# Friday February 20 at MSR

Please join us for the next installment of Crypto Day on Friday, February 20 at Microsoft Research, New England.

**Location and Arrival Instructions:**

Microsoft New England Research and Development Center

One Memorial Drive, Cambridge MA 02142

Upon arrival, be prepared to show a picture ID and sign the Building Visitor Log when approaching the Lobby Floor Security Desk. Alert them to the name of the event, and ask them to direct you to the appropriate floor. The talks will be held the First Floor Conference Center, in the Horace Mann Conference Room. Detailed guidance on directions, via car or public transportation, is available here. Parking will be available for the on-site parking garage for $27/day.

### Program:

9:30 – 10:00. | Introduction/Coffee |

10:00 – 11:00. |
Tal Malkin, Columbia
The Power of Negations in Cryptography |

11:30 – 12:30. | Rachel Lin, USCBConstant-Round Concurrent Zero-knowledge from Indistinguishability Obfuscation |

12:30 – 2:00. | Lunch (provided) |

2:00 – 3:00. | Alessandra Scaffuro, BU and NortheasternGarbled RAM From One-Way Functions |

3:30 – 4:30. | Henry Corrigan-Gibbs, StanfordBuilding Anonymous Messaging Systems that ‘Hide the Metadata’ |

### Abstracts:

**Speaker: Tal Malkin **

**Title: The Power of Negations in Cryptography **

The study of monotonicity and negation complexity for Boolean functions has been prevalent in complexity theory as well as in computational learning theory, but little attention has been given to it in the cryptographic context. Recently, Goldreich and Izsak (2012) have initiated a study of whether cryptographic primitives can be monotone, and showed that one-way functions can be monotone (assuming they exist), but a pseudorandom generator cannot.

In this work, we start by filling in the picture and proving that many other basic cryptographic primitives cannot be monotone. We then initiate a quantitative study of the power of negations, asking how many negations are required. We provide several lower bounds, some of them tight, for various cryptographic primitives and building blocks including one-way permutations, pseudorandom functions, small-bias generators, hard-core predicates, error-correcting codes, and randomness extractors. Among our results, we highlight the following.

i) Unlike one-way functions, one-way permutations cannot be monotone.

ii) We prove that pseudorandom functions require log n−O(1) negations (which is optimal up to the additive term).

iii) Error-correcting codes with optimal distance parameters require log n−O(1) negations (again, optimal up to the additive term).

iv) We prove a general result for monotone functions, showing a lower bound on the depth of any circuit with t negations on the bottom that computes a monotone function f in terms of the monotone circuit depth of f. This result addresses a question posed by Koroth and Sarma (2014) in the context of the circuit complexity of the Clique problem.

Joint work with Siyao Guo, Igor Carboni Oliveira, and Alon Rosen.

**Speaker: Rachel Lin **

**Title: Constant-Round Concurrent Zero-knowledge from Indistinguishability Obfuscation **

We present a constant-round concurrent zero-knowledge protocol for NP. Our protocol relies on the existence of families of collision-resistant hash functions, one-way permutations, and indistinguishability obfuscators for P/poly (with slightly super-polynomial security).

**Speaker: Alessandra Scafuro**

**Title: Garbled RAM From One-Way Functions **

Yao’s garbled circuit construction is a fundamental construction in cryptography and recent efficiency optimizations have brought it much closer to practice. However these constructions work only for circuits and garbling a RAM program involves the inefficient process of first converting it into a circuit. Towards avoiding this inefficiency, Lu and Ostrovsky [Eurocrypt 2013] introduced the notion of “garbled RAM” as a method to garble RAM programs directly. It can be seen as a RAM analogue of Yao’s garbled circuits such that, the size of the garbled program and the time it takes to create and evaluate it, is proportional only to the running time on the RAM program rather than its circuit size.

Known realizations of this primitive, either rely on stronger computational assumptions such as the existence of

Identity-Based Encryption, or rely on one-way functions only but do not achieve the aforementioned efficiency [Gentry, Halevi, Lu, Ostrovsky, Raykova and Wichs, EUROCRYPT 2014].

In this work we provide the first construction with strictly poly-logarithmic overhead in both space and time based only on the minimal assumption

that one-way functions exist.

Join work with Sanjam Garg, Steve Lu and Rafail Ostrovsky.

**Speaker:
Henry Corrigan-Gibbs **

**Title: Building Anonymous Messaging Systems that ‘Hide the Metadata’**

Encryption can protect the contents of a message being sent over an open network. In many situations, though, hiding the contents of a communication is not enough: parties to a conversation want to conceal the fact that they ever communicated. In this talk, I will explain how anonymity-preserving messaging systems can help ‘hide the metadata’ pertaining to a conversation and I will survey the state of the art in anonymous messaging protocols.

A limitation of existing protocols is that they exhibit computation and communication costs that scale linearly with the number of users (i.e., the anonymity set size) or they require expensive zero-knowledge proofs. In recent work, we have designed Riposte, a new system for anonymous messaging that applies private-information-retrieval and secure multi-party computation techniques to circumvent these limitations.

An implementation and experimental evaluation of Riposte demonstrates that, for latency-tolerant applications, the system can provide near-ideal anonymity for groups of millions of users—two orders of magnitude more than current systems support. I will conclude the talk with a discussion of open problems and directions for future work.

Joint work with: Dan Boneh and David Mazières