Mathematical Methods of Cryptography

Threshold Diffie — Hellman Protocol

D. N. Kolegov^a, Yu. R. Khalniyazova<sup>b

a</sup> Tomsk State University
^b BI.ZONE

Abstract: We introduce a threshold elliptic curve Diffie — Hellman (ECDH) scheme which allows to generate and store private keys in a distributed way so that the private key doesn't have to be recomputed in order to perform a cryptographic operation. The main idea is to use a dealerless DKG scheme based on Feldman's VSS to generate shares of a private key without ever having the private key computed. To complete a cryptographic operation, a shareholder performs some computations on the share and sends the resulting piece to the other participating shareholders. Combined together, those values give the expected result of the cryptographic operation without ever giving a clue on the share values themselves.

Keywords: threshold cryptography, threshold Diffie — Hellman, ECDH.

UDC: 004.056.55

DOI: 10.17223/2226308X/14/17