May 26th, 2012, 12:08 PM  #1 
Member Joined: Mar 2012 Posts: 32 Thanks: 0  a multiplicative cipher
[Moderator note: question was deleted by user; see the nowrestored third post.]

May 26th, 2012, 03:10 PM  #2 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: a multiplicative cipher
Lots isn't clear here. Since you are using z26, I assume you are associating every letter of the alphabet with a number between 0 and 25 inclusive. Is that correct? If so, do you start with 0 or 1 (or some other number, for that matter)? It'll make a difference. If w=23, it looks like the answers to my questions are yes and 1. If so and 'multiplicative' means you multiply the numerical values of the letters together, then 'when' = 23*8*5*14 mod 26 and I'm getting 16. I'm too tired to recheck my arithmetic. If this is the way this is supposed to work, this an odd cipher, since many different numbers can multiply out to the same number, especially in modular arithmetic, and decrypting even if you know the key is therefore not just difficult but impossible, as information is irretrievably lost. 
May 27th, 2012, 01:51 PM  #3 
Member Joined: Mar 2012 Posts: 32 Thanks: 0  Re: a multiplicative cipher
A multiplicative cipher is defined on Z26 by the rule M5(m) = 5×26 m. Messages in English are coded numerically using the correspondence below. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 (i) Encipher the message ‘Who’ using M5 (that is, find the ciphertext for this message). i just need to get a little start off with the w.. i got w=15 when i worked this out as i got my multiplicatice inverse of 5 in z26 to be 21 is this correct 
May 27th, 2012, 05:11 PM  #4  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: a multiplicative cipher Quote:
5*5 = 25 = 1 mod 26 Yes, 21 is the multiplicative inverse of 5 mod 26 w = 23 in this system. 23 = 3 and 3*5 = 15 mod 26 So, if you are taking the numbers initially assigned value and multiplying it by the multiplicative inverse of 5 mod 26, you are right.  
May 28th, 2012, 12:07 AM  #5 
Member Joined: Mar 2012 Posts: 32 Thanks: 0  Re: a multiplicative cipher
Thanks johnr

May 28th, 2012, 02:54 AM  #6 
Newbie Joined: May 2012 From: Surrey, UK Posts: 6 Thanks: 0  Re: a multiplicative cipher
So does this mean that H = 8 = 17 (mod26) ?

May 28th, 2012, 03:36 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1016 Math Focus: Elementary mathematics and beyond  Re: a multiplicative cipher
The account for milly2012 has been deactivated.

May 28th, 2012, 04:17 AM  #8 
Newbie Joined: May 2012 From: Surrey, UK Posts: 6 Thanks: 0  Re: a multiplicative cipher
Hmmm. No that's not right. Certainly. Could you clear up how to go about this, please. You don't necessarily have to use the letters above, but a swift run through any of them would set me at rest. Thank you. 

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