Googling for NP-complete and Public key encryption finds False positives ... that are actually insecure. This cartoonish pdf appears to show a public key encyption algorithm based on the minimium dominating set problem. Reading further it then admits to lying that the algorithm is secure ... the underlying problem is NP-Complete but it's use in the PK algorithm does not preserve the difficulty.
Another False positive Google find: Cryptanalysis of the Goldreich-Goldwasser-Halevi cryptosystem from Crypto '97. From the abstract:
At Crypto '97, Goldreich, Goldwasser and Halevi proposed a public-key cryptosystem based on the closest vector problem in a lattice, which is known to be NP-hard. We show that there is a major flaw in the design of the scheme which has two implications: any ciphertext leaks information on the plaintext, and the problem of decrypting ciphertexts can be reduced to a special closest vector problem which is much easier than the general problem.
