Distributed key generation

Distributed key generation (DKG) is an encryption process in which multiple parties contribute to the calculation of a shared public and private key set. Unlike most public key encryption models, distributed key generation does not rely on Trusted Third Parties. Instead, the participation of a threshold of honest parties determines whether a key pair can be computed successfully. Distributed key generation prevents single parties from having access to a private key. The involvement of many parties requires Distributed key generation to ensure secrecy in the presence of malicious contributions to the key calculation. Distributed key generation (DKG) is an encryption process in which multiple parties contribute to the calculation of a shared public and private key set. Unlike most public key encryption models, distributed key generation does not rely on Trusted Third Parties. Instead, the participation of a threshold of honest parties determines whether a key pair can be computed successfully. Distributed key generation prevents single parties from having access to a private key. The involvement of many parties requires Distributed key generation to ensure secrecy in the presence of malicious contributions to the key calculation. Distributed Key Generation is commonly used to decrypt shared ciphertexts or create group digital signatures. Distributed key generation protocol was first specified by Torben Pedersen in 1991. This first model depended on the security of the Joint-Feldman Protocol for verifiable secret sharing during the secret sharing process. In 1999, Rosario Gennaro, Stanislaw Jarecki, Hugo Krawczyk, and Tal Rabin produced a series of security proofs demonstrating that Feldman verifiable secret sharing was vulnerable to malicious contributions to Pedersen's distributed key generator that would leak information about the shared private key. The same group also proposed an updated distributed key generation scheme preventing malicious contributions from impacting the value of the private key. The distributed key generation protocol specified by Gennaro, Jarecki, Krawczyk, and Rabin assumes that a group of players has already been established by an honest party prior to the key generation. It also assumes the communication between parties is synchronous. In many circumstances, a robust distributed key generator is necessary. Robust generator protocols can reconstruct public keys in order to remove malicious shares even if malicious parties still remain in the qualified group during the reconstruction phase. For example, robust multi-party digital signatures can tolerate a number of malicious users roughly proportionate to the length of the modulus used during key generation. Distributed key generators can implement a sparse evaluation matrix in order to improve efficiency during verification stages. Sparse evaluation can improve run time from O ( n t ) {displaystyle O(nt)} (where n {displaystyle n} is the number of parties and t {displaystyle t} is the threshold of malicious users) to O ( l o g 3 n ) {displaystyle O(log^{3}n)} . Instead of robust verification, sparse evaluation requires that a small set of the parties verify a small, randomly picked set of shares. This results in a small probability that the key generation will fail in the case that a large number of malicious shares are not chosen for verification. Distributed key generation and distributed key cryptography are rarely applied over the internet because of the reliance on synchronous communication. Distributed key cryptography is useful in key escrow services where a company can meet a threshold to decrypt a ciphertext version of private key. This way a company can require multiple employees to recover a private key without giving the escrow service a plaintext copy.