mpc

Secure Multi-Party Computation with Go. This project implements secure two-party computation with Garbled circuit protocol. The main components are:

garbled: command-line program for running MPCL programs
compiler: Multi-Party Computation Language (MPCL) compiler
circuit: garbled circuit parser, garbler, and evaluator
ot: oblivious transfer library

Getting started

The easiest way to experiment with the system is to compile the garbled application and use it to evaluate MPCL programs. The garbled application takes the following command line options:

-O: optimization level (default 1 enabling all current optimizations).
-circ: compile inputs to circuit format.
-cpuprofile: write cpu profile to the specified file.
-d: enable diagnostics outputs.
-dot: generate Graphviz DOT output.
-e: specifies circuit evaluator / garbler mode. The circuit evaluator creates a TCP listener and waits for garblers to connect with computation.
-format: specifies circuit format for the -circ output file. Possible values are: mpclc (default), bristol.
-i: specifies comma-separated input values for the circuit.
-memprofile: write memory profile to the specified file.
-ssa: compile MPCL input to SSA assembly.
-stream: streaming mode.
-v: enabled verbose output.

The examples directory contains various MPCL example programs which can be executed with the garbled application. For example, here's how you can run the Yao's Millionaires' Problem which can be found from the millionaire.mpcl file:

package main

func main(a, b int64) bool {
    if a > b {
        return true
    } else {
        return false
    }
}

First, start the evaluator (these examples are run in the apps/garbled directory):

$ ./garbled -e -i 800000 examples/millionaire.mpcl
 - In1: a{1,0}i64:int64
 + In2: b{1,0}i64:int64
 - Out: %_{0,1}b1:bool1
 -  In: [800000]
Listening for connections at :8080

The evaluator's input is 800000 and it is set to the circuit inputs In2. The evaluator is now waiting for garblers to connect to the TCP port :8080.

Next, let's start the garbler:

$ ./garbled -i 750000 examples/millionaire.mpcl
 + In1: a{1,0}i64:int64
 - In2: b{1,0}i64:int64
 - Out: %_{0,1}b1:bool1
 -  In: [750000]
Result[0]: false

The garbler's input is 750000 and it is set to the circuit inputs In1. The garbler connects to the evaluator's TCP port and they run the garbled circuit protocol. At the end, garbler (and evaluator) print the result of the circuit, which is this case is single bool value Result[0]:

Result[0]: false

In our example, the evaluator's argument In2 is bound to the MPCL program's b int64 argument, and garbler's In1 to a int64. Therefore, the result of the computation is false because In1=750000 <= In2=800000. If we increase the garbler's input to 900000, we see that the result is now true since the garbler's input is now bigger than the evaluator's input:

$ ./garbled -i 900000 examples/millionaire.mpcl
 + In1: a{1,0}i64:int64
 - In2: b{1,0}i64:int64
 - Out: %_{0,1}b1:bool1
 -  In: [900000]
Result[0]: true

Ed25519 Key Generation and Signature Computation

The ed25519 directory contains Ed25519 key generation and signature computation examples.

Key Generation

$ ./garbled -stream -e -v -i 0x784db0ec4ca0cf5338249e6a09139109366dca1fac2838e5f0e5a46f0e191bae,0xd0da45d3c99e756da831d1e7d696eae3fa9fe39d3b1b2618c7ff997d17777989b5cf415b114298c8b10bed0f0eff118e43ab606ab01143151dff89171307dffa,0x44bf09357e19b1f96f9cf6d9e7d25a0e8dd62d6e0d4bba2bec4c59983c7dc84d1486677b6d8837746cd948c881913c36faeaee08e8309afac58be4757a1c544e

$ ./garbled -stream -v -i 0x57c0e59c20ac7d75ef7e3188fdd7f5876abee1cab394af8125acaca9760bb54c,0x76b42e6292f4a3dc339d208481abeb9a24e08127c7cd8dbde62abcddc0c0e6f7a0f740e756b44dae137f0e7ff8eae0ceb1a962c130fdcbe8cbee3e31ab55b8dc,0xeb83eb1f5203f5b752c96264a21ff4a27fa60cf2313f5f53c3fa96e0b52a2814b786e43a3af64b66291b5b29f432cb8d5a930e31f4e6f072a6d33b861b5b5f13 examples/ed25519/keygen.mpcl
┏━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━┓
┃ Op          ┃            Time ┃      % ┃ Xfer ┃
┡━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━┩
│ Init        │      2.039289ms │  0.00% │   0B │
│ OT Init     │    248.443521ms │  0.27% │ 21kB │
│ Peer Inputs │   10.330183787s │ 11.10% │  1MB │
│ Eval        │ 1m22.462325965s │ 88.63% │ 14GB │
│ Total       │ 1m33.042992562s │        │ 14GB │
└─────────────┴─────────────────┴────────┴──────┘
Max permanent wires: 52138674, cached circuits: 23
#gates=824319227 (XOR=529672017 XNOR=28633983 AND=265892049 OR=116232 INV=4946 xor=558306000 !xor=266013227) #w=847060405
Result[0]: 8ae64963506002e267a59665e9a2e6f9348cc159be53747894478e182ece9fcb
Result[1]: 4ded80ae09692306c9659307f522f5dba1d96e48cde9f4f6e22fb340629db76aa2bee5867d009e008b6fb85902273acda8910c9a740a788f70c28ca0a3093835
Result[2]: cd5c37f4497fd56e236aa858442b3ff90f7a6401ee2186ea18d074fe93d8f9d18b582fa47a1ee0f0a9083ddd9e262b8f3c642dfad68f667f87dddd4bec80aca3

Signature Computation

$ ./garbled -stream -e -v -i 0x46eb82a021d88960fb13388b0e76ba13b84524ffe114d7f3a728b39efc185eeaa7137132182bab7504daf200d882b787ee8b9b1c9f41be9c38fb4e0ba1aff326

$ ./garbled -stream -v -i 0x4d61726b6b7520526f737369203c6d747240696b692e66693e2068747470733a2f2f7777772e6d61726b6b75726f7373692e636f6d2f,0x5e768ad83640b43d93d6c26b34021d0a0cda6bf5eb962970554d7ab074e2f4cd49bc6fef2fa4dc2f763c1f70b751b7f03d398e8930d837130426454ea52d4449 examples/ed25519/sign.mpcl
┏━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op          ┃            Time ┃      % ┃  Xfer ┃
┡━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━┩
│ Init        │      1.303611ms │  0.00% │    0B │
│ OT Init     │    131.270606ms │  0.15% │  16kB │
│ Peer Inputs │    4.123998305s │  4.69% │ 667kB │
│ Eval        │ 1m23.745891208s │ 95.16% │  15GB │
│ Total       │  1m28.00246373s │        │  15GB │
└─────────────┴─────────────────┴────────┴───────┘
Max permanent wires: 53913890, cached circuits: 25
#gates=830082709 (XOR=533261481 XNOR=28815787 AND=267491441 OR=494216 INV=19784 xor=562077268 !xor=268005441) #w=853799279
Result[0]: b71a55aece64574bedd94729a9ca95a87b5fe0a587fecf50ff0238805132c1291e08cb871016cb4f3935bd45423626f61dc648a91affda3671b19d7b28e03505

Multi-Party Computation Language (MPCL)

The multi-party computation language is heavily inspired by the Go programming language, however it is not using the Go's compiler or any other related components. The compiler is an independent implementation of the relevant parts of the Go syntax.

Compiler

The parser parses the MPCL input files, including any referenced packages, and creates an abstract syntax tree (AST).

The AST is then converted into Static Single Assignment form (SSA) where each variable is defined and assigned only once. The SSA transformation does also type checks so that all variable assignments and function call arguments and return values are checked (or converted) to be or correct type.

Types

Name	Size	Signed
bool	1	no
uint	unspecified	no
int	unspecified	yes
uintN	N	no
intN	N	yes
floatN	N	yes
stringN	N	no

The unsized uint and int types can be used as function arguments and return values. Their sizes are resolved during compilation time. The only exception is the main function. Its arguments must use fixed type sizes. The following example shows a MinMax function that returns the minimum and maximum arguments. This function works for all argument sizes.

func MinMax(a, b int) (int, int) {
    if a < b {
        return a, b
    } else {
        return b, a
    }
}

Builtin functions

The MPCL runtime defines the following builtin functions:

copy(dst, src): copies the content of the array src to dst. The function returns the number of elements copied, which is the minimum of len(src) and len(dst).
len(value): returns the length of the value as integer:
- array: returns the number of array elements
- string: returns the number of bytes in the string
make(type, size): creates an instance of the type type with size bits.
native(name, arg...): calls a builtin function name with arguments arg.... The name can specify a circuit file (*.circ) or one of the following builtin functions:
- hamming(a, b uint) computes the bitwise hamming distance between argument values
size(variable): returns the bit size of the argument variable.

SSA (Static single assignment form)

package main

func main(a, b int4) int4 {
    if a > b {
        return a
    }
    return b
}

The compiler creates the following SSA form assembly:

# Input0: a{1,0}i4:int4
# Input1: b{1,0}i4:int4
# Output0: %_{0,1}i4:int4
# main#0:
	igt     a{1,0}i4 b{1,0}i4 %_{0,0}b1
	mov     a{1,0}i4 %ret0{1,1}i4
	mov     b{1,0}i4 %ret0{1,2}i4
# main.ret#0:
	phi     %_{0,0}b1 %ret0{1,1}i4 %ret0{1,2}i4 %_{0,1}i4
	gc      %_{0,0}b1
	gc      %ret0{1,1}i4
	gc      %ret0{1,2}i4
	gc      a{1,0}i4
	gc      b{1,0}i4
	ret     %_{0,1}i4

The SSA assembly (and logical circuit) form a Directed Acyclic Graph (DAG) without any mutable storage locations. This means that all alternative execution paths must be evaluate and when the program is returning its computation results, any conflicting values from different execution paths must be resolved with the branching condition. This value resolution is implemented as the phi assembly instruction, which effectively implements a MUX logical circuit:

O=(D0 XOR D1)C XOR D0

D0	D1	C	D0 XOR D1	AND C	XOR D0
0	0	0	0	0	0
0	1	0	1	0	0
1	0	0	1	0	1
1	1	0	0	0	1
0	0	1	0	0	0
0	1	1	1	1	1
1	0	1	1	1	0
1	1	1	0	0	1

Circuit generation

The 3rd compiler phase converts SSA form assembly into logic gate circuit. The following circuit was generated from the previous SSA form assembly:

TODO

Benchmarks and tests

Please, see the benchmarks.md file for information about various benchmarks.

Develoment ideas

Mathematical operations

package main

func main(a, b int) (int, int) {
    q, r := a / b
    return q, r
}

easecell/mpc

mpc