Grincon U.S. 2019 Proof of Work

grincon<US>(0)
19.01.28 // hero city, san mateo (CA)
Grin Proof of Work
@tromp

grincon<US>(0) // 19.01.28 // hero city, san mateo (CA)
Overview
● What is proof-of-work
● Hash tables
● Cuckoo Hashtable
● Cuckoo Cycle
● Scary Math
● Cycle finding
● Edge Trimming
● Lean and Mean
● Cuckatoo Cycle
2

What is Proof of Work?
CRYPTO 92, Cynthia Dwork and Moni Naor
A Puzzle
1. Hard to Solve
2. Easy to verify
3. Tied to some message
3

Key ingredient in cryptocurrencies
● Consensus
by Longest Chain Rule
● Distribution
4. Can randomly generate puzzles
of any desired hardness
4

Hashcash Adam Back 1997
5
Given message m and target T
find n such that Hash(m | n) < T

Asymmetric PoWs
● July 2013 Primecoin Cunningham chains e.g. 5, 11, 23, 47
● Nov 2013 Momentum Hash(x) = Hash(y)
● Jan 2014 Cuckoo Cycle announced 42-way collision
● Jan 2015 Cuckoo Cycle presented at Bitcoin2015
● Sep 2015 Equihash Xor(2^k Hashi
) = 0
●
● Apr 2014 ethash
○ Verification actually slower than proof attempt
○ Miners use multiple GB dataset computed every epoch
○ Verifiers use smaller 30 MB dataset
6

Hashtable
7
2 11 8
Hash(11) Hash(8)

Cuckoo Hashtable
Hash0(8)
Hash1(8)
8
2 11
19
Pagh & Rodler 2004

Cuckoo Hashtable
Hash0(8)
Hash1(8)
9
2 11
30 19

Cuckoo Hashtable
Hash0(8)
Hash1(8)
10
2 8
30 19
11

Cuckoo Hashtable
Hash0(11)
Hash1(11)
11
2 8
30 19

Cuckoo Hashtable
12
2 8 19
30 11

Cuckoo Hashtable
13
30 19 8
2 11

grincon<US>(0) // 19.01.28 // hero city, san mateo (CA) 14
30 19 8
2 11
Cuckoo Hashtable
7

Cuckoo Cycle
15
19
11
8
30 2
N edges between N + N nodes

Cuckoo graph, 2^8 edges
16

Cuckoo graph, 2^12 edges
17

How many 42-cycles?
18
i40
i2
i41
i42
. . . N
. . . N
i1
i3 i39
Thm: E[# anchored cycles] = #PACs * Prob(PAC is cycle) ~ N42
* (1/N)42
~ 1
=> E[# cycles] ~ 1 / 42
Every sequence of 42 edge indices
i1, i2, … , i42 is potential anchored cycle (PAC)

How many L-cycles among N edges?
Expected # L-cycles =
19
N Exp[ # 42-cycles ]
2^6 0.0000000000095 / 42
2^8 0.0052600 / 42
2^10 0.2821445 / 42
2^12 0.7307900 / 42
2^15 0.9616480 / 42
2^20 0.9987791 / 42
2^25 0.9999618 / 42
2^30 0.9999988 / 42
NL
= N * (N-1) * … * (N-L+1)
1 NL
(NL/2
)2
L NL
NL
**

Cycle finding
● Two algorithms
● consider additional edges one at a time
○ Cuckoo miner -> cyclebase
○ Graph miner -> all cycles
20

Cuckoo Miner
● Emulates Cuckoo Hashtable
● Storing alternative location
● Maintain directed forest
21

Cuckoo Miner
○ When adding edge (u,v)
○ both have outgoing edges
○ Compare their roots
22
node u
node v
root u
root v

Cuckoo Miner
23
node u
node v
root u
root v

Cuckoo Miner
● Finds cycle base
● Uses 2 * 32 = 64 bits per edge
● High latency
24
node u
node v
root u
==
root v

Graph Miner
● explore all paths of
length at most 42
● iterate over all
adjacent edges
● Store (half)edges in
adjacency lists
● 32 bits per node
● 64 bits per half-edge
● Total 192 bits per edge
● High latency
25

Cycle finding
Combination of
● lots of memory
● random (high latency) access
● single-threading
slows down mining
In 2014, David Andersen identified a fast preprocessing
phase, that can reduce the problem a thousandfold.
26

Edge Trimming
27

Edge Trimming
28

Edge Trimming
29

Edge Trimming
30

Edge Trimming
31

Edge Trimming
32

grincon<US>(0) // 19.01.28 // hero city, san mateo (CA) 331024 edges

Lean vs Mean
● Bitmap
● 1
● Node degrees
● 2 (or 1*)
● Random
58
● List
● CPU 32 GPU 64
● Bucket sort
● CPU+1% GPU+65%
● Sequential
● Remaining edges
● Bits per edge
● Identify leaf edges
● Bits used
● Access Pattern
1 >=2 >=2 10 >=2 0
8 1415
4
2 105
9 13

Cuckatoo Graph off-by-1 adjacency
59
a b c d
a adjacent to b adjacent to c
c NOT adjacent to d

Cuckatoo Graph
60

Cuckatoo Graph
61

Cuckatoo Graph
62

Cuckatoo Cycle
63

Grin Mainnet PoWs
● for GPUs: Cuckaroo on 2^29 edges
○ Variant of Cuckoo that enforces Mean mining
○ Takes 5.5 GB of memory (perhaps 4 GB with slowdown)
○ CPUs run about 10x slower, needing under 4 GB
○ Tweaked every 6 month to maintain ASIC resistance
○ 90% of rewards at launch, linearly decreasing to 0 in 2 years
● for ASICs: Cuckatoo on 2^31 or more edges
○ Variant of Cuckoo that simplifies ASIC design
○ Takes 512 MB of memory, with random single-bit accesses to half
○ Takes 2^k GB after 2^(1+k) years, by phasing out smaller sizes
○ 10% of rewards at launch, linearly increasing to 100% in 2 years
○ Mean mineable in 11 GB with NVIDIA 2080 Ti achieving 1.7 GPS
64

grincon<US>(0) // 19.01.28 // hero city, san mateo (CA) 65

Any questions?
Where’s the White King?
66
Raymond Smullyan The Chess Mysteries of the Arabian Knights

Grincon U.S. 2019 Proof of Work

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Grincon U.S. 2019 Proof of Work