Cryptography Reference
In-Depth Information
p
2
, ...,
p
n
are all that is needed to read a record from the database; thus, we call them the
read subkeys. Note that
C
, by construction, is congruent
R
i
modulo
p
i
for any
i
; that is,
C
R
i
(mod
p
i
)
i
= 1, 2, . . . ,
n
.
Each individual
i
gets the pair of values
w
i
, and
p
i
; this gives them read/write access to
only their data.
E
XAMPLE
.
Suppose the records in our database are
R
1
= 234
R
2
= 201
R
3
= 147.
We choose 3 primes, each greater than their associated record; say
p
1
= 499
p
2
= 503
p
3
= 563.
To encipher the database, we must find an integer
C
that simultaneously solves
C
234 (mod 499)
C
201 (mod 503)
C
147 (mod 563).
Thus, we compute
M
= 141311311
M
1
= 141311311/499 = 283189
M
2
= 141311311/503 = 280937
M
3
= 141311311/563 = 250997.
and we find inverses of each
M
i
modulo
p
i
.
M
1
= 283189
384 (mod 499)
M
2
= 280937
350 (mod 503)
M
3
= 250997
301 (mod 563)
Thus, the write subkeys are
w
1
= 283189
384 = 108744576
w
2
= 280937
350 = 98327950
w
3
= 250997
301 = 75550097.
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