Recent times have seen fantastic advances in the general area of "computing on encrypted data". Of particular importance, is the fast-growing area of functional encryption (FE). Functional encryption is a generalization of public key encryption which allows tremendous flexibility and control in learning information from encrypted data. In functional encryption, a user's secret key corresponds to some function f, denoted by SK f . The ciphertext corresponds to some input x chosen from the domain of f. Given SK f and ciphertext CT x , the user may run the decryption procedure to learn f(x). Security of the system guarantees that nothing beyond f(x) can be learned from CT x and SK f . We will study how lattices can be used for the construction of functional encryption schemes. Of special interest to us will be the "learning with errors" (LWE) assumption, which enjoys strong worst case guarantees that makes it very desirable for the construction of cryptographic primitives. We will review known constructions of functional encryption from LWE, including FE for point functions or "identity based encryption", FE for linear functions or "inner product" encryption" and FE for more general circuits or "attribute based encryption for circuits". We will also discuss some open problems in this fast growing area.
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