<s>
Algebraic	B-Protocol
Eraser	I-Protocol
(	O
AE	O
)	O
is	O
an	O
anonymous	O
key	B-Protocol
agreement	I-Protocol
protocol	I-Protocol
that	O
allows	O
two	O
parties	O
,	O
each	O
having	O
an	O
AE	O
public	O
–	O
private	O
key	O
pair	O
,	O
to	O
establish	O
a	O
shared	O
secret	O
over	O
an	O
insecure	O
channel	O
.	O
</s>
<s>
This	O
shared	O
secret	O
may	O
be	O
directly	O
used	O
as	O
a	O
key	O
,	O
or	O
to	O
derive	B-Algorithm
another	I-Algorithm
key	I-Algorithm
that	O
can	O
then	O
be	O
used	O
to	O
encrypt	O
subsequent	O
communications	O
using	O
a	O
symmetric	B-Algorithm
key	I-Algorithm
cipher	I-Algorithm
.	O
</s>
<s>
Algebraic	B-Protocol
Eraser	I-Protocol
was	O
developed	O
by	O
Iris	O
Anshel	O
,	O
Michael	O
Anshel	O
,	O
Dorian	O
Goldfeld	O
and	O
Stephane	O
Lemieux	O
.	O
</s>
<s>
SecureRF	O
owns	O
patents	O
covering	O
the	O
protocol	B-Protocol
and	O
unsuccessfully	O
attempted	O
(	O
as	O
of	O
July	O
2019	O
)	O
to	O
standardize	O
the	O
protocol	B-Protocol
as	O
part	O
of	O
ISO/IEC	O
29167-20	O
,	O
a	O
standard	O
for	O
securing	O
radio-frequency	B-Application
identification	I-Application
devices	O
and	O
wireless	B-Architecture
sensor	I-Architecture
networks	I-Architecture
.	O
</s>
<s>
a	O
set	O
of	O
conjugates	O
in	O
the	O
braid	B-Application
group	I-Application
designed	O
to	O
commute	O
with	O
each	O
other	O
.	O
</s>
<s>
The	O
fundamental	O
operation	O
of	O
the	O
Algebraic	B-Protocol
Eraser	I-Protocol
is	O
a	O
one-way	O
function	O
called	O
E-multiplication	O
.	O
</s>
<s>
Given	O
a	O
matrix	O
,	O
permutation	O
,	O
an	O
Artin	O
generator	O
in	O
the	O
braid	B-Application
group	I-Application
,	O
and	O
T-values	O
,	O
one	O
applies	O
E-multiplication	O
by	O
converting	O
the	O
generator	O
to	O
a	O
colored	B-Algorithm
Burau	I-Algorithm
matrix	I-Algorithm
and	O
braid	O
permutation	O
,	O
,	O
applying	O
the	O
permutation	O
and	O
T-values	O
,	O
and	O
then	O
multiplying	O
the	O
matrices	O
and	O
permutations	O
.	O
</s>
<s>
Suppose	O
Alice	O
wants	O
to	O
establish	O
a	O
shared	B-Algorithm
key	I-Algorithm
with	O
Bob	O
,	O
but	O
the	O
only	O
channel	O
available	O
may	O
be	O
eavesdropped	O
by	O
a	O
third	O
party	O
.	O
</s>
<s>
Each	O
party	O
must	O
know	O
the	O
other	O
party	O
's	O
public	O
key	O
prior	O
to	O
execution	O
of	O
the	O
protocol	B-Protocol
.	O
</s>
<s>
So	O
,	O
no	O
party	O
other	O
than	O
Alice	O
can	O
determine	O
Alice	O
's	O
private	O
key	O
,	O
unless	O
that	O
party	O
can	O
solve	O
the	O
Braid	B-Application
Group	I-Application
Simultaneous	O
Conjugacy	O
Separation	O
Search	O
problem	O
.	O
</s>
<s>
Ephemeral	B-General_Concept
keys	I-General_Concept
are	O
temporary	O
and	O
not	O
necessarily	O
authenticated	O
,	O
so	O
if	O
authentication	O
is	O
desired	O
,	O
authenticity	O
assurances	O
must	O
be	O
obtained	O
by	O
other	O
means	O
.	O
</s>
<s>
Holders	O
of	O
static	O
private	O
keys	O
should	O
validate	O
the	O
other	O
public	O
key	O
,	O
and	O
should	O
apply	O
a	O
secure	O
key	B-Algorithm
derivation	I-Algorithm
function	I-Algorithm
to	O
the	O
raw	O
Diffie	O
–	O
Hellman	O
shared	O
secret	O
to	O
avoid	O
leaking	O
information	O
about	O
the	O
static	O
private	O
key	O
.	O
</s>
<s>
The	O
security	O
of	O
AE	O
is	O
based	O
on	O
the	O
Generalized	O
Simultaneous	O
Conjugacy	O
Search	O
Problem	O
(	O
GSCSP	O
)	O
within	O
the	O
braid	B-Application
group	I-Application
.	O
</s>
<s>
This	O
is	O
a	O
distinct	O
and	O
different	O
hard	O
problem	O
than	O
the	O
Conjugacy	O
Search	O
Problem	O
(	O
CSP	O
)	O
,	O
which	O
has	O
been	O
the	O
central	O
hard	O
problem	O
in	O
what	O
is	O
called	O
braid	B-Algorithm
group	I-Algorithm
cryptography	I-Algorithm
.	O
</s>
<s>
The	O
authors	O
of	O
Algebraic	B-Protocol
Eraser	I-Protocol
followed	O
up	O
with	O
a	O
preprint	O
on	O
how	O
to	O
choose	O
parameters	O
that	O
are	O
n't	O
prone	O
to	O
the	O
attack	O
.	O
</s>
<s>
B	O
.	O
Robshaw	O
published	O
a	O
range	O
of	O
practical	O
attacks	O
against	O
the	O
January	O
2016	O
draft	O
of	O
the	O
ISO/IEC	O
29167-20	O
over-the-air	O
protocol	B-Protocol
,	O
including	O
impersonation	O
of	O
a	O
target	O
tag	O
with	O
negligible	O
amount	O
of	O
time	O
and	O
memory	O
and	O
full	O
private	O
key	O
recovery	O
requiring	O
249	O
time	O
and	O
248	O
memory	O
.	O
</s>
<s>
Atkins	O
and	O
Goldfeld	O
responded	O
that	O
adding	O
a	O
hash	B-Algorithm
or	O
message	B-Algorithm
authentication	I-Algorithm
code	I-Algorithm
to	O
the	O
draft	O
protocol	B-Protocol
defeats	O
these	O
attacks	O
.	O
</s>
