multiplicative cipher calculator

Vigenre cipher - online encoder / decoder - Calcoolator.eu I found a-1 = 2 by simply testing the integers in Z5*={1,2,3,4}. Modular inverse of a matrix. 3. Which number would that be? 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. It is suitable for small-scale applications but not recommended for practical purposes. 2) u(pn)= pn - pn-1, if M is a power of a prime M= pn. 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. So which ones do? You are asked to enter your plain letter in cin >> pl; As long as you dont enter ~ the while-condition while(pl!='~') is fulfilled and the entered plain letter (=pl) is being encoded. 3) u(p*q) = (p-1)*(q-1), if M is a product of two primes M=p*q. 3) ((p*q) = (p-1)*(q-1) for two distinct primes p and q. Consider the letters and the associated numbers to be used as shown below , The numbers will be used for multiplication procedure and the associated key is 7. This encoding and decoding is working based on alphabet shifting & transforming the letters into numbers . The basic task behind the multiplicative cipher is to use a large prime number as a multiplication key, and then use the modular arithmetic of the integers modulo, the key to encode and decode the plaintext. Text is divided into blocks of size n, and each block forms a vector of size n. Each vector is multiplied by the key matrix of n x n. The result, vector of size n, is a block of encrypted text. Secondly, we would translate every upper case plain letter into a lower case cipher letter so that we dont reveal information about the beginning of a sentence. Therefore, since there are no other prime divisors and thus no multiples, all integers less than M serve as good keys. The reason is (M-1) * (M-1) = (-1) * (-1) = 1 MOD M. For example: when using an alphabet length of M = 27 and an encoding key a=26 then its decoding key is a-1 =26. 3 We then write them in the form (1-1/p), multiply them and that product by M yielding ((M). Multiplicative Inverse Calculator - The Best Free Online Calculator Modular Multiplicative Inverse a -1. So, lets understand why the bad keys a = 2,4,6,8,10,12,13,14,16,18,20,22,24 dont produce a unique encryption. The solution can be found with the Extended Euclidean algorithm. color: #ffffff; Why is that? Affine cipher - encoder / decoder. RSA Calculator - College of Computing & Informatics In such case, divide M by that factor: M/=factor; and start checking M/factor for factors less than M/factoretc. These calculations were correct but almost required a calculator. We can therefore always find a-1 for a given good key a. For example, take the list L = "ABCD", whose length is 4. 28 equals 2*2*7 so that all the keys that are multiples of 2 or 7 do not and all non-multiples of 2 or 7 do produce a unique encryption: Z28* = {1, 3, 5, 9, 11, 13, 15, 17, 19, 23, 25, 27} allowing only 12 different unique encryptions. 0x95 = 1001 0101 = x 7 + x 4 + x 2 + 1 0x8A = 1000 1010 = x 7 + x 3 + x And the product of the two polynomial reduced modulo the irreductible polynomial is 1, as expected. b ^ ^ ^ 8 ^ a G n n n n n R R R f h h h h h h $ u R ` R R R n n n n 7 R j n n n f R f k \ ^ % n n `d P ^ v$ .$ r % T 0 G $ r 2 % n n n n Chapter 2 Multiplicative Cipher In this chapter we will study the Multiplicative Cipher. For example if we use "abcdefghijklmnopqrstuvwxyz" and a multiplier of 3, gives "adgjmpsvybehknqtwzcfilorux". The message "ACDC" should be encrypted with the key "ABBA" according to the Vigenre method. How many multiples of 3 will not produce a unique encryption? Technically 1 too, but this would be no change from plaintext. In general we have the: Formula for the number of good keys if M is a prime If the alphabet length M=p is prime, the number of good keys is u(p) = p-1. An affine cipher is a cipher belonging to the group of monoalphabetic substitution ciphers. Viewed 4k times . The x values are the ones that we can choose independently, here the length of the alphabet M. Each y-value is dependent on the choice of x, i.e. ((21)=________________________ as 1,2,4,5,8,10,11,13,16,17,19,20 are relative prime to 21. This process repeats until M is reduced to 1 and therefore less than the smallest factor possible, 2. Encrypt and decrypt any cipher created in a Playfair cipher. Example: Encrypt DCODE with the key k= 17 k = 17 and the 26-letter alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZ Finally, I have to add the usual 65 = A (why?) Then the if-condition if (ans=='e') is fulfilled so that we enter the encoding part of the program. Also, there is no general match on how to handle digits or special characters. Can I use an 11 watt LED bulb in a lamp rated for 8.6 watts maximum. Just as the regular multiplication of two integers is commutative (i.e. Definition of an inverse number: A number a-1 that yields 1 when multiplied by a is called the inverse of a. Online calculator: Modular inverse of a matrix - PLANETCALC We also turn the plaintext into digraphs (or trigraphs) and each of these into a column vector. If a=4,6,8,,24, we encounter the same dilemma as for a=2. Affine cipher: Encode and decode - cryptii 2.2 Decryption of the Multiplication Cipher Now that the virus carrier message was encoded in a unique manner how can it be decoded? Say you first want to encode the letter c then you have to enter e when asked. 9 How do you find the key domain of the multiplication cipher efficiently Why is that? } Therefore, no matter how he decides to crack the cipher text, it wont take long. } 23 For a given alphabet, there are only a few possible keys. It describes the multiplicative property of (. This requires additional meta-information of the letters that must be recorded before encryption. or . //Author: Nils Hahnfeld 10-16-99 //Program to determine ((M)using M*(1-1/p1)*(1-1/p2)* #include #include void main() { int factor, M, m; float phi; clrscr(); cout << "This programs uses M*(1-1/p1)*(1-1/p2)* to calculate phi(M). They are trade-offs in terms of their efficiency: the gain of not having to determine the most frequent letter in the cipher text for the brute force approach is at the cost of producing all possible cipher codes. Step 2: The basic formula that can be used to implement Multiplicative Cipher is: Decryption= (C * Multiplication inverse of the key) Mod 26. It surely acquires this simple form for any number of primes or prime powers. Cite as source (bibliography): In order to have a modular multiplicative inverse, determinant and modulo (length of the alphabet) should be coprime integers, refer to Modular Multiplicative Inverse Calculator. To find a multiplicative inverse We need to find a number x such that: If we find the number x such that the equation is true, then x is the inverse of a, and we call it a^-1. Therefore, a simple prime check program would be sufficient to find the divisors p of M. We then set up the factors of the form (1- 1/p), multiply them and eventually multiply that answer by M. Example1: Say M=180, then a prime check program yields the prime factors 2,3 and 5, so that ((180) = 180 * (1-1/2) * (1-1/3) * (1-1/5) = 180 * (1/2) * (2/3) * (4/5) = 90 * (2/3) * (4/5) = 60 * (4/5) = 48 Example2: Say M=360, since 360=2*180 the prime factors are again 2,3 and 5, so that ((360) = 360 * (1-1/2) * (1-1/3) * (1-1/5) = 360 * (1/2) * (2/3) * (4/5) = 180 * (2/3) * (4/5) = 120 * (4/5) = 96 Example3 is for you: Say M=90, since 90=____ the prime factors are _______, so that ((90) = 90 * (1-1/__) * (1-1/__) * (1-1/__) = 90 * ____________________ = _______________ = _______________ = ___ Of course, I could have computed the answers in the above examples right away but I wanted to give you the chance of brushing up on your skills to multiply fractions. Each odd plain letter translates into 13 (=n): a=13 odd letters 13*1 = 13 MOD 26, 13*3 = 13*2 + 13*1 = 0 + 13 = 13 MOD 26, 13*5 = 13*4 + 13*1 = 0 + 13 = 13 MOD 26, 13*7 = 13*6 + 13*1 = 0 + 13 = 13 MOD 26, etc. The plain letter c is stored as 103, however, I want the c to equal 2 in compliance with our translation a=0, b=1, c=2, etc. It would take quite a long time for a . An easier way to determine the decoding key a-1 Decoding a message turns out to be really easy once we know the decoding key a-1. Now, lets come to the highlight of this section: I will show you in a few steps how to compute ((M) for any M from one equation instead of combining the four properties? 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! Say, the lower case plain letter c is entered, then the condition if ((pl>='a') && (pl<='z')) is fulfilled and the encryption is being executed by this one seemingly weird command cl='a' + (a*(pl -'a'))%26; Let me explain that to you in detail: First you need to know that each letter is stored as a number: i.e. This is not a useful encryption system since it may yield ambiguous messages. By subtracting a (=101) from the entered plain letter in (pl -'a');. This eventually enables us to calculate the number of integers that are relative prime to these primes and prime powers. The 14 as the possible cipher E then tells him to test the keys a=10 and a=23. As 36=2*2*3*3, the possible keys are basically all numbers not multiples of 2 and/or 3. The following C++ program firstly determines the factors for an entered alphabet length M and secondly their multiples, the bad keys. Well, I leave all the entered non-letters such as ! Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. color: #ffffff; 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.) Instead of adding a number as we did in the Caesar Cipher, we will now multiply each plain letter by an integer a, our secret encoding key. In the process you'll become comfortable with modular arithmetic and begin to understand its importance to modern cryptography. For larger integers, however, dividing by every integer less than M slows the program down enormously. Please enable JavaScript to use all functions of this website. Step 4: So, once the calculation part is done now you can easily encrypt your given plain text. padding-right: 20px; Lets simply test all possible keys of the multiplication ciphers MOD 26: PLAIN LETTER 0000000000000000000000000 a ABCDEFGHIJKLMNOPQRSTUVWXYZ00000000000000000000000000010123456789101112131415161718192021222324252024681012141618202224024681012141618202224303691215182124147101316192225258111417202340481216202426101418220481216202426101418225051015202549141924381318232712172216111621606121824410162228142006121824410162228142070714212916234111825613201815223101724512198081624614224122021018081624614224122021018909181101921120312214132251423615247162581710010204142481821222616010204142481821222616110112271831425102161721324920516112238194151201224102282061841621401224102282061841621413013013013013013013013013013013013013013140142164186208221024120142164186208221024121501541982312116520924132176211025143187221116016622122188241442010016622122188241442010170178251672415623145221342112320112191011891801810220124221462416801810220124221462416819019125241710322158120136251811423169221147200201482221610424181260201482221610424181262102116116122171272231813832419149425201510522022181410622420161284022181410622420161284230232017141185225221916131074124211815129632402422201816141210864202422201816141210864225025242322212019181716151413121110987654321 We learned already that the key a=2 (as can be seen in the 3rd row) does not produce a unique encryption. A corresponding warning is displayed. This corresponds to the K. If "GEHEIMNIS" would be completely encoded by this procedure, the ciphertext would be: "SMVMYKNYC". Example1: When using fractions, 5-1=1/5 is the inverse number to 5, 3-1=1/3 is the inverse number to 3, 3/2 is the inverse number to 2/3. This means that the cipher E does not equal 7. In order to be able to use the command setw() we have to include the iomanip.h library in #include . M23456789101112131415161718192021( (M)12242648121041268816618812 Similar to our notation, the properties of Eulers (-function that computes the number of integers that are relatively prime to M and wrote similarly to our notation: Eulers (-function: 1) ((p) = p-1 for a prime p. 2) ((pn) = pn - pn-1 for a prime power pn. They are very special primes as they must consist of 100 digits or more. Again, we just have to find the cipher numbers in the 5th row and then go up that column to the very top to find the corresponding plain letter. Coincidence? Longer messages reveal the most the letter e equivalent, however, this is not necessarily so for our message. Although the function is well-defined when a letter occurs more than once, this makes little sense in encryption algorithms, since the reversibility suffers. Thus our decoding function P = a-1*C MOD 26 tells us to simply multiply each cipher letter by the inverse of the encoding key a=5, namely by the decoding key a-1=21 MOD 26 and we can eventually decode: Cipher textanromrjukahhouh013171412179201007714207 0131981819742017178417PLAIN TEXTANTISTHECARRIER For example, multiplying the cipher letter r=17 by a-1 = 21 decodes the r to T=19 since 21*17 = 357 = 19 MOD 26. where c is the modular multiplicative inverse of a. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Solution of Multipilicative Inverse of 7. Step 2: The basic formula that can be used to implement Multiplicative Cipher is: Decryption= (C * Multiplication inverse of the key) Mod 26 Here, c = ciphertext Mod = Modulo Step 3: Let's see how decryption can be done using the above formula: Ciphertext = QCCSWJUPQCCSW and multiplication inverse key = 15