
## 1. Public Key Encryption

1. #### Problem 1.1.

[Amit Sahai] Provide a public key encryption scheme using only a one-way function given as a circuit.
1. Remark. It is known that if the One-Way Function is given as a black box then this is provably impossible.
• Remark. If we can provably show obfuscation then this is possible. This was elaborated on in Rachel Lin’s talk.
• #### Problem 1.2.

[Sanjam Garg] Construct a PKE scheme from hardness of discrete-log problem in a specific group.
• #### Problem 1.3.

[Dan Boneh] Explore security of obfuscation constructions that use current candidate multilinear maps.
1. Remark. [Garg] One example of this would be the "MDDH without zeroes" assumption that will be described in detail in Zhandry’s talk.
• #### Problem 1.4.

[Rachel Lin] What is the security of d-local pseudorandom number generators? This means that each bit of the string depends on at most d bits of the seed.
1. Remark. [Lin] If $d \le 4$ then these are broken, but very little is known for $d \ge 5$.
• #### Problem 1.5.

[Rachel Lin] Can we construct local pseudorandom number generators from algebraic methods?

Cite this as: AimPL: Constructing cryptographic multilinear maps, available at http://aimpl.org/cryptomultilin.