This work describes a class of Algorithm Substitution Attack (ASA) generically targeting the receiver of a communication between two parties. Our work provides a unified framework that applies to any scheme where a secret key is held by the receiver; in particular, message authentication schemes (MACs), authenticated encryption (AEAD) and public key encryption (PKE). Our unified framework brings together prior work targeting MAC schemes (FSE’19) and AEAD schemes (IMACC’19); we extend prior work by showing that public key encryption may also be targeted. ASAs were initially introduced by Bellare, Paterson and Rogaway in light of revelations concerning mass surveillance, as a novel attack class against the confidentiality of encryption schemes. Such an attack replaces one or more of the regular scheme algorithms with a subverted version that aims to reveal information to an adversary (engaged in mass surveillance), while remaining undetected by users. Previous work looking at ASAs against encryption schemes can be divided into two groups. ASAs against PKE schemes target key generation by creating subverted public keys that allow an adversary to recover the secret key. ASAs against symmetric encryption target the encryption algorithm and leak information through a subliminal channel in the ciphertexts. We present a new class of attack that targets the decryption algorithm of an encryption scheme for symmetric encryption and public key encryption, or the verification algorithm for an authentication scheme. We present a generic framework for subverting a cryptographic scheme between a sender and receiver, and show how a decryption oracle allows a subverter to create a subliminal channel which can be used to leak secret keys. We then show that the generic framework can be applied to authenticated encryption with associated data, message authentication schemes, public key encryption and KEM/DEM constructions. We consider practical considerations and specific conditions that apply for particular schemes, strengthening the generic approach. Furthermore, we show how the hybrid subversion of key generation and decryption algorithms can be used to amplify the effectiveness of our decryption attack. We argue that this attack represents an attractive opportunity for a mass surveillance adversary. Our work serves to refine the ASA model and contributes to a series of papers that raises awareness and understanding about what is possible with ASAs.