In the area of white-box cryptography implementations, many existing protections are susceptible to attacks derived from physical cryptanalysis, which can be applied with minimal human effort and no prior design knowledge. The absence of a clear and comprehensive security model hinders the development of effective countermeasures against these attacks. We introduce the Haystack ciphers, a formal model for the security of white-box countermeasures against such attacks. In this model, the countermeasures are represented simply as symmetric-key encryption schemes. We show that their chosen-plaintext (IND-CPA) security is closely related to the resistance of the countermeasures against computational trace-based attacks. Similarly, their chosen-ciphertext (IND-CCA) security is closely associated with the resistance against fault injection attacks in the white-box model. Secure Haystack ciphers constitute the next formal milestone for advancing white-box designs and countermeasures, the minimal requirement that is not currently clearly achieved but is plausibly feasible with available tools. We review the white-box literature with respect to our model and bridge the gap between white-box and fault attacks, which are very powerful but were only partially considered in the white-box literature so far. We study known fault protections from the physical cryptography literature and present new fault attacks in the white-box setting, which raises the need and shapes the requirements for future secure countermeasures against fault attacks.