THRESHOLD CRYPTOSYSTEM, CORRESPONDING ELECTRONIC DEVICES AND COMPUTER PROGRAM PRODUCTS

摘要

In one embodiment, it is proposed a method for encrypting a plaintext M ∈ , where is a DDH-hard group of prime order p. The method is executed by an electronic device, and is remarkable in that it comprises:
obtaining a public key PK=(, N, g, h, X, H, G) where N is a RSA module, elements g, h are random elements belonging to said group , X=gxhy ∈ , where elements x, y are random values from a ring p, and H, G are hash functions;obtaining two random elements r, s, each element belonging to the ring p;determining a vector being (C0, C1, C2)=(M.Xr, gr, hr);determining a proof π that logg(C1)=logh(C2), said proof comprising two components c, t′, with c=H(C0, C1, C2, gs, hs) and t′=s+c.r mod p;delivering a ciphertext C=(C0, C1, C2, π)=(C0, C1, C2, c, t′) ∈ 3×p2.

主权项

1. A method for encrypting a plaintext M ∈, where is a DDH-hard group of prime order p, the method being executed by an electronic device, and comprising:
obtaining a public key PK=(, N, g, h, X, H, G) where N is a RSA module, elements g, h are random elements belonging to said group , X=gxhy ∈ , where elements x, y are random values from a ring p, and H, G are hash functions; obtaining two random elements r, s, each element belonging to the ring p; determining a vector being (C0, C1, C2)=(M.Xr, gr, hr); determining a proof π that logg(C1)=logh(C2), said proof comprising two components c, t′, with c=H(C0, C1, C2, gs, hs) and t′=s+c.r mod p; delivering a ciphertext C=(C0, C1, C2, π)=(C0, C1, C2, c, t′) ∈ 3×p2.