We, therefore, name the good keys as follows: Definition of numbers that are relative prime: Two integers are called relative prime if their greatest common divisor equals 1. Each character is multiplied with this key and the corresponding letter is substituted. Each letter is enciphered with the function (ax + b) mod 26. 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? Online calculator: Modular inverse of a matrix - PLANETCALC Aha, there is 105 = 21*5 so that 21*5 = 1 MOD 26. How to encrypt using Multiplicative cipher? Here, it reduces the number of possible good keys to two. Affine cipher - encoder / decoder. We will check in the Abstract Algebra section at the end of this chapter that the set of good keys MOD 26, Z26* = {1,3,5,7,9,11,15,17,19,21,23,25}, does form a multiplicative group. QCCSWJUPQCCSW as an example to perform decryption using the multiplicative cipher. Finally, I have to add the usual 65 = A (why?) An affine cipher is a cipher belonging to the group of monoalphabetic substitution ciphers. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. and all data download, script, or API access for "Multiplicative Cipher" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app! 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. Multiply It! Modulo Arithmetic & Ciphers In our example, after subtracting 101 from the plain letter c we get the desired 2 that is now multiplied by a=5 yielding 10. The inverse function returns the n-th character for a number n in L. To n, the length of the list L is added or subtracted as often as necessary until the index lies in the list. Identify blue/translucent jelly-like animal on beach. As some of them fail to produce a unique encryption, we will discover an easy criterion for keys that produce the desired unique encryptions (the good keys) and apply it to different alphabet lengths. I leave the translation from an upper case plain letter to a lower case cipher letter as an easy exercise for you. Once we have the solution, our x is the modular multiplicative inverse of a modulo m. Rewrite the above equation like that For classical methods, the alphabet often consists only of the uppercase letters (A-Z). You now understand why cryptographers have an affection for prime numbers. Moreover, since a=13 is a bad key its multiples 26, 39, must also be bad keys. The Caesar cipher is a special case of the Affine cipher where A is 1 and B is the shift/offest. If multiplication is used to convert to cipher text, it is called a wrap-around situation. 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. Decrypt, In a Multiplicative cipher, each character of the alphabet is assigned a value (starting at a zero index [A=0, B=1, etc]) and a coprime key to the length of the alphabet is chosen. 2) The setwidth command setw() assigns as many spaces as entered in the parentheses for a numerical output in order to have a well-formatted output. Divide the letters of the message into groups of two or three. It is easy to implement and easy to understand, and it does not require any large amount of computational power. Affine cipher: Encode and decode - cryptii Long Multiplication Calculator Options regulate the case when a letter does not appear in any alphabet: it is not encrypted, but transferred directly to the output. margin-bottom: 16px; The best answers are voted up and rise to the top, Not the answer you're looking for? In fact, any character is stored as a number: i.e. Can we do even better with M=28 ? Modular Multiplicative Inverse Calculator - High accuracy calculation Additional restrictions to the key are imposed by the need to decrypt encrypted text :). If you are able to invent a fast factoring algorithm, you will not have to worry about a future job. (Definition). We make use of First and third party cookies to improve our user experience. Examples for property 2): 8 and 25 are prime powers. 2 What would you do? The trick is now that if we enter more than one letter all but the first entered letter are buffered (which means temporarily stored in the computers RAM) until read in in cin >> pl; inside the while loop. We will multiply MOD 26 as we are using the 26 letters of the English alphabet. 1 If a single character is encrypted by E(C) = (c * k) % 36 then possible keys k are numbers that are coprime to 36, ie.gcd(k,36)=1.Furthermore it makes not much sense to consider numbers not between 1 and 36, because of the modulo. The Multiplicative Cipher is an Affine cipher (ax+b) with the value b null (equal to 0), so a multiplication by $ a $. Affine cipher - online encoder / decoder - Calcoolator.eu 9,15,21 and 25). The Multiplicative Cipher is an Affine cipher (ax+b) with the value b null (equal to 0), so a multiplication by a a. In this video u will learn how to encrypt the message using multiplicative cipher technique.Plain text to cipher text.Calculator tricks. background-color: #620E01; Example: Encrypt DCODE with the key $ k = 17 $ and the 26-letter alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZ. PLAIN LETTERNATANTSecret key a=2130190131900120012Cipher letteraamaam You can see the dilemma of this message. If a=4,6,8,,24, we encounter the same dilemma as for a=2. Finally I understand how to calculate the modular multiplicative inverse :) $\endgroup$ - np00. Since 36 is greater than the length of the used alphabet, 36 modulo 26 = 10 is calculated. As a small example we consider Vigenre with the following two alphabets: In both cases, both the plaintext and the key should both consist of the text "0123456789abcdABCD". Consider an alphabet length of M=35: the bad key a=5 (why?) First, symbols of the used alphabet (alphabet as a set of symbols, for example, the alphabet in the above calculator includes space, comma, and dot symbols) are encoded with digits, for example, symbol's order number in the set. We have to understand why multiplying by a bad key a MOD 26 yields some integers more than once and others not at all. The key should not be easily guessable or should not be easily cracked. Code Thank you! Multiplicative Inverse Calculator - The Best Free Online Calculator gcd(k,36)=1. This process repeats until M is reduced to 1 and therefore less than the smallest factor possible, 2. 9 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. If a = 1, the Affine cipher is equivalent of a Caesar cipher. Simply: Z26 = {0,1,2,3,, 24,25}. 11 How to calculate the modular multiplicative inverse for the Affine Cipher 5 7 11 13 17 19 23 25 29 31 35 For example, if the key is 7 and the plaintext letter is s, the numerical value of s is 18, and so the ciphertext letter is (18*7) mod 26 = 22. Finding the decoding keys for each good key a in the same manner, we obtain the following key pairs: Good Encoding key aIts decoding key a-111395217159311191571723191121523172525 Three important observations: All decoding keys a-1 in the right column are among the set of all encoding keys a. Variant Beaufort cipher Base32 Hash function Morse code to text Z-Base-32 View Affine cipher Slope / a Step Down Step Up Then the Vigenre encryption for an input character in and a key key can be described as: The letters of in and key are converted into numbers, these numbers are added, and the sum is re-converted to a letter. Combining our three formulas for the number of good keys, we will then be able to develop a general formula for the number of good keys for any given alphabet length M. Lets start with Example1: M=26=p*q=2*13. Since the bool.h library is very short I want to show you its contents: typedef int bool; const int false = 0; const int true = 1; In the first line the new data type bool is defined of type int so that the (two) bool-variables are just regular integers. Thirdly, listing the good keys would be best done using C++ vectors or even C-style arrays which you might know. In fact, I always have to subtract 101 from each entered lower case plain letter to get its corresponding number. What are the variants of the Multiplicative cipher. RSA Calculator - College of Computing & Informatics Our alphabet length of 28 now yields how many unique encryptions? 21 is an inverse to 5 MOD 26, therefore 5 is inverse to 21 and the two 1s are mirrored over the diagonal line. Why is that? Thus, the encryption process is a Caesar cipher merged with a multiplication cipher. The basic formula to be used in such a scenario to generate a multiplicative cipher is as follows . In the next chapter, I will show you one principle of increasing the safety of a cipher code. for M=29 we have u(29)=28. ~=.., $=.. etc. using properties 1) and 2) yields = (3-1)*(23-22) = 2*4 = 8. I.e. , In, this way you can implement Encrypt a plain text and Decrypt a cipher text for Multiplicative cipher in cryptography. What is the inverse of 7 MOD 11? The key should be changed frequently to prevent cryptographic attacks. Calculates a modular multiplicative inverse of an integer a, which is an integer x such that the product ax is congruent to 1 with respect to the modulus m. ax = 1 (mod m) ax aa1 1 (mod m) a x a a 1 1 ( mod m) Integer a. The encryption of upper case plain letter works similarly except that I have to subtract A=65 (instead of a=101 as above) to obtain our desired plain letter number. Among the 12 good keys we pick a=5 to encode the virus carrier message as follows: PLAIN TEXTANTISTHECARRIER0131981819742017178417 013171412179201007714207Cipher textanromrjukahhouh Exercise1: Encrypt the same plain text using the key a=7. We know already that: ((60) = ((22*3*5) = (22-21)*(3-1)*(5-1)((M) = ((p12* p2* p3) = (p12- p11)*( p2-1)*( p3-1). Now the cipher letter cl equals k and we can end the lower case encoding. In order to be able to use the command setw() we have to include the iomanip.h library in #include . After finding each factor of M, I just print them out in for (j=1;j #include #include #include void main() { int M, m, j, factor, factor2; bool prime; clrscr(); cout << "This program finds the 'bad' keys for an entered alphabet length M." << endl; cout << "===========================================================================" << endl; do { cout << "Enter the alphabet length or 0 to exit: M="; cin >> M; m=M; factor=2; prime=0; //initialization while(factor <= m) { if (m%factor==0) { if (factor!=M) { cout << "Divisor of "<< M << " =" << setw(3) <. The first character G corresponds to the six. WAP to find the solutions of equations: a.14x=12mod 18 b.3x+4=6 mod 132. Extracting arguments from a list of function calls. To find the multiplicative inverse of a real number, simply divide 1 by that number. This requires additional meta-information of the letters that must be recorded before encryption. He obtains: Cipher textanromrjukahhouh013171412179201007714207 013116711232140151519215PLAIN TEXTANLGHLXCOAPPTCP That message does not reveal a virus carrier. In fact, the sets of the encoding and decoding keys are identical. A multiplicative cipher is a type of cipher that comes under a monoalphabetic cipher, in which each letter that is present in the plaintext is replaced by a corresponding letter of the ciphertext, according to a fixed multiplication key.
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