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Affine Cipher I have been trying to s...

# Affine Cipher I have been trying to solve for hours.

Posted in the Cryptography Forum

Staz

Auckland, New Zealand

#1 Jun 11, 2006
I know that E is encrypted to R and that V is encrypted to Q. But that is all I know!!:( I need to decrypt : FMMOVSR.

Oh, and originally, A = 0 B= 1 etc.. up to Z = 25

Thanks so much!
Not An Option

Oyster Bay, Australia

#2 Jun 11, 2006
solving 4a + b = 17 (mod 26) and 21a + b = 16 (mod 26) gives a = 3, b = 5. You can do the last step yourself, I'm sure, and then you're all done.

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Cipher decode
#3 Jul 7, 2008
Can anyone explain how did he solved for a and b in detail . Thanks.
Jeff Dege
#4 Jul 7, 2008
4*a + b = 17
21*a + b = 16

b = 17-4*a

21*a +(17-4*a)= 16

21*a + 17 - 4*a = 16
17*a + 17 = 16
17*a = 16-17 = 25 (Remember, it's mod-26)

And so we want to multiply by the multiplicative inverse of 4, mod-26.

23*17*a = 23*25
1*a = 3

a = 3

b = 17-4*a
b = 17 - 4*3
b = 5

The trick is that you can't divide, in modular arithmetic. Instead you multiply by the multiplicative inverse - which is the number that when multiplied by gives you 1.

The multiplicative inverse of 3 mod 26 is 9, because 3*9 = 27 = 1 mod 26.

Not every integer in modular arithmetic has a multiplicative inverse, only those that are relatively prime to the modulus. So mod 26, only the odd numbers other than 13 are prime. Numbers that are multiples of 2 or 13 are not relatively prime to 26, and thus do not have multiplicative inverses.

And hence, cannot be used as the multiplier in affine ciphers.

Which is why affine ciphers have a keyspace of 312 (12*26), instead of 676 (26*26). There are only 12 possible multipliers.
Anathema
#5 Sep 9, 2008
Jeff Dege wrote:
And so we want to multiply by the multiplicative inverse of 4, mod-26.
23*17*a = 23*25
I think you mean the inverse of 17, not 4.
dev

Jabalpur, India

#6 Oct 2, 2009
Tkmax

Nottingham, UK

#7 Oct 31, 2009
Jeff Dege wrote:
4*a + b = 17
17*a = 16-17 = 25 (Remember, it's mod-26)
And so we want to multiply by the multiplicative inverse of 4, mod-26.
23*17*a = 23*25
1*a = 3
a = 3
can you please explain what happened to the 16-17 when working out "a", because in the formula,

it goes from 17*a = 16-17 = 25
to 23*17a = 23*25

Also where did the 23 and 25 come from.

jdege
#8 Oct 31, 2009
All values, when working mod-26, are between 0 and 25. Numbers less than 0 or greater than 25 have 26 added or subtracted until the result is between 0 and 25.

17*a + 17 = 16 mod 26

First step is to subtract 17 from each side:

17*a = 16 - 17 mod 26

Now, 16 - 17 is -1, which is not between 0 and 25, so we add 26 to get us back in our range of mod-26 values.

-1 + 26 = 25

So:

17*a = 25 mod 26

Next step is to divide each side by 17:

a = 25/17 mod 26

The question is, what does division mean, when dealing with modular numbers? Just what it does with regular numbers - multiplication by the inverse.

a = 25 * 1/17 mod 26

And what is the multiplicative inverse of 17, mod 26? It's the number that when multiplied by 17, yields 1.

So:

23 * 17 = 391 = 26*15 + 1 = 1 mod 26

So:

1/17 = 23 mod 26

And:

a = 25 * 23 mod 26
Anomalous

UK

#9 Nov 1, 2009
Jeff Dege wrote:
And so we want to multiply by the multiplicative inverse of 4, mod-26.
23*17*a = 23*25
1*a = 3
a = 3
b = 17-4*a
b = 17 - 4*3
b = 5
how do you find this 23 number you multiply on each side of the equation??? And then how do you find 1*a = 3???
Anomalous

UK

#10 Nov 1, 2009
ignore my last message!!! I hadn't reload the page since yesterday and i didnt notice the last 2 comments!!!
jdege
#11 Nov 1, 2009
Actually, finding the multiplicative inverse of a number, in modular arithmetic, isn't easy. The available algorithms are a lot more expensive than long division.(And, of course, not all numbers have a multiplicative inverse, if the modulus isn't prime.)

http://en.wikipedia.org/wiki/Modular_multipli...

For relatively small modulos, like 26, the easiest thing to do is simply to create a multiplication table.
seccs

Pakistan

#12 Nov 19, 2009
how would i find {95}^1 to find multiplicative inverse for construction of s box in aes...plz reply
{95} is in hexa decimal
trellmix

United States

#13 Dec 8, 2009
Hey can anyone help me decipher the following affine........
Pjxfjswjnkjmrtjfvsujoojwfovajr wheofjrwjodjffzbjf
Almanak

Albania

#14 Dec 19, 2009
Hash and MAC Algorithms, can u help me telling anything about these terms(problems)?
Thank you so much
thanks
#15 Sep 1, 2010
Thanks for posting a bit about this topic-- I was working on a problem for my class, and I got lost reading my teacher's notes-- this helped out a lot.
must

#16 Jan 21, 2013
decipher the following cryptogram glzoxa knowing that an affine cipher with k2=4 was used and that the plaintext is a word of the english language ? can any one help me to solve this equation
must

Iraq

#17 Jan 21, 2013
glzoxa is the cipher message ???
Bob

Southall, UK

#18 Jan 26, 2013
Using the formula c = 7p + 10 glzoxa deciphers as:

SPRING

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