<s>
In	O
group	O
theory	O
,	O
a	O
branch	O
of	O
mathematics	O
,	O
the	O
baby-step	B-Language
giant-step	I-Language
is	O
a	O
meet-in-the-middle	O
algorithm	O
for	O
computing	O
the	O
discrete	O
logarithm	O
or	O
order	O
of	O
an	O
element	O
in	O
a	O
finite	O
abelian	O
group	O
by	O
Daniel	O
Shanks	O
.	O
</s>
<s>
The	O
discrete	O
log	O
problem	O
is	O
of	O
fundamental	O
importance	O
to	O
the	O
area	O
of	O
public	B-Application
key	I-Application
cryptography	I-Application
.	O
</s>
<s>
The	O
baby-step	B-Language
giant-step	I-Language
algorithm	O
is	O
based	O
on	O
rewriting	O
:	O
</s>
<s>
The	O
best	O
way	O
to	O
speed	O
up	O
the	O
baby-step	B-Language
giant-step	I-Language
algorithm	O
is	O
to	O
use	O
an	O
efficient	O
table	O
lookup	O
scheme	O
.	O
</s>
<s>
The	O
best	O
in	O
this	O
case	O
is	O
a	O
hash	B-Algorithm
table	I-Algorithm
.	O
</s>
<s>
Since	O
hash	B-Algorithm
tables	I-Algorithm
can	O
retrieve	O
and	O
add	O
elements	O
in	O
time	O
(	O
constant	O
time	O
)	O
,	O
this	O
does	O
not	O
slow	O
down	O
the	O
overall	O
baby-step	B-Language
giant-step	I-Language
algorithm	O
.	O
</s>
<s>
The	O
Baby-step	B-Language
giant-step	I-Language
algorithm	O
is	O
often	O
used	O
to	O
solve	O
for	O
the	O
shared	O
key	O
in	O
the	O
Diffie	B-Protocol
Hellman	I-Protocol
key	I-Protocol
exchange	I-Protocol
,	O
when	O
the	O
modulus	O
is	O
a	O
prime	O
number	O
.	O
</s>
