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Fig. 2 | BMC Bioinformatics

Fig. 2

From: A covert authentication and security solution for GMOs

Fig. 2

Proof that (K 1,K 2) is the encryption of the given message M under ElGamal. If the prover can successfully answer two distinct challenges c 1,c 2 with two acceptable answers s 1,s 2 then the verification step results in \( y^{s_{1}-s_{2}} = W^{c_{1}-c_{2}} \text {and} g^{s_{1}-s_{2}} = K_{1}^{c_{1}-c_{2}}\) (see [27]). Thus, if c 1c 2<p q a value r exists such that r=log y W=log g K 1=(s 1s 2)/(c 1c 2) mod p q . Consequently, W=y r, K 1=g r, and K 2=M y r. This proves that (K 1,K 2) is indeed an encryption of the message M under ElGamal that can be translated into a ZKPOK according to [20]

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