and the size of the CRS.
8/ Ideally, the CRS should be small and secure. Techniques like universal hash functions and the Fiat-Shamir transformation have been proposed to achieve this balance.
9/ Despite the challenges and limitations, NIZKPs remain an active area of research and are expected to play a significant role in the #blockchain ecosystem in the coming years.
10/ Stay tuned for follow-up threads investigating zk-proofs in more depth! ๐งโโ๏ธโจ
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0/ What is Homomorphic Encryption (HE)? ๐งโโ๏ธโจ
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1/ HE is a cryptographic tool that allows you to perform certain types of computations directly on the homomorphically encrypted ciphertext, generating the same results as if you performed the operations on the plaintext.
2/ There are two types of HE: partially homomorphic encryption (PHE) & fully homomorphic encryption (FHE). PHE allows for a limited number of operations on the ciphertext (e.g. addition or multiplication), while FHE allows for any computation to be performed on the ciphertext.
1/ Ring signatures are a privacy technology that aims to keep user's identities private when making (signing) transactions in public #blockchain networks
2/ In ring signature schemes, a group of users, called the "ring," can sign a message anonymously using their personal secret keys.
1/ Hash pointers are a type of pointer that point to a specific location in a data structure, specifically a block in a blockchain. They are an essential part of the structure and security of blockchains.
2/ To understand hash pointers, it's helpful to know what pointers are more generally. Pointers are variables that store the address of another variable, allowing you to indirectly access and manipulate the value of a variable by referring to its memory location.
1/ A hash function is a function that converts data into a fixed-size output, also known as a hash.
2/ Cryptographic hash functions are a type of hash function that are designed to be one-way functions, meaning it is computationally infeasible to find the original input from the hash output.
0/ What is the Elliptic Curve Digital Signature Algorithm (ECDSA)? ๐งโโ๏ธโจ
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1/ The Elliptic Curve Digital Signature Algorithm (ECDSA) is a digital signature scheme that is based on the algebraic structure of elliptic curves. It is widely used in many #cryptographic systems, including $ETH, $BTC, and other blockchains.
2/ In the #Ethereum blockchain, ECDSA is used to sign transactions and messages to prove the authenticity of the sender.