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I believe a zero knowledge proof that $-1$ is a quadratric nonresidue would accomplish that. If we know that $n$ has two prime factors, and that $n \equiv 1 \pmod{4}$, then $n$ is either a product of two primes both $1 \bmod 4$, or two primes both $3 \bmod 4$. If it were the former, then $-1$ is a QR modulo $p$, and $-1$ is a QR modulo $q$, and hence $-1$ ...


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This has some issues, with both soundness and zero-knowledge. The issue with zero-knowledge is that an eavesdropper who knows $L$ and overhears legitimate traffic can compromise the secret quite easily. While factoring is hard, taking a GCD is very efficient. That means that given $M=pr$ and $L=pq$, an eavesdropper Eve can efficiently compute $\gcd(M,L)=p$. ...



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