Jonathan KatzProfessor, Computer Science, UMD

Director, Maryland Cybersecurity Center

Secure Computation

MathematicsComplexity

theory

Cryptography

Cybersecurity

Science of Cybersecurity

Cryptography

Importance of cryptography

• Cryptography is a key component in many (all?) security solutions

• The cryptographic approach provides a way to move beyond the “design-break-patch” cycle• Define (even informally) what you want to achieve• State your assumptions explicitly• Prove that your construction achieves your goal

• Cryptography is a nucleus for cybersecurity research– Foundations for a “secure networked world” … with end-

to-end formal guarantees

Scope of modern cryptography

“Foundations”:Number theory,

block ciphers, hardware, …

“Primitives”:encryption/signature schemes, …

“Protocols”:key exchange,

secure distributed computing, …

“Systems”:DB privacy,

voting, bitcoin,trust/reputation, …

Secure computation

A dilemma

Can Alice and Bob determine their shared interests, without revealing any interests they don’t have in common?

Bob Alice

Hi…

What are yourhobbies?

…, bird watching, …

bird watching?!

Secure two-party computation

Bob Alice

bird watching!!

Let’s run a protocol!

hobby 1hobby 2

…hobby n

hobby 1hobby 2

…hobby n

{…,bird watching,…} {…,bird watching,…}

Hi…

What are yourhobbies?

Secure two-party computation

Are any passengerson the no-fly list?

Person 1Person 2

…Person n

Passenger 1Passenger 2

…Passenger n

Natural question I

• How can these parties (who don’t trust each other) “securely” perform the computation?– While preserving secrecy of their inputs (to the

extent possible)– While ensuring correctness of outputs

• Techniques/ideas from crypto, programming languages, distributed computing

Natural question II

• Why are these questions important?

• Candidate application domains– [DoD/IC]

Secure search, cloud storage– [OFR, Treasury]

More transparency, better regulation– Industry interest

Howcan parties securely compute f ?

A protocol is secure if it emulates the use of a trusted party

In particular, this implies:• The computed results are correct• Parties’ inputs remain private (except for what is

implied by the outputs)• Parties’ inputs are chosen independently• And more…

Threat models

• Semi-honest (honest-but-curious) adversaries– Adversary follows the protocol faithfully, but tries

to learn information from the protocol execution– A reasonable threat model in some settings• Trusted parties under legal/policy constraints• Software attestation, auditing, etc.

• Malicious adversaries– May behave arbitrarily; still cannot violate security

guarantees

Is secure computation possible?

Protocols for secure computation of any function, with security against

malicious behavior of any number of parties,have been known since the ’80s

These protocols are generic, and work for any function represented

as a boolean circuit

Using generic secure 2PC

PSSW (2009)

Protocol computing f

Express f in suitable representation

Express f in high-level language

Fairplay (2004)TASTY (2010)

Is secure computation practical?

• The general perception in the ’80s/’90s was that garbled circuits were hopelessly inefficient– Need to express f as a boolean circuit– Circuits get big quickly! (>230 gates)

– Symmetric-key operations linear in the circuit size

– Public-key operations linear in the input length

Performance (-2010)

Fairplay04 [PSSW09] TASTY100

500

1000

1500

2000

2500

3000

3500

4000

4500

gates/sec

Fairplay04 [PSSW09] TASTY100

5

10

15

20

25

Max gates (log scale)

Using generic secure 2PC

Protocol computing f

Express f in suitable representation

Express f in high-level language

Efficient implementation

Protocol optimizationsBetter crypto primitives

Notable improvements

• Protocol level– OT extension [IKNP03]– Better garbling (free-XOR [KS08], row reduction

[PSSW09], half gates [ZRE15])– Cut-and-choose [LP07, LP11, HKE14, L14, …], new

models [MF06, HKE12], amortization [LR14, H+14]

• Implementation level [HEKM11]– “Pipelining” – Reducing number of wires/gates– Optimized circuit libraries

Fairplay [PSSW09] TASTY Here0

200000000

400000000

600000000

800000000

1000000000

1200000000

max gates

Huge impact

Fairplay [PSSW09] TASTY Here0

20000

40000

60000

80000

100000non-free gates/s

Performance Scalability

[HEKM11] [HEKM11]

Secure computation is efficient(for moderately-sized circuits,

and semi-honest security)

Huang et al., “Faster Secure Two-Party Computation Using Garbled Circuits,” USENIX Security 2011

Using generic secure 2PC

Protocol computing f

Express f in suitable representation

Express f in high-level language

Compile-time optimizations?Choice of representation

Which representation?

Which protocol?Efficient implementation

Protocol optimizationsBetter crypto primitives

Expressiveness?Support for low-level optimizations?

Type checking?

Recent results

• Secure 2PC in the RAM model*

– Represent f as a RAM program rather than as a boolean circuit

• Better compilers/programming languages for secure 2PC (in the RAM model)**

– Allow programmers to code as usual• Secure 2PC of native MIPS code***

– Language-agnostic* Gordon et al., ACM CCCS 2012** Liu et al., IEEE S&P 2014*** Gordon et al., in submission

Why the RAM model?

• Efficiency– Running time for a RAM program can be much

better than the circuit size (e.g., binary search)• Sublinear-time computation for “big data”?– The circuit for any non-trivial function must have

size at least linear in the input length– In fact, linear complexity is inherent for secure

computation of any non-trivial function• This is not true for amortized complexity!

Why the RAM model?

• Better alignment with how programmers think about algorithms and write their code– What is the complexity of sorting?– Dynamic memory accesses (e.g., count[a[i]]++;)– General-purpose computation on a von Neumann

architecture• Input-dependent running time

Key tool: ORAM

• Allows oblivious access to stored data, with polylog overhead [GO96, …, S+11, S+13, …]

Client Server

ORAM state

D:

Key tool: ORAMClient Server

ORAM stateO

RAM

read, i1

D[i1]

(writes also supported)

Security: accessed positions are independent of i1, i2, …

read, i2

D[i2]

Secure 2PC of RAM programs?

st

st = xd = while (1) { (inst, st) = Π(st, d) if inst==done, return d if inst==(read, i): d=D[i] if inst==(write, i): D[i]=d}

Client (x) Server (D)

ORAM state

ORAM

D[i]

Problems?

• If server initializes the ORAM itself, access patterns are no longer oblivious to the server!

• No security against the client!– Client learns st– Client learns ORAM state– Client learns intermediate results of the

ORAM computation

Conceptually…

st

Client (x) Server (D)

[ORAM state][ORAM state]

[st] [st]

“Trusted 3rd party”

Conceptually…Client (x) Server (D)

[ORAM state][ORAM state]

st = xd = while (1) { (inst, st) = Π(st, d) if inst==done, return d if inst==(read, i): d=D[i] if inst==(write, i): D[i]=d}

[d][st] [st]

[d]

ORAM

[d’][d’]

Repeat until inst = done, thenreconstruct final output

A secure protocol!Client (x) Server (D)

[ORAM state][ORAM state]

st = xd = while (1) { (inst, st) = Π(st, d) if inst==done, return d if inst==(read, i): d=D[i] if inst==(write, i): D[i]=d}

[st] [st]

ORAM

[d’][d’]

Have we gained anything?

• After the initialization, all circuits computed have small size, independent of |D|

• Amortized complexity:– Say original computation requires T steps for

memory of size SÞ ORAM protocol needs O(T polylog S) lookupsÞ O(T polylog S) secure-computation sub-protocols

on small circuits of size polylog SÞ If T is sublinear, sublinear complexity overall!

Performance results

(512-bit entries)

Limitations

• Programmers still limited to using a fixed (toy?) language to express their programs

• No support for legacy code• Although programs can be made instruction

oblivious, doing so increases the number of instructions executed– Existing compilers for secure computation are not

as good as gcc…

Secure 2PC of MIPS machine code

• Programmers can write code in a language of their choice (so long as it compiles to MIPS)

• Existing MIPS code supported “for free”• Number of instructions securely executed is

exactly* the number of instructions executed in the insecure version

• Can leverage optimizations already present in existing compilers

MIPS execution (high level)

MIPS CPU

RAM

ProgramRegisters

PC

Fetch next instructionExecute instructionRead or write to memory

Conceptually…P1 (x) P2 (y)

[regs][regs]

ORAM

MIPS CPU

[PC] [PC][regs’][regs’]

xy

Whyare these questions important?

DoD

• IARPA: secure database search– Now being piloted by NCTC

• DARPA: fully homomorphic encryption (PROCEED); private search (BRANDEIS)

• Air Force: detecting potential satellite collisions

OFR (US Dept. of the Treasury)

• Looking at using secure computation and differential privacy for facilitating data sharing– Among regulators– Between firms– With researchers and the public

• Obtain the benefits of transparency, while complying with policy regulations and reducing concerns about confidentiality

Flood et al., “Cryptography and the Economics of Supervisory Information: Balancing Transparency and Confidentiality,” Financial Stability Conference 2013

Industry

• Partisia – Danish sugar-beet auction (2008-present)– Wireless-spectrum auctions

• Sharemind– Statistical analysis of financial data

• Sepior, Dyadic– Threshold AES decryption

Conclusions

• Tremendous advances in theory and practice of secure 2PC in past few years

• Real-world deployment is already here!– Will continue to grow in importance and impact

Acknowledgments

• Research supported by – NSF (“TC: Large: Collaborative Research: Practical Secure Computation:

Techniques, Tools, and Applications”)– DARPA (“Toward Practical Cryptographic Protocols for Secure

Information Sharing”)– ARL-ITA (“Secure Information Flow in Hybrid Coalition Networks”)

Papers and code available athttp://www.cs.umd.edu/~jkatz/papers.html

Questions?