3746. 1008, 372 3746, 1098, 3712 2. The enciphered message: (239, 1093, 3145, 22

Question

3746. 1008, 372 3746, 1098, 3712 2. The enciphered message: (239, 1093, 3145, 2258, 336, 637, 1528, 259, 1633, 2258, 1902, 427, 1048, 1637, 1198, 1694] The keys: n 3953, d 5. The task: Decipher this message using the RSA algorithm. Then decompose each of the integers in the deciphered message into two integers as in the ex amples. (Be careful when it comes to 3-digit numbers! The correspondence: Associate each number between 1 and 26 with the letter occupying that alphabetic position. Associate the number 27 with the apos- trophe, the number 28 with the space, and the number 29 with the question !) mark.

Explanation / Answer

USING RSA ALGORITHM :

DECRYPTION : cd mod n

c = enciphered text

d = 5

n = 3953

so . Decryption :

D(239) = 2395 mod 3953 = 2308

D(1093) = 10935 mod 3953 = 2528

D(3145) = 31455 mod 3953 = 0919

D(336) = 3365 mod 3953 = 0202

D(3746) = 37465 mod 3953 = 1805

D(1098) = 10985 mod 3953 = 2209

D(3712) = 37125 mod 3953 = 120

D(637) = 6375 mod 3953 = 915

D(1528) = 15285 mod 3953 = 1428

D(259) = 2595 mod 3953 = 1921

D(1633) = 16335 mod 3953 = 308

D(2258) = 22585 mod 3953 = 2801

D(1902) = 19025 mod 3953 = 2812

D(427) = 4275 mod 3953 = 1514

D(1048) = 10485 mod 3953 = 728

D(1637) = 16375 mod 3953 = 2315

D(1198) = 11985 mod 3953 = 1804

D(1694) = 16945 mod 3953 = 2928

NOW ASSOCIATING THESE CERYPTED IMFORMATION WITH THE GIVEN FUNCTION

Associate a number from 1 to 26 : by theier alphabet position

27 : ' (apostrophe)

28 : " " (space)

29 : ?

for 3 digit integer, we added 0 at the starting ...

i.e 919 = 0919 = 09 + 19 = IS

for 4 digit number , just divide them in equal partss :

1223 = 12 + 23 = LW

---------------------------------------Result-------------------------

We are considering res[ a] as the final result of associating decryption of a

res [ 239] = (2308) = 23 08 = WH

res[ 1093] = (2528) = 25 28 = Y" " (Y space)

res[3145] = 0919 = 09 19 = IS

res[2258] = 2801 = 28 01 = " "A (28 = space. 01 = A)

res[336] = 0202 = 02 02 = BB

res[ 3746] = 1805 = 18 05 = RE

res[1098] = 2209 = 22 09 = VI

res[ 3712] = 0120 = 02 20 = BT

res[637] = 0915 = 09 15 = IO

res[1528] = 1428 = 14 28 = N" " (14 = N, 28 = space)

res[259] = 1921 == 19 21 == SU

res[1633] = 0308 = = 03 08 = CH

res[2258] = 2801 == 28 01 = " "A (28 = space)

res[1902] = 2812 == 28 12 = " "L (28 = space)

res[427] = 1514 == 15 14 == ON

res[1048] == 0728 == 07 28 === G" " (28 = space)

res[1637] == 2315 == 23 15 === WO

res[1198] == 1804 === 18 04 ==== RD

res[1694] == 2928 == 29 28 ==== ?" " (29 = ? and 28 == space)

--------------------------------------

so final result:

[ WH, Y" ", IS, " "A, BB, RE, VI, BT, IO, N" ", SU, CH, " "A, " "L, ON, G" ", WO, RD, ?" " ]

Here " " ,means space..

thanks

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