Skip to content
/ mpc Public

Secure Multi-Party Computation (MPC) with Go. This project implements secure two-party computation with Garbled circuit protocol.

www.markkurossi.com/mpcl/index.html

License

MIT license
110 stars 22 forks Branches Tags Activity
Star
Notifications You must be signed in to change notification settings

markkurossi/mpc

BranchesTags

Repository files navigation

mpc

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

  • ot: oblivious transfer library
  • circuit: garbled circuit parser, garbler, and evaluator
  • compiler: Multi-Party Computation Language (MPCL) compiler

Getting started

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

  • -e: specifies circuit evaluator / garbler mode. The circuit evaluator creates a TCP listener and waits for garblers to connect with computation.
  • -i: specifies comma-separated input values for the circuit.
  • -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

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

  • Phase 0
    • Oblivious Transfer
    • Garbled circuit garbling and evaluation
    • MPCL compiler for basic arithmetics
  • Phase 1
    • Compiler
      • Conditionals
      • Struct input types
      • Binary serialization format for circuits
      • RSA 128-bit signature
    • Circuit & garbling
      • RSA 128-bit signature
      • BMR multi-party protocol
  • Phase 2
    • Incremental compiler
      • Constant folding
        • Implement using AST rewrite
        • binary expressions
        • if-blocks
        • For-loop unrolling
        • Function call and return
      • peephole optimization
        • sort blocks in topological order
        • peephole optimization over block boundaries
        • SSA aliasing is 1:1 but amov has 2:1 relation
        • variable liveness analysis for templates
      • Signed / unsigned arithmetics
      • unary expressions
        • logical not
      • BitShift
    • Circuit & garbling:
      • Incremental (streaming) garbling and evaluation
      • Row reduction
      • Half AND
      • Oblivious transfer extensions
    • Misc:
      • TLS for garbler-evaluator protocol
  • Ed25519
    • Parsing Ed25519 MPCL files
      • for-range statements
      • local variables in for-loop unrolling
    • Pointer handling
      • Pointer to struct field
      • Cleanup pointer r-value handling
    • Compound init values must be zero-padded to full size
    • Circuit generation:
      • SSA variable liveness analysis must be optimized
      • Optimizing ssa.Value memory usage

Benchmarks and tests

Running benchmark: 32-bit RSA encryption (64-bit modp)

Circuit: #gates=7366376 (XOR=3146111 AND=3133757 OR=1032350 INV=54158)
┏━━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃          Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃  10.72622192s ┃ 75.33% ┃       ┃
┃ Recv   ┃  2.501608027s ┃ 17.57% ┃ 364MB ┃
┃ Inputs ┃  232.257386ms ┃  1.63% ┃  41kB ┃
┃ Eval   ┃  778.170361ms ┃  5.47% ┃       ┃
┃ Result ┃     158.838µs ┃  0.00% ┃   1kB ┃
┃ Total  ┃ 14.238416532s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Optimized full-adder:

Circuit: #gates=7366376 (XOR=5210811 AND=2101407 OR=0 INV=54158)
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃   7.9561241s ┃ 76.09% ┃       ┃
┃ Recv   ┃ 1.660386022s ┃ 15.88% ┃ 199MB ┃
┃ Inputs ┃ 232.583145ms ┃  2.22% ┃  41kB ┃
┃ Eval   ┃ 606.479521ms ┃  5.80% ┃       ┃
┃ Result ┃    304.202µs ┃  0.00% ┃   1kB ┃
┃ Total  ┃ 10.45587699s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Karatsuba multiplication algorithm:

Circuit: #gates=6822632 (XOR=4828475 XNOR=58368 AND=1874719 OR=0 INV=61070)
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃ 6.672590283s ┃ 75.99% ┃       ┃
┃ Recv   ┃ 1.320621876s ┃ 15.04% ┃ 179MB ┃
┃ Inputs ┃ 231.659961ms ┃  2.64% ┃  41kB ┃
┃ Eval   ┃ 555.192105ms ┃  6.32% ┃       ┃
┃ Result ┃    298.855µs ┃  0.00% ┃   1kB ┃
┃ Total  ┃  8.78036308s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Optimized INV-gates:

Circuit: #gates=6769820 (XOR=4836732 XNOR=58368 AND=1874719 OR=0 INV=1)
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃ 6.338729612s ┃ 75.20% ┃       ┃
┃ Recv   ┃ 1.352880139s ┃ 16.05% ┃ 177MB ┃
┃ Inputs ┃  227.12815ms ┃  2.69% ┃  41kB ┃
┃ Eval   ┃ 509.574258ms ┃  6.05% ┃       ┃
┃ Result ┃    344.425µs ┃  0.00% ┃   1kB ┃
┃ Total  ┃ 8.428656584s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Labels by value:

Circuit: #gates=6717340 (XOR=4787324 XNOR=108545 AND=1821471 OR=0 INV=0)
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃ 6.117743762s ┃ 77.25% ┃       ┃
┃ Recv   ┃ 1.196140342s ┃ 15.10% ┃ 172MB ┃
┃ Inputs ┃ 236.647371ms ┃  2.99% ┃  41kB ┃
┃ Eval   ┃ 368.944904ms ┃  4.66% ┃       ┃
┃ Result ┃    347.483µs ┃  0.00% ┃   1kB ┃
┃ Total  ┃ 7.919823862s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Labels by value in protocol, garbler, and evaluator:

Circuit: #gates=6717340 (XOR=4787324 XNOR=108545 AND=1821471 OR=0 INV=0)
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃ 5.076677475s ┃ 78.67% ┃       ┃
┃ Recv   ┃ 940.758975ms ┃ 14.58% ┃ 143MB ┃
┃ Inputs ┃ 229.741398ms ┃  3.56% ┃  41kB ┃
┃ Eval   ┃ 205.513944ms ┃  3.18% ┃       ┃
┃ Result ┃    185.197µs ┃  0.00% ┃   1kB ┃
┃ Total  ┃ 6.452876989s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Gate wires by value in garbler:

Circuit: #gates=6717340 (XOR=4787324 XNOR=108545 AND=1821471 OR=0 INV=0)
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃  4.37061338s ┃ 76.48% ┃       ┃
┃ Recv   ┃  962.20669ms ┃ 16.84% ┃ 143MB ┃
┃ Inputs ┃ 229.360283ms ┃  4.01% ┃  41kB ┃
┃ Eval   ┃ 152.258636ms ┃  2.66% ┃       ┃
┃ Result ┃    162.316µs ┃  0.00% ┃   1kB ┃
┃ Total  ┃ 5.714601305s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Garbler keeping wires in an array instead of map:

Circuit: #gates=6717340 (XOR=4787324 XNOR=108545 AND=1821471 OR=0 INV=0)
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃ 1.710655914s ┃ 53.63% ┃       ┃
┃ Recv   ┃ 1.088403425s ┃ 34.12% ┃ 143MB ┃
┃ Inputs ┃ 243.393526ms ┃  7.63% ┃  41kB ┃
┃ Eval   ┃ 146.879726ms ┃  4.61% ┃       ┃
┃ Result ┃      222.8µs ┃  0.01% ┃   1kB ┃
┃ Total  ┃ 3.189555391s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Pruning dead gates:

Circuit: #gates=5972956 (XOR=4315452 XNOR=53761 AND=1603743 OR=0 INV=0)
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃  1.28140619s ┃ 55.30% ┃       ┃
┃ Recv   ┃ 676.432166ms ┃ 29.19% ┃ 126MB ┃
┃ Inputs ┃ 229.527559ms ┃  9.91% ┃  41kB ┃
┃ Eval   ┃ 129.623668ms ┃  5.59% ┃       ┃
┃ Result ┃    203.248µs ┃  0.01% ┃   1kB ┃
┃ Total  ┃ 2.317192831s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Optimized garbling:

Circuit: #gates=5972956 (XOR=4315452 XNOR=53761 AND=1603743 OR=0 INV=0)
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┣━━━━━━━━╋━━━━━━━━━━━━━━╋━━━━━━━━╋━━━━━━━┫
┃ Wait   ┃ 700.031233ms ┃ 38.57% ┃       ┃
┃ Recv   ┃ 706.339086ms ┃ 38.92% ┃ 126MB ┃
┃ Inputs ┃ 233.615365ms ┃ 12.87% ┃  41kB ┃
┃ Eval   ┃  174.84741ms ┃  9.63% ┃       ┃
┃ Result ┃    215.733µs ┃  0.01% ┃   1kB ┃
┃ Total  ┃ 1.815048827s ┃        ┃       ┃
┗━━━━━━━━┻━━━━━━━━━━━━━━┻━━━━━━━━┻━━━━━━━┛

Optimized dynamic memory allocations from garbling:

Circuit: #gates=5972956 (XOR=4315452 XNOR=53761 AND=1603743 OR=0 INV=0) #w=5973116
┏━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━┓
┃ Op     ┃         Time ┃      % ┃  Xfer ┃
┡━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━┩
│ Wait   │ 574.859679ms │ 35.11% │       │
│ Recv   │ 678.520719ms │ 41.44% │ 126MB │
│ Inputs │  274.49709ms │ 16.77% │  41kB │
│ Eval   │   109.1673ms │  6.67% │       │
│ Result │    158.416µs │  0.01% │   1kB │
│ Total  │ 1.637203204s │        │ 126MB │
└────────┴──────────────┴────────┴───────┘

Ed25519 signature computation

The first signature computation without SHA-256:

┏━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━┓
┃ Op          ┃            Time ┃      % ┃ Xfer ┃
┡━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━┩
│ Init        │       141.651µs │  0.00% │ 276B │
│ OT Init     │    243.714662ms │  0.06% │ 264B │
│ Peer Inputs │     69.857046ms │  0.02% │ 10kB │
│ Eval        │ 6m55.975310366s │ 99.92% │ 25GB │
│ Total       │ 6m56.289023725s │        │ 25GB │
└─────────────┴─────────────────┴────────┴──────┘
Max permanent wires: 43786395, cached circuits: 26
#gates=935552365, #non-XOR=291882258

Optimized p2p.Conn.SendUint{16,32}() not to allocate memory:

┏━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━┓
┃ Op          ┃            Time ┃      % ┃ Xfer ┃
┡━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━┩
│ Init        │        41.043µs │  0.00% │ 276B │
│ OT Init     │     166.70528ms │  0.07% │ 264B │
│ Peer Inputs │     66.153689ms │  0.03% │ 10kB │
│ Eval        │ 3m48.820978578s │ 99.90% │ 25GB │
│ Total       │  3m49.05387859s │        │ 25GB │
└─────────────┴─────────────────┴────────┴──────┘
Max permanent wires: 43786395, cached circuits: 26
#gates=935552365, #non-XOR=291882258

Added one missing ed25519.ScReduce() (+1220540 gates, +381217 non-XOR gates):

┏━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━┓
┃ Op          ┃            Time ┃      % ┃ Xfer ┃
┡━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━┩
│ Init        │        64.159µs │  0.00% │ 276B │
│ OT Init     │    317.026065ms │  0.14% │ 264B │
│ Peer Inputs │     66.088379ms │  0.03% │ 10kB │
│ Eval        │ 3m46.188650399s │ 99.83% │ 25GB │
│ Total       │ 3m46.571829002s │        │ 25GB │
└─────────────┴─────────────────┴────────┴──────┘
Max permanent wires: 43892147, cached circuits: 26
#gates=936772905, #non-XOR=292263475

Optimizing p2p.Conn.SendLabel() not to allocate memory:

┏━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━┓
┃ Op          ┃            Time ┃      % ┃ Xfer ┃
┡━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━┩
│ Init        │        73.349µs │  0.00% │ 276B │
│ OT Init     │    231.818904ms │  0.13% │ 264B │
│ Peer Inputs │     67.641816ms │  0.04% │ 10kB │
│ Eval        │ 2m57.583645976s │ 99.83% │ 25GB │
│ Total       │ 2m57.883180045s │        │ 25GB │
└─────────────┴─────────────────┴────────┴──────┘
Max permanent wires: 43892147, cached circuits: 26
#gates=936772905, #non-XOR=292263475

RSA signature computation

Input MODP Gates Non-XOR Stream Gates Stream Non-XOR
2 4 708 201 730 205
4 8 5596 1571 5640 1579
8 16 44796 12423 44884 12439
16 32 374844 102255 375052 102287
32 64 2986556 801887 2986972 801951
64 128 23171068 6137023 23171900 6137151
128 256 177580028 46495359 177581692 46495615
256 512 1356768508 351848191

Multiplication

Input Size Total gates Non-XOR gates
2 7 3
4 29 13
8 145 57
16 655 241
32 3347 1100
64 13546 4242
128 49249 14986
256 167977 50167
512 549965 162147
1024 1752826 512099
2048 5485700 1592234
4096 16954032 4897756
8192 51940803 14953708

Mathematic operations with compiler and optimized circuits

Optimized circuits from pkg/math/:

Implementation XOR gates AND gates % of circ
add64.circ 313 63
sub64.circ 442 63
mul64.circ 9707 4033
div64.circ 25328 4664
MPCL a+b 316 63 100
MPCL a-b 319 63 100
MPCL a*b 9304 4242 105.2
MPCL a/b 24833 8192 175.6

Develoment ideas

Mathematical operations

package main

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

About

Secure Multi-Party Computation (MPC) with Go. This project implements secure two-party computation with Garbled circuit protocol.

www.markkurossi.com/mpcl/index.html

Topics

go programming-language golang mpc ed25519 sha-256 sha-512 oblivious-transfer hmac-sha512 hmac-sha256 multi-party-computation multiparty-computation logical-circuits aes-128-cbc yao-millionaires garbled-circuit aes-128-gcm

Resources

Readme

License

MIT license

Code of conduct

Code of conduct
Activity

Stars

110 stars

Watchers

5 watching

Forks

22 forks
Report repository

Releases

No releases published

Packages

No packages published

Contributors 3

  •  
  •  
  •  

Languages