<s>
Equihash	B-Protocol
is	O
a	O
memory-hard	O
Proof-of-work	O
algorithm	O
introduced	O
by	O
the	O
University	O
of	O
Luxembourg	O
's	O
Interdisciplinary	O
Centre	O
for	O
Security	O
,	O
Reliability	O
and	O
Trust	O
(	O
SnT	O
)	O
at	O
the	O
2016	O
Network	O
and	O
Distributed	O
System	O
Security	O
Symposium	O
.	O
</s>
<s>
The	O
algorithm	O
is	O
based	O
on	O
a	O
generalization	O
of	O
the	O
Birthday	O
problem	O
which	O
finds	O
colliding	O
hash	B-Algorithm
values	O
.	O
</s>
<s>
ASIC	O
resistance	O
in	O
Equihash	B-Protocol
is	O
based	O
on	O
the	O
assumption	O
that	O
commercially-sold	O
hardware	O
already	O
has	O
quite	O
high	O
memory	O
bandwidth	O
,	O
so	O
improvements	O
made	O
by	O
custom	O
hardware	O
may	O
not	O
be	O
worth	O
the	O
development	O
cost	O
.	O
</s>
<s>
Equihash	B-Protocol
was	O
proposed	O
by	O
Alex	O
Biryukov	O
and	O
Dmitry	O
Khovratovich	O
as	O
part	O
of	O
the	O
University	O
of	O
Luxembourg	O
research	O
group	O
CryptoLUX	O
.	O
</s>
<s>
Notable	O
blockchain-based	O
projects	O
such	O
as	O
ZCash	B-Protocol
,	O
BitcoinZ	O
,	O
Horizen	O
,	O
Aion	O
,	O
Hush	O
,	O
and	O
Pirate	O
Chain	O
have	O
integrated	O
Equihash	B-Protocol
for	O
reasons	O
such	O
as	O
security	O
,	O
privacy	O
,	O
and	O
ASIC	O
miner	O
resistance	O
.	O
</s>
<s>
The	O
manufacturer	O
Bitmain	O
has	O
succeeded	O
in	O
optimizing	O
the	O
processing	O
of	O
Zcash	B-Protocol
's	O
Equihash-200	O
,	O
9	O
with	O
an	O
ASIC	O
.	O
</s>
<s>
Equihash	B-Protocol
has	O
three	O
parameters	O
–	O
,	O
,	O
and	O
–	O
which	O
determine	O
the	O
algorithm	O
's	O
time	O
and	O
memory	O
requirements	O
.	O
</s>
<s>
The	O
problem	O
in	O
Equihash	B-Protocol
is	O
to	O
find	O
distinct	O
,	O
-bit	O
values	O
to	O
satisfy	O
such	O
that	O
has	O
leading	O
zeros	O
,	O
where	O
is	O
a	O
chosen	O
hash	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
A	O
memory-less	O
verification	O
requires	O
hashes	B-Algorithm
and	O
XORs	O
.	O
</s>
<s>
It	O
is	O
proposed	O
that	O
the	O
puzzle	O
in	O
Equihash	B-Protocol
be	O
solved	O
by	O
a	O
variation	O
of	O
Wagner	O
's	O
algorithm	O
for	O
the	O
generalized	O
birthday	O
problem	O
.	O
</s>
<s>
refute	O
Equihash	B-Protocol
’s	O
security	O
claims	O
,	O
concluding	O
that	O
no	O
tradeoff-resistance	O
bound	O
is	O
in	O
fact	O
known	O
for	O
Equihash	B-Protocol
.	O
</s>
<s>
The	O
cryptocurrency	O
Zcash	B-Protocol
implements	O
Equihash	B-Protocol
with	O
and	O
.	O
</s>
<s>
The	O
cryptocurrency	O
BitcoinGold	B-Protocol
implements	O
Equihash	B-Protocol
with	O
and	O
.	O
</s>
