# Tag Info

7

Apparently, Schnorr was quite adamant, at that time, about the applicability of his patent to DSS. See this message and that one. These are from 1998, but the controversy had begun earlier; see for instance this bulletin from NIST, from late 1994, where references to it can be found in the "Patent Issues" section. Interestingly, NIST not only tried to avoid ...

7

On a general basis, you want to keep encryption and signature keys disjoint, because they tend to have distinct life cycles. In broad terms, an encryption key should be escrowed, because loss of the private key implies loss of the data which is encrypted relatively to the public key. However, a signature key must not be escrowed, since the proof value of a ...

6

Despite their theoretical security advantages, Schnorr signatures aren't very popular. Probably because they were patented. Since the patents expired in 2008 they might rise a bit in popularity. But probably only in the elliptic curve form, and not in finite fields. I don't know of any application actually using Schnorr signatures, but I know several that ...

4

The paper "On the Joint Security of Encryption and Signature in EMV" shows that ECIES and EC-Schnorr signatures can be used together without compromising security: In the random oracle model ECIES-KEM and EC-Schnorr are jointly secure if the gap-DLP problem and gap-DH problem are both hard Ed25519 is extremely similar to EC-Schnorr, and both ECIES ...

3

Yes, there are some examples of Schnorr signature in real world applications, although I can not provide you the names of the products. (Edit: OpenSSH contains a reference implementation in schnorr.c). The good feature of Schnorr signature is that by design it does not require lot of computations on the signer side. Therefore, you can use it even on a ...

3

First of all, while Schnorr Signatures are usually described that way, the two primes are not necessary for it to work. In principle, Schnorr works in any cyclic group. However, to achieve security we need that the discrete logarithm problem in that group is hard. So the reason for the choice of $q$ (which is the group order) is that DL is believed to be ...

3

As noted by Perseids in a comment to this answer, the formula $s = r + c + x$ would allow an adversary (who has completed the protocol once in the role as verifier with $P$ and already got one valid triplet $t_1,c_1,s_1$) to compute responses to any arbitrary challenge, simply using the formulas $t_2 = t_1$, $s_2 = s1 + c_2 - c_1$. Your other alternative $s ... 2 Schnorr can be proven zero knowledge when the challenge$e$is restricted to a small set (typically$0$and$1$). Recall that in the Schnorr protocol, the prover knows the logarithm$u$of$y$to base$g$. He chooses a random value$r$, computes$a = g^r$and sends$a$to the verifier. The verifier chooses a random challenge$e$from some set and sends it ... 1 It is important to consider the model in which security is proved. In this case, the attack proceeds in two phases: first a phase where the adversary as a verifier interacts with the honest prover, then a phase where the adversary as a prover interacts with an honest verifier. The adversary wins if the honest prover accepts. The paper proves, under ... 1 Given the definition of a zero-knowledge proof, it must satisfy three properties: Completeness: if the statement is true, the honest verifier (that is, one following the protocol properly) will be convinced of this fact by an honest prover. Soundness: if the statement is false, no cheating prover can convince the honest verifier that it is true, ... 1 You have to look at the response from the perspective of the verifier. This specific construction allows him/her to verify the$P$'s knowledge of$x$: If$P$could answer two different request$c_1,c_2$in step 2) then we would have$g^{s_1}=ty^{c_1}$and$g^{s_2}=ty^{c_2}$. Dividing one equation by the other we get$g^{s_1-s_2}=y^{c_1-c_2}\$. Let ...

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