<s>
In	O
cryptography	O
,	O
FourQ	B-Application
is	O
an	O
elliptic	O
curve	O
developed	O
by	O
Microsoft	O
Research	O
.	O
</s>
<s>
It	O
is	O
designed	O
for	O
key	O
agreements	O
schemes	O
(	O
elliptic-curve	B-Protocol
Diffie	I-Protocol
–	I-Protocol
Hellman	I-Protocol
)	O
and	O
digital	O
signatures	O
(	O
Schnorr	B-Algorithm
)	O
,	O
and	O
offers	O
about	O
128	O
bits	O
of	O
security	O
.	O
</s>
<s>
The	O
open	B-License
source	I-License
implementation	O
is	O
called	O
FourQlib	B-Application
and	O
runs	O
on	O
Windows	O
and	O
Linux	B-Application
and	O
is	O
available	O
for	O
x86	O
,	O
x64	B-Device
,	O
and	O
ARM	O
.	O
</s>
<s>
It	O
is	O
licensed	O
under	O
the	B-License
MIT	I-License
License	I-License
and	O
the	O
source	O
code	O
is	O
available	O
on	O
GitHub	B-Application
.	O
</s>
<s>
The	O
currently	O
best	O
known	O
discrete	O
logarithm	O
attack	O
is	O
the	O
generic	O
Pollard	B-Algorithm
's	I-Algorithm
rho	I-Algorithm
algorithm	I-Algorithm
,	O
requiring	O
about	O
group	O
operations	O
on	O
average	O
.	O
</s>
<s>
Most	O
cryptographic	O
primitives	O
,	O
and	O
most	O
notably	O
ECDH	B-Protocol
,	O
require	O
fast	O
computation	O
of	O
scalar	O
multiplication	O
,	O
i.e.	O
</s>
<s>
For	O
FourQ	B-Application
it	O
turns	O
that	O
one	O
can	O
guarantee	O
an	O
efficiently	O
computable	O
solution	O
with	O
.	O
</s>
<s>
Both	O
properties	O
(	O
four	O
dimensional	O
decomposition	O
and	O
Mersenne	O
prime	O
characteristic	O
)	O
,	O
alongside	O
usage	O
of	O
fast	O
multiplication	O
formulae	O
(	O
extended	O
twisted	O
Edwards	O
coordinates	O
)	O
,	O
make	O
FourQ	B-Application
the	O
currently	O
fastest	O
elliptic	O
curve	O
for	O
the	O
128	O
bit	O
security	O
level	O
.	O
</s>
<s>
FourQ	B-Application
is	O
implemented	O
in	O
the	O
cryptographic	O
library	O
,	O
published	O
by	O
Cloudflare	B-Application
.	O
</s>
