While interesting, it's not really applicable to cryptography utilized by Monero as the trapdoored one is specific to 1024-bit prime numbers.
Monero utilizes elliptic curve cryptography, more specifically the curve Ed25519, which has been time tested as it has been pointed out here. The DH scheme is indeed used, but it's not the same kind, but the one adapted for elliptic curve cryptography - Diffie-Hellman (ECDH). See also here for a nice explanation.
Also, when EC is used, the key sizes are smaller when compared directly with other schemes. Our curve has 128 bits of security, which would be equivalent to 3072-bit key if compared against integer factorization based scheme.
From the CryptoNote whitepaper:
We propose a solution allowing a user to publish a single address and
receive unconditional unlinkable payments. The destination of each
CryptoNote output (by default) is a public key, derived from
recipient’s address and sender’s random data
First, the sender performs a Diffie-Hellman exchange to get a shared
secret from his data and half of the recipient’s address. Then he
computes a one-time destination key, using the shared secret and the
second half of the address. Two different ec-keys are required from
the recipient for these two steps, so a standard CryptoNote address is
nearly twice as large as a Bitcoin wallet address. The receiver also
performs a Diffie-Hellman exchange to recover the corresponding secret
From here we can see that in order to break this, someone would first have to find a weakness in Ed25519 curve, and then find a way to make the users generate some of those weak keys (public view key, in Monero context). Considering this, I think we're pretty safe considering that the keys generated are entirely random (or derived from random).