# Is Guillou-Quisquater existentially unforgeable against adaptive message attack under a random oracle model?

First of all, the Guillou-Quisquater digital signature scheme is:

Note everything is $\bmod n$. Message is denoted by $m$.

Private key: $s$

Public key: Hash function $H$, $e$, $L=s^e\bmod n$

To sign: Alice chooses random $r$. Computes $c=H(m||x)$ with $x=r^e\bmod n$; $y=r\cdot s^c\bmod n$; send Bob $x$ and $y$.

To verify: Bob computes $c=H(m||x)$ and accept if $y^e \equiv x\cdot L^c\pmod n$.

I'm wondering what the strongest known security of this is, in particular the question in the title. If not, what's the best research that's been done on this scheme?

I've scoured the internet for such a proof, but I can't find anything. I was also told by my supervisor that if I could find such a proof for El Gamal it might be easily adaptable, so that would also be much appreciated. Thanks!

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Question may or may not get a better answer at crypto.stackexchange.com . – Qiaochu Yuan Feb 22 '13 at 21:42
It's been up there for a day and hasn't got much activity, so I thought I'd ask it here, too. – Samuel Reid Feb 22 '13 at 21:48