Cryptography Reference
In-Depth Information
073674266728597908901785500052357159821947443150603075554861577713129845
7166748765201121009594717.
A then calculates
r
, the lnr of
g
k
modulo
p
:
r
= 754980689309015967134652122289681073011337085880931754788354434950465
868945202772744073062829346744777955627154546239814497986673097913596618
187706415730448305962740003790259873593478841192742794988274985183707335
088576870708479793565047483444344434823417504303091568416797285536744959
93894473633702658894519225.
The value for
r
is the first part of the signature. Now, A must find an inverse of
k
mod-
ulo
p
1; this is easily done using the extended Euclidean algorithm:
k
= 41476618378700412297173224500420810670339064876850101272695099201480
409096613565495099867137782188429871575488175498185490101859098759692392
347429741878039564964082396789943865344588220167170614361150870833650116
512052394573930927553494824898854134339214385016217721200185633500260411
302215163263988431152856749.
A must compute a digest of the plaintext message. A uses the public hash function
d
(
x
)
x
(mod
q
)
0
≤
d
(
x
) <
q
where the prime
q
is:
q
= 10931809682175872911
= 1001011110110101100101101111110010011010010001001100111110001111
base 2
.
(Note that the binary representation of
q
is 64 bits; it will produce a 64-bit digest.) A cal-
culates
d
(
P
):
d
(
P
)
7763193083250062093 (mod
q
).
Now, A calculates the final part of the signature:
s
k
(
d
(
P
)
ar
)
504129645472912448866079239459312209155283159891818206116181584336284774
060877780128027574808314656854901317166655437096228316557996491503697413
041178568111884781202739723644461510362506102063431227543591653744230589
232661184347273905109607430598564690942443238612401218536035199345301596
39900593535677309588849 (mod
p
1).
The values of
r
and
s
are sent to B. To verify that this signature is valid, B must first
check that
r
is between 1 and
p
1. This checks, so B continues in this way:
B then calculates the two values
v
and
w
. B can compute
w
because the hash function is
public:
v
y
r
r
s
438908365050492172112141159266916014689430122622767850409990603339138565
278995621692689044958914233869339458908488816024934068379856100514306151
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