<s>
In	O
a	O
cryptographic	O
digital	O
signature	O
or	O
MAC	B-Algorithm
system	O
,	O
digital	B-General_Concept
signature	I-General_Concept
forgery	I-General_Concept
is	O
the	O
ability	O
to	O
create	O
a	O
pair	O
consisting	O
of	O
a	O
message	O
,	O
,	O
and	O
a	O
signature	O
(	O
or	O
MAC	B-Algorithm
)	O
,	O
,	O
that	O
is	O
valid	O
for	O
,	O
but	O
has	O
not	O
been	O
created	O
in	O
the	O
past	O
by	O
the	O
legitimate	O
signer	O
.	O
</s>
<s>
There	O
are	O
different	O
types	O
of	O
forgery	B-General_Concept
.	O
</s>
<s>
A	O
signature	O
scheme	O
is	O
secure	O
by	O
a	O
specific	O
definition	O
if	O
no	O
forgery	B-General_Concept
of	O
the	O
associated	O
type	O
is	O
possible	O
.	O
</s>
<s>
Universal	O
forgery	B-General_Concept
is	O
the	O
creation	O
(	O
by	O
an	O
adversary	O
)	O
of	O
a	O
valid	O
signature	O
,	O
,	O
for	O
any	O
given	O
message	O
,	O
.	O
</s>
<s>
An	O
adversary	O
capable	O
of	O
universal	O
forgery	B-General_Concept
is	O
able	O
to	O
sign	O
messages	O
they	O
chose	O
themselves	O
(	O
as	O
in	O
selective	B-General_Concept
forgery	I-General_Concept
)	O
,	O
messages	O
chosen	O
at	O
random	O
,	O
or	O
even	O
specific	O
messages	O
provided	O
by	O
an	O
opponent	O
.	O
</s>
<s>
Selective	B-General_Concept
forgery	I-General_Concept
is	O
the	O
creation	O
of	O
a	O
message/signature	O
pair	O
by	O
an	O
adversary	O
,	O
where	O
has	O
been	O
chosen	O
by	O
the	O
attacker	O
prior	O
to	O
the	O
attack	O
.	O
</s>
<s>
may	O
be	O
chosen	O
to	O
have	O
interesting	O
mathematical	O
properties	O
with	O
respect	O
to	O
the	O
signature	O
algorithm	O
;	O
however	O
,	O
in	O
selective	B-General_Concept
forgery	I-General_Concept
,	O
must	O
be	O
fixed	O
before	O
the	O
start	O
of	O
the	O
attack	O
.	O
</s>
<s>
The	O
ability	O
to	O
successfully	O
conduct	O
a	O
selective	B-General_Concept
forgery	I-General_Concept
attack	O
implies	O
the	O
ability	O
to	O
successfully	O
conduct	O
an	O
existential	O
forgery	B-General_Concept
attack	O
.	O
</s>
<s>
Existential	O
forgery	B-General_Concept
(	O
existential	O
unforgeability	O
,	O
EUF	O
)	O
is	O
the	O
creation	O
(	O
by	O
an	O
adversary	O
)	O
of	O
at	O
least	O
one	O
message/signature	O
pair	O
,	O
,	O
where	O
has	O
never	O
been	O
signed	O
by	O
the	O
legitimate	O
signer	O
.	O
</s>
<s>
The	O
adversary	O
can	O
choose	O
freely	O
;	O
need	O
not	O
have	O
any	O
particular	O
meaning	O
;	O
the	O
message	O
content	O
is	O
irrelevant	O
as	O
long	O
as	O
the	O
pair	O
,	O
,	O
is	O
valid	O
,	O
the	O
adversary	O
has	O
succeeded	O
in	O
constructing	O
an	O
existential	O
forgery	B-General_Concept
.	O
</s>
<s>
Thus	O
,	O
creating	O
an	O
existential	O
forgery	B-General_Concept
is	O
easier	O
than	O
a	O
selective	B-General_Concept
forgery	I-General_Concept
,	O
because	O
the	O
attacker	O
may	O
select	O
a	O
message	O
for	O
which	O
a	O
forgery	B-General_Concept
can	O
easily	O
be	O
created	O
,	O
whereas	O
in	O
the	O
case	O
of	O
a	O
selective	B-General_Concept
forgery	I-General_Concept
,	O
the	O
challenger	O
can	O
ask	O
for	O
the	O
signature	O
of	O
a	O
“	O
difficult	O
”	O
message	O
.	O
</s>
<s>
The	O
RSA	B-Architecture
cryptosystem	I-Architecture
has	O
the	O
following	O
multiplicative	O
property	O
:	O
.	O
</s>
<s>
A	O
common	O
defense	O
to	O
this	O
attack	O
is	O
to	O
hash	B-Error_Name
the	O
messages	O
before	O
signing	O
them	O
.	O
</s>
<s>
This	O
notion	O
is	O
a	O
stronger	O
(	O
more	O
secure	O
)	O
variant	O
of	O
the	O
existential	O
forgery	B-General_Concept
detailed	O
above	O
.	O
</s>
<s>
Weak	O
existential	O
forgery	B-General_Concept
is	O
the	O
creation	O
(	O
by	O
an	O
adversary	O
)	O
of	O
at	O
least	O
one	O
message/signature	O
pair	O
,	O
,	O
given	O
a	O
message	O
and	O
different	O
signature	O
produced	O
by	O
the	O
legitimate	O
signer	O
.	O
</s>
<s>
Strong	O
existential	O
forgery	B-General_Concept
is	O
essentially	O
the	O
weakest	O
adversarial	O
goal	O
,	O
therefore	O
the	O
strongest	O
schemes	O
are	O
those	O
that	O
are	O
strongly	O
existentially	O
unforgeable	O
.	O
</s>
