Cryptography Reference
In-Depth Information
757470680422409493015066111115629539866372845967402086055376212896177870
76209187671392407592174797.
This choice of
p
is a safe prime; we know the factorization of
p
1, which has at least
one large prime factor; in this case,
p
1 = 2
zt
, where
z
= 362,
and
t
= 106134897172928103943918854073295879814210153054070185316305605667648
115167285318268319586681005150020607472483671576748374031351891166746019
548973818467282112460367080990486066014392977005040386442558294459608658
668158933760001311189926258441385295561653708006547249455162460344775949
000288933247779568497479.
A chooses a generator modulo
p
,
g
= 2.
A chooses a private value for
a
:
a
= 45366932286305017454823998962543872234171279575807307127836833791199
106589647221361411404680513932826550438110018938792808421883674318765239
855541004504826749690514434467452187115574562871476458097782440492959459
114595918998192357354718847375845084259186299700677238352348768625876330
302043529365424071172153676.
A computes the public value of
y
, the lnr of
g
a
modulo
p
:
y
= 724055273252881509576588841040152725840811907267226166652168857689817
926487564907954651926297199335221112806345258137591945857251048343201130
805689635851693738336967838518779547772897009773874067873510422086447659
524797666800500925069823070582327783189100853134197262953696156421360406
76327159300158548622476503.
The plaintext message which A must sign is
P
= 47495233644665988426542797641862170747046710526789245391156504620320
517515571648723939384358595186200968673256615798341680398991554123874397
908150043241195926795222914754565141859355539104925268550584190056601904
838582629751247671428189205507655795265722620866029099708789775077073512
480224582285200694189809167.
We will assume
P
has already been encrypted using public information of the recipient
B, and sent to B. A creates a signature for this message by doing the following:
A selects a random integer
k
such that 0
≤
k
≤
p
2 and (
k
,
p
1) = 1; say
k
= 828569173899706322862537866306640776566352364751963244609011965664662
488417460387862608694420472286305311556299061959003482409233005037723040
325579207521157865540839175624706248094985512559552109060621372261182159
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