<s>
In	O
post-quantum	O
cryptography	O
,	O
NewHope	B-Protocol
is	O
a	O
key-agreement	B-Protocol
protocol	I-Protocol
by	O
Erdem	O
Alkim	O
,	O
Léo	O
Ducas	O
,	O
Thomas	O
Pöppelmann	O
,	O
and	O
Peter	O
Schwabe	O
that	O
is	O
designed	O
to	O
resist	O
quantum	B-Architecture
computer	I-Architecture
attacks	O
.	O
</s>
<s>
NewHope	B-Protocol
is	O
based	O
on	O
a	O
mathematical	O
problem	O
ring	O
learning	O
with	O
errors	O
(	O
RLWE	O
)	O
that	O
is	O
believed	O
to	O
be	O
difficult	O
to	O
solve	O
.	O
</s>
<s>
NewHope	B-Protocol
has	O
been	O
selected	O
as	O
a	O
round-two	O
contestant	O
in	O
the	O
NIST	O
Post-Quantum	O
Cryptography	O
Standardization	O
competition	O
,	O
and	O
was	O
used	O
in	O
Google	B-Application
's	I-Application
CECPQ1	B-Protocol
experiment	O
as	O
a	O
quantum-secure	O
algorithm	O
,	O
alongside	O
the	O
classical	O
X25519	B-Application
algorithm	O
.	O
</s>
<s>
The	O
designers	O
of	O
NewHope	B-Protocol
made	O
several	O
choices	O
in	O
developing	O
the	O
algorithm	O
:	O
</s>
<s>
Error	O
Reconciliation	O
:	O
What	O
distinguishes	O
NewHope	B-Protocol
from	O
its	O
predecessors	O
is	O
its	O
method	O
for	O
error	O
reconciliation	O
.	O
</s>
<s>
Previous	O
ring	O
learning	O
with	O
error	O
key	O
exchange	O
schemes	O
correct	O
errors	O
one	O
coefficient	O
at	O
a	O
time	O
,	O
whereas	O
NewHope	B-Protocol
corrects	O
errors	O
2	O
or	O
4	O
coefficients	O
at	O
a	O
time	O
based	O
on	O
high-dimension	O
geometry	O
.	O
</s>
<s>
Base	O
Vector	O
Generation	O
:	O
The	O
authors	O
of	O
NewHope	B-Protocol
proposed	O
deriving	O
the	O
base	O
"	O
generator	O
"	O
vector	O
(	O
commonly	O
denoted	O
as	O
A	O
or	O
)	O
from	O
the	O
output	O
of	O
the	O
XOF	O
function	O
SHAKE-128	B-Algorithm
in	O
order	O
to	O
prevent	O
"	O
back-doored	O
"	O
values	O
from	O
being	O
used	O
,	O
as	O
may	O
happen	O
with	O
traditional	O
Diffie	B-Protocol
–	I-Protocol
Hellman	I-Protocol
through	O
Logjam	B-Protocol
attack	I-Protocol
.	O
</s>
<s>
Security	O
Levels	O
:	O
In	O
the	O
early	O
versions	O
of	O
the	O
papers	O
describing	O
NewHope	B-Protocol
,	O
authors	O
proposed	O
using	O
1024-degree	O
polynomial	O
for	O
128-bit	O
"	O
post-quantum	O
"	O
security	O
level	O
,	O
and	O
a	O
512-degree	O
polynomial	O
as	O
"	O
toy	O
"	O
instance	O
for	O
cryptanalysis	O
challenge	O
.	O
</s>
