multiplicative cipher calculator
Except explicit open source licence (indicated Creative Commons / free), the "Multiplicative Cipher" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Multiplicative Cipher" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) Credit goes to the Swiss Mathematician Leonard Euler (pronounced Oiler, 1707-1783). When you study the a=2 row precisely, you will see that the original 26 plain letters are converted into 13 even cipher letters (the even cipher letters are those whose numerical equivalent is an even number.) The ultimate trick to yet produce the same format is factoring: from each parentheses we factor the first integer (which is a divisor of M) and obtain: ((60) = 22*(1 -1/2) * 3*(1 -1/3) * 5 * (1 -1/5)((M) = p12 * (1 -1/ p1) * p2*(1 -1/ p2) * p3 * (1 -1/ p3) = 22*3*5*(1 -1/2)*(1 -1/3)*(1 -1/5) = p12* p2* p3*(1 -1/ p1)*(1 -1/ p2) * (1 -1/ p3) = 60*(1 -1/2)*(1 -1/3)*(1 -1/5) = M * (1 -1/ p1) * (1 -1/ p2) * (1 -1/ p3). One of the major goals of current Mathematics research is to design faster factoring algorithms as todays are fairly slow. Please enable JavaScript to use all functions of this website. Key = I.e. In affine cipher each letter in an alphabet is mapped to its numeric equivalent, encrypted using a simple mathematical function, and converted back to a letter. Thus, the encryption process is a Caesar cipher merged with a multiplication cipher. Here is the C++ Code for the encryption and decryption of the multiplication cipher: //Multiplication Cipher using the good key a=5 //Author: Nils Hahnfeld, 9/22/99 #include #include void main() { char cl,pl,ans; int a=5, ainverse=21; //as a-1*a=21*5=105=1 MOD 26 clrscr(); do { cout << "Multiplication Cipher: (e)ncode or (d)ecode or (~) to exit:" ; cin >> ans; if (ans=='e') { cout<< "Enter plain text: "<< endl; cin >> pl; while(pl!='~') { if ((pl>='a') && (pl<='z')) cl='a' + (a*(pl -'a'))%26; else if ((pl>='A') && (pl<='Z')) cl='A' + (a*(pl -'A'))%26; else cl=pl; cout << cl; cin >> pl; } } else if (ans=='d') { cout << "Enter cipher text: " << endl; cin >> cl; while(cl!='~') { if ((cl>='a') && (cl<='z')) pl='a' + (ainverse*(cl -'a'))%26; else if ((cl>='A') && (cl<='Z')) pl='A' + (ainverse*(cl -'A'))%26; else pl=cl; cout << pl; cin >> cl; } } } while(ans!='~'); } Programmers Remarks: Can you understand the code yourself? In order to create unique cipher characters, we must use a multiplier which is co-prime (the values do not share any factors when dividing - see Try GCD of 5) in relation to the size of the alphabet (26), so you should use either 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 or 25. 5 7 11 13 17 19 23 25 29 31 35 However, we dont need to consider keys that are greater than 26 since each of them has an equivalent key less than 26 that yields the same encryption: the even multiples of 13 (i.e. 2.4 Varying the Alphabet Length varies the Number of Good Keys Using an alphabet length of M=27: Say for legibility reasons we add a blank symbol as our 27th plain letter. QCCSWJUPQCCSW as an example to perform decryption using the multiplicative cipher. How do you find the key domain of the multiplication cipher efficiently? 2) u(pn)= pn - pn-1, if M is a power of a prime M= pn. =CODE("a") yields 97). 23 To encrypt a message using the Hill Cipher we must first turn our keyword into a key matrix (a 2 x 2 matrix for working with digraphs, a 3 x 3 matrix for working with trigraphs, etc). If M=60=22*3*5, then ((60) = ((22*3*5) using property __ yields = ((22)*((3*5) using property __ yields = ((22)*((3)*((5) using properties __ and __ yields = (22 21)*2*4 = 2*2*4 = 16. Step 3: Lets see how decryption can be done using the above formula: Ciphertext = QCCSWJUPQCCSW and multiplication inverse key = 15, Ciphertext: Q > 16 Decryption: (16*15) mod 26 Plaintext: 6 > G, Ciphertext: C > 2 Decryption: (2*15) mod 26 Plaintext: 4 > E, Ciphertext: S > 18 Decryption: (18*15) mod 26 Plaintext: 10 > K, Ciphertext: W > 22 Decryption: (22*15) mod 26 Plaintext: 18 > S, Ciphertext: J > 9 Decryption: (9*15) mod 26 Plaintext: 5 > F, Ciphertext: U > 20 Decryption: (20*15) mod 26 Plaintext: 14 > O, Ciphertext: P > 15 Decryption: (15*15) mod 26 Plaintext: 17 > R, After decryption the plain text = GEEKSFORGEEKS. When a letter occurs in several alphabets, the first of these alphabets is used. The number fetched through output is mapped in the table mentioned above and the corresponding letter is taken as the encrypted letter. By subtracting a (=101) from the entered plain letter in (pl -'a');. The use of several alphabets does not require the algorithms to distinguish between upper and lower case letters. Those are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75 and 78 as the multiples of 3 that are less than 81. How to encrypt using Multiplicative cipher? The first character G corresponds to the six. div#home { By substitution, in fact, during encryption each letter is associated with only one other, by calculating all the possible associations (by encrypting the 26 letters of the alphabet) then it is possible to deduce an alphabet substitution that will serve as a decryption table. 9 ((3)=3-1=2 as 1 and 2 are relative prime to 3. Our alphabet length of 28 now yields how many unique encryptions? Method 1: Separated: In each sub-alphabet, mod 16 is calculated (hex addition), since each sub-alphabet contains 16 elements, and it remains in the same partial alphabet from which the plaintext letter originates. Try to understand as much as possible first, then continue reading. It is possible to distinguish between 2 types of actions in the plain text: uppercase letters [A-Z] and digits [0-9]. 24 "Signpost" puzzle from Tatham's collection, xcolor: How to get the complementary color. The decryption process is simply the reverse of the encryption process, i.e., by dividing the numerical value of each letter in the ciphertext by key and then taking the result modulo of the key. Can I use an 11 watt LED bulb in a lamp rated for 8.6 watts maximum. The o =14 decodes to I = 8 since 21*14 = 224 = 8 MOD 26, the m =12 decodes to S=18 since 21*12 = 252 = 18 MOD 26. Then we perform the reverse operations performed by the encryption algorithm. Moreover, you can see that the plain letter V encrypts to the cipher text letter b (=1) when using a=5 as the encoding key. The key should be relatively prime to the length of the alphabet. In linear algebra, an n-by-n (square) matrix A is called invertible if there exists an n-by-n matrix such that. However, there are some additional integers that are not prime (i.e. You can change your choice at any time on our, Modular Multiplicative Inverse Calculator. That is, they mustn't have any common divisors. So in our case, it was GEEKSFORGEEKS, so it will become: Multiplicative Cipher text = QCCSWJUPQCCSW. the commonly used RSA Cipher is based on the relative slowness of such factoring programs. Certainly none of the cryptosystems we have considered thus far. Aha, there is 105 = 21*5 so that 21*5 = 1 MOD 26. Thank you! In fact, the cipher E can only be an even cipher letter as only even numbers appear in the E-column. Simply by looking at the table, we find that the following keys (whose rows are bold) produce a unique encryption and therefore call them the good keys: a = 1,3,5,7,9,11,15,17,19,21,23,25 Why those and what do they have in common? Here is a non-calculator way to understand why 25 is inverse to itself: Since 25 = -1 MOD 26, it follows 25 * 25 = (-1) * (-1) = 1 MOD 26. Each row that contains each integer from 0 to 25 exactly once and therefore yields a unique cipher letter will serve. Or can we even increase the mere 12 unique encryptions for the Multiplication Cipher by varying the alphabet length? Additionally, you will learn that the RSA Cipher uses prime numbers as well. Note that you may need to run it several times to find completely accurate solution. What would you do? The key should be changed frequently to prevent cryptographic attacks. This formula can be simplified into the product of two factors. Lets check this for an alphabet length of M=29. Even products of 3 primes or prime powers like 30 or 60 can now be dealt with due to the 4th property: Example2: If M=30=2*3*5, then ((30) = ((2*3*5) using property 4) yields = ((2)*((3*5) again property 4) yields = ((2)*((3)*((5) now using property 1) yields = 1*2*4 = 8. Modulo Arithmetic & Ciphers. We then perform matrix multiplication modulo the length of the . 1 Example4: What is the inverse of 3 MOD 11? unchanged so that you can detect the format of the original message easier. Here, it reduces the number of possible good keys to two. Can you? To do so, I distinguish between upper and lower case letters since they are encoded slightly different. Although the function is well-defined when a letter occurs more than once, this makes little sense in encryption algorithms, since the reversibility suffers. If a=1 is used as a key, each cipher letter equals its plain letter which shows that it does produce a unique encryption. Agree Code To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Feedback and suggestions are welcome so that dCode offers the best 'Multiplicative Cipher' tool for free! Note the difference in 'D' and 'd': The index value is the same, but the 'd' is. Example3: For M=16=24 we have u(16) = 24 - 23 = 8 which are the 8 good keys a=1,3,5,7,9,11,13,15. These are valuable information for an eavesdropper that help cracking the message. The best answers are voted up and rise to the top, Not the answer you're looking for? ((21)=________________________ as 1,2,4,5,8,10,11,13,16,17,19,20 are relative prime to 21. Ask Question Asked 9 years, 11 months ago. If the plaintext is made of both letters (a to z) and digits (0 to 9), how do you find the key domain of the multiplication cipher? We can also calculate all the possible keys for the Affine Cipher. For separate partial alphabets the following results: For a merged alphabets, the encrypted text is "02468ACEacACEae024". (Definition). each occurring exactly twice. In case you wonder why the discussion of cracking codes is made public; why is it not kept secret to maintain the security of ciphers? I found a-1 = 2 by simply testing the integers in Z5*={1,2,3,4}. Example1: M=9=32 has the only prime divisor 3 and thus b=9/3 1 = 2 bad keys which are 3 and 6 as the multiples of 3 that are less than 9. div#home a:link { No, 13 is missing. Also, there is no general match on how to handle digits or special characters. Now every row contains exactly one 1 revealing that there exists an inverse for each a which is precisely the reason why those as are the good keys. Therefore, Formula for the number of good keys if M is a prime power: If M = pn , the number of good keys is u(M) = pn - pn-1. The statements while(cl!='~') and cout << cl; cin >> pl; are in charge of it. Examples for property 2): 8 and 25 are prime powers. In fact, all the upper case letters on Excel are 65 numbers higher than those we are using, the lower case letters on Excel are 97 numbers above ours (i.e. 19 This principle of finding the number of bad keys holds true for any alphabet length that is a prime power: There are M/p multiples of p less or equal to M, and therefore M/p - 1 many less than M. And we are only interested in those integers less than M since we are calculating MOD M which involves the integers 0 to M-1. It may be denoted as , where the fact that the inversion is m-modular is implicit. What really matters is not the alphabet length M but rather the number of multiples of the prime factors of M that are less than M: the less multiples of prime factors (as for the alphabet length of 27), the more as produce a unique encryption and vice versa. There are several way to implement the inversion and the affine transformation described in the AES to get the final SBox. The 14 as the possible cipher E then tells him to test the keys a=10 and a=23. 0 div#home a:active { You can verify this as follows: out of the 38 (=p*q-1) integers that are less than 39, we first cross out all the 12 (=13-1) multiples of 3 {3,6,9,12,15,18,21,24,27,30,33,36} and then cross out the 2 (=3-1) multiples of 13 {13,26} resulting in 38 12 2 = 24 good keys. div#home a:hover { This is not very useful. Step 4: So, once the calculation part is done now you can easily encrypt your given plain text. Each character from the plaintext is always mapped to the same character in the ciphertext as in the Caesar cipher. Mathematically: a-1 * a = a * a-1 = 1. Does the increase of our alphabet length by 1 increase the number of unique encryptions obtained? Ok, lets continue with the encoding part. I do not think any special calculator is needed in each of these cases. You can verify this as follows: out of the __ integers that are less than 65, we first cross out all the ___ multiples of __ and then cross out the __ multiples of __ resulting in ______ = 48 good keys. 2) Learn how to compute and use the modular inverse to decode. We also turn the plaintext into digraphs (or trigraphs) and each of these into a column vector. We will multiply MOD 26 as we are using the 26 letters of the English alphabet. You may see ads that are less relevant to you. We can see in the table that an A will always translate into 0 (=a) since the product of any such key a with 0 (=A) yields 0. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. If we extract those rows with the good keys a = 1,3,5,7,9,11,15,17,19,21,23,25 and their corresponding columns, we obtain: 13579111517192123251135791115171921232533915211719255111723551525919323717111217721923112511531751999119113215231572517111173252117951231915151519231591721253711171725715235213111919191951731512511239217212111117723319925155232317115251971211593252523211917151197531 This reduced table shows i.e. Since, for the standard alphabet, there are 12 numbers less than 26 which are .
Cheshire Recycling Schedule 2022,
Ganellen Voluntary Administration,
University Of Missouri Columbia School Of Medicine Class Profile,
Articles M