Foundations of Smart Encryption

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We would like to lay the foundations for a new cryptographic primitive called Smart Encryption. Smart Encryption is the most advanced for of encryption and provides more a more fine-grained approach to cryptography. Classical asymmetric encryption meant that only the person who had the corresponding secret key could decrypt any ciphertext under their public key. This was extended by Attribute-Based Encryption, where any user who had the correct attributes could decrypt a ciphertext encrypted under their attributes. However, this is simply a linear predicate and we wish to go further. Taking inspiration from the concept of Smart Contracts from blockchain based cryptocurrencies, we propose Smart Encryption. The intuitive idea is that any user who fulfils a Smart Contract on a blockchain can then decrypt a ciphertext encrypted under this Smart Contract. Since there are Smart Contract languages that are Turing Complete, we are able to achieve far more than previous schemes. While this idea is intuitively clear, it is not obvious that this is secure. We aim to show how one can use this idea to build a secure Smart Encryption scheme. However, to do this, we would need the appropriate formalisations and definitions of both Smart Contract and Smart Encryptions, which we aim to establish. We will then further investigate if we can build these schemes with variants of well-known blockchains, or indeed even other primitives. We also hope to build candidate schemes for specific Smart Encryption applications, realising real-world scenarios, as well as new applications.