Multiplicative cipher encryption|Multiplicative cipher|Multiplicative cipher example|What is multiplicative cipher PLAYFAIR CIPHER WITH EXAMPLE||SUBSTITUTION TECHNIQUE||MATHEMATICS OF. How do you find the key domain of the multiplication cipher efficiently? Multiplicative encryption uses a key k k (an integer) and an alphabet. Thus, among those numbers that occur twice in the cipher code, 14, 17 and 20, we can eliminate the odd 17. 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. This means that the cipher E does not equal 7. cryptography - Affine cipher - Modular multiplicative inverse Affine cipher - Encoder and decoder-ME2 Online Tools Contributed by: Shawna Martell (March 2011) Open content licensed under CC BY-NC-SA Snapshots Therefore, an eavesdropper simply has to count letter frequencies to identify the most frequent cipher letter. div#home a:active { 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. How could it be broken? CacheSleuth - Multiplicative Cipher Here both approaches are treated: for separate partial alphabets and for a memorized alphabet. 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. 11 For an alphabet length of 26 this corresponds to 12 keys: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 and 25. Examples for property 3): 15 and 21 are products of two primes. For the fraction a/b, the multiplicative inverse is b/a. Subsequently, that difference is multiplied by the good key a=5 which I defined as such in int a=5. 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. How to make sense of the decryption formula for Affine ciphers? Convert each letter in the plain text alphabet to a corresponding integer in the range of 0 to m -1; 2. For illustration purposes we use the message "GEHEIMNIS" and the key 3. WAP to implement Additive cipher(key=20), Multiplicative cipher(key=15)and affine cipher(key=15,20). A corresponding warning is displayed. By using this website, you agree with our Cookies Policy. Modular inverse of a matrix. We will multiply MOD 26 as we are using the 26 letters of the English alphabet. rev2023.5.1.43405. 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. It is actually less secure than the Caesar cipher because the number of possible keys is smaller. To do so, we have to look at the encryption equation C=a*P MOD 26 and solve it for the desired plain text letter P. In order to solve an equation like 23=5*P for P using the rational numbers, we would divide by 5 or multiply by 1/5 to obtain the real solution P=23/5. Alphabets (yes, there may be several: more below) can be described by a list L of letters. Multiplicative Inverse Calculator - The Best Free Online Calculator Are these quarters notes or just eighth notes? Furthermore it makes not much sense to consider numbers not between 1 and 36, because of the modulo. 22 Now, how do you decrypt the above message? 2.5 Counting the Number of Good Keys for various Alphabet Lengths M An Introduction to the Euler Function. Example1: If M=24=3*8=3*23, then ((24) = ((3*23) using property 4) yields = ((3)*((23). Try to understand as much as possible first, then continue reading. 17 More precisely: Out of the 25 (= p * q - 1) integers that are smaller than 26, we had 12 (=13-1) multiples of 2 {2,4,6,8,10,12,14,16,18,20,22,24} and the 1 (=2-1) multiple of 13 {13} as bad keys, so that 25-12-1=12 good keys are remaining: a = 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 Notice that u(26) = 12 = 25-12-1 = (p*q - 1) (p-1) - (q-1) Example2: For M=10=5*2, we obtain u(10)=4 good keys which are obtained by crossing out the 4 (=5-1) multiples of 2 and the 1 (=2-1) multiples of 5 as bad keys: a = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Notice that again u = 4 = 9 4 1 = (p*q - 1) (p-1) (q-1) Example3: For M=15=5*3, we obtain u(15)=8 good keys which are obtained by crossing out the 4 (=5-1) multiples of 2 and the 2 (=3-1) multiples of 5: a = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 Notice that again u = 8 = 14 4 2 = (p*q - 1) (p-1) (q-1) The number of good keys can always be computed by u(p*q) = (p*q - 1) - (p-1) -(q-1). > m o ` a b c d e f g h i j k l 7 9 bjbjUU (> 7| 7| ). 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. Each letter is associated with its rank $ c $ in the alphabet (starting from 0). color: #ffffff; 1) Learn how to decode the Multiplication Cipher. Extracting arguments from a list of function calls. Once we have the solution, our x is the modular multiplicative inverse of a modulo m. Rewrite the above equation like that We just had to multiply each cipher letter by a-1. RSA Calculator - College of Computing & Informatics For classical methods, the alphabet often consists only of the uppercase letters (A-Z). First we need to calculate the modular multiplicative inverse of keyA. Options: Multiplier: filter whitespace characters group 5 characters filter non-alphabet characters convert to first alphabet Modular arithmetic is used; that is, all operations (addition, subtraction, and multiplication) are done in the ring of integers, where the modulus is m - the length of the alphabet. Thus, we now go ahead and practice a bit more computer programming. We first found the bad keys as the multiples of the prime divisors of the alphabet length M. Consequently, the good keys are the remaining integers less than M. Again a perfect task for a computer, especially when we have to find the prime divisors of bigger integers. (Attacks). Step 2: First of all we will require an alphabet table with numeric values attached to each alphabet so that we can do the encryption process fastly. Example5: If M=65=5*13=p*q, then the formula yields u(65) = (5-1)*(13-1) = 4*12 = 48. It is not difficult to find the encoded E in English documents as every 8th letter on average is an E (about 13%), it is therefore by far the most frequent letter. This table shows the occurances of the letters in the text (ignoring the case of the letters): This table shows how the text matches a normal probability to text (where 'E' has the highest level of occurance and 'Z' has the least). I will complete the first ones and leave the second ones for you as exercises. We factor p1=2 yielding = 2*(2-1)*(3-1)*(5-1) = p1* (p1- 1)*( p2-1)*( p3-1). From property 1) we know that ((2)=1 and ((13)=12, and consequently, ((2*13) = ((2)*((13) = 1*12 = 12 which is exactly property 3). 0 How many multiples of 3 will not produce a unique encryption? Thank you! Again, I found the inverse of a=3 by testing the integers in Z7* ={1,2,3,4,5,6} The inverse of a=4 is 2 since a * a-1 = 4 * 2 = 8 = 1 MOD 7. a=6 is inverse to itself MOD 7 since a * a-1 = 6 * 6 = 36 = 1 MOD 7. Credit goes to the Swiss Mathematician Leonard Euler (pronounced Oiler, 1707-1783). Take a moment now to verify the Rule for finding the decoding key a-1: 1) For a given good key a, find the unique 1 in the a-row, 2) From that 1 go all the way up that column, 3) The letters numerical equivalent that you hit on the very top is the inverse of a. This calculator uses an adjugate matrix to find the inverse, which is inefficient for large matrices due to its recursion, but perfectly suits us. Ubuntu won't accept my choice of password. Lets check why: 1*1=1 MOD 26 which explains a = a-1 = 1 (Big deal!). Back to the virus carrier message. We make use of First and third party cookies to improve our user experience. In such case, divide M by that factor: M/=factor; and start checking M/factor for factors less than M/factoretc. 21 Example2: M=81=34 has again 3 as the only prime divisor and thus b = 81/3 1 = 34/3 1 = 33 1 = 26 bad keys. The Multiplicative Cipher is an Affine cipher (ax+b) with the value b null (equal to 0), so a multiplication by a a. Online calculator: Hill cipher - PLANETCALC However, it yields the original text. 3.0.4224.0, The greatest common divisor of two integers, The greatest common divisor and the least common multiple of two integers, Solution of nonhomogeneous system of linear equations using matrix inverse. This encoding and decoding is working based on alphabet shifting & transforming the letters into numbers . Say M=26=2*13=n*m. Since n and m are two distinct primes, they certainly are relative prime, so that the condition for property 4) is fulfilled. Calculator Use Multiplication of positive or negative whole numbers or decimal numbers as the multiplicand and multiplier to calculate the product using long multiplication. Definition of an inverse number: A number a-1 that yields 1 when multiplied by a is called the inverse of a. We get the following encoding and decoding table. Key = If a=4,6,8,,24, we encounter the same dilemma as for a=2. Affine Cipher - Online Decryption, Decoder, Encoder, Calculator Zero has no modular multiplicative inverse. It uses genetic algorithm over text fitness function to break the encoded text. The letter A remains unchanged ans id always encoded A. Write to dCode! 2.2 Decryption of the Multiplication Cipher Now that the virus carrier message was encoded in a unique manner how can it be decoded? Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 23 Modular Multiplicative Inverse a -1. The explanation of cipher, which is below the calculator, assumes an elementary knowledge of matrices. For a check: the eight integers 1,5,7,11,13,17,19,23 are relative prime to 24 and thus the good keys for M=24. I will answer it at the end of this chapter in the Abstract Algebra section. To decode the above virus carrier message we found the inverse of a=5 through a clever check of the products of a and a-1 that produced one more than multiples of 26. Note that you may need to run it several times to find completely accurate solution. block cipher - Multiplicative Inverse in AES - Cryptography Stack Exchange Therefore, a translation must take place, which can on the one hand transform letters in numbers and, conversely, re-generate letters again. 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. We have to understand why multiplying by a bad key a MOD 26 yields some integers more than once and others not at all. Can we do even better with M=28 ? If we had a video livestream of a clock being sent to Mars, what would we see? Multiplicative Simplified variant of the affine cipher Cipher Description Security About alphabets Plaintext: The quick brown fox jumps over the lazy dog. The 26-letter Latin alphabet allows only 11 keys: 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 and 25 (these are coprime numbers with 26). For a given alphabet, there are only a few possible keys. Why is that? where the operation of multiplication substitutes the operation of division by the modular multiplicative inverse. The reason for that is that a prime number has per definition no prime divisor except for 1 and itself. Before we conclude this section with the highlight of creating a sole formula for ((M) from these four properties, we will consider 2 examples for each of the 4 properties of Eulers (-function. Since we calculate MOD 26, thus dealing with integers from 0 to 25, we now have to find an integer a-1 among those integers that yields 1 MOD 26 . If so please go ahead and modify the following program. Lets add a dot to our alphabet to denote the end of a sentence in the original message. The multiplicative inverse of a modulo m exists if and only if a and m are coprime (i.e., if gcd(a, m) = 1). The message "ACDC" should be encrypted with the key "ABBA" according to the Vigenre method. What are the variants of the Multiplicative cipher. 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. Each letter is enciphered with the function (ax + b) mod 26. What would you do? The procedure to use the multiplicative inverse calculator is as follows: Step 1: Enter the values in the numerator and denominator input field Step 2: Now click the button "Solve" to get the output Step 3: The multiplicative inverse value will be displayed in the "Answer" field What is Multiplicative Inverse? Therefore, no matter how he decides to crack the cipher text, it wont take long. 23 N (=13) translates into a for any even key a aswell because even keys N 4*13 = 2*(2*13) = 2*0 = 0 MOD 26, 6*13 = 3*(2*13) = 3*0 = 0 MOD 26, 8*13 = 4*(2*13) = 4*0 = 0 MOD 26, etc. 19 Two MacBook Pro with same model number (A1286) but different year. That is That means the key should not have any common factors with the alphabet or plaintext except for 1. 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. Try to answer it for yourself. Moreover, multiplying any two good keys yields again a good key. 9 Equivalently stated: what product of a-1 and 5 equals 1 more than a multiple of 26 such as 27, 53, 79, 105, etc? 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. So in our case, it was GEEKSFORGEEKS, so it will become: Multiplicative Cipher text = QCCSWJUPQCCSW. 5 PLAIN LETTER:ABCDEFGHIJKLMNOPQRSTUVWXYZ Secret key: a=2012345678910111213141516171819202122232425 024681012141618202224024681012141618202224 Cipher letter:acegikmoqsuwyacegikmoqsuwy Notice, that only every other cipher letter appears, and that exactly twice. 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. To have the solution, the right part of the linear diophantine equation should be a multiple of the . Now when a=25, we have: 25*25 = 625. Notice, that all we need to find are the different primes, say p1, p2,, pn, as our explicit formula for the number of unique encryptions appears to be: Formula for the number of good keys for any alphabet length M: For an alphabet length M, there are ((M) = M * (1- 1/p1) * (1- 1/p2) ** (1- 1/pn) good keys where each pi is a prime divisor of M. It is really enjoyable to use this simple formula as we just need to find all prime divisors of M and dont have to worry about how often they occur. Affine Cipher Calculator - Math Celebrity background-color: #620E01; 4 This corresponds to the K. If "GEHEIMNIS" would be completely encoded by this procedure, the ciphertext would be: "SMVMYKNYC". The conversion to letters takes place modulo to the alphabet length: If a 1 is added to the last character, the result of the sum is the first character of the alphabet. } 27=3*3*3, so that only the multiples of the only prime divisor 3 such as a=3, 9 and 27 will not yield a unique encryption, all the other integers will: The good keys a are therefore Z27* = {1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26} allowing 18 different unique encryptions, 6 more than before. Parabolic, suborbital and ballistic trajectories all follow elliptic paths. 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. From now on we will use a handy Notation for the set of possible and good keys: 1) All the possible keys for an alphabet length of 26 are clearly all the numbers between 1 and 26, denoted as Z26. The multiplicative cipher is a simplification of the Affine cipher. He obtains: Cipher textanromrjukahhouh013171412179201007714207 013116711232140151519215PLAIN TEXTANLGHLXCOAPPTCP That message does not reveal a virus carrier. The only disadvantage is that the minus sign itself has to be written as "---", so as not to be confused as a range operator. Example the letter M (12th letter in this zero indexed alphabet) and key 3 would be 12 * 3 = 36. When doing so we will discover very important mathematical encryption tools such as Eulers (-function, Eulers and Lagranges Theorem and study further examples of groups, rings and fields. To use this worksheet, you must supply: a modulus N, and either: 36 modulo 26 = 10 so the letter K would be chosen. div#home a:hover { RSA Express Encryption/Decryption Calculator This worksheet is provided for message encryption/decryption with the RSA Public Key scheme. That is weird! Other frequent letters such as T, A, O and N occurring with about (8%) might be of further help to crack the cipher text. So in our above example, the key is 7. The algorithm memorizes the alphabet with which it has determined the number of the plaintext. Examples for property 4): 24 and 28 are products of primes and prime powers. In fact, the cipher E can only be an even cipher letter as only even numbers appear in the E-column. In order to increase the probability of this, the alphabet is expanded, so its length becomes the prime integer. Example4: What is the inverse of 3 MOD 11? In some secret manner, the sender and the recipient had to agree on the encoding key a. So there is an infinite number of possible keys, but many will give identical messages, because for a $ k $ key, then the $ k + 26 $ key gives an identical cipher. Therefore, since there are no other prime divisors and thus no multiples, all integers less than M serve as good keys. Does the increase of our alphabet length by 1 increase the number of unique encryptions obtained? That means: Because a=2 is a bad key all the multiples of a must be bad keys aswell. 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. 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. This process repeats until M is reduced to 1 and therefore less than the smallest factor possible, 2. In order to be able to use the command setw() we have to include the iomanip.h library in #include . This eventually enables us to calculate the number of integers that are relative prime to these primes and prime powers. It is suitable for small-scale applications but not recommended for practical purposes. The odd multiples of 13 (i.e. The MOD 26 calculation leaves the 10 unchanged. 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. In fact, the sets of the encoding and decoding keys are identical. Implementation of Affine Cipher - GeeksforGeeks Are they the odd numbers between 1 and 25? Therefore, we just have to add a number in order to get k=111. Examples for property 2): 8 and 25 are prime powers. This shows that when using an encoding key that is one less than the alphabet length M, namely a = M-1, then the decoding key must also equal M-1, a-1 = M-1. There are other numbers co-prime with 26 (which are greater than 26) but they give alphabets identical to those above. 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. Thus they have the following restrictions: a=4 is inverse to itself modulo 5 since a * a-1 = 4 * 4 = 16 = 1 MOD 5. } 1 Reciprocal (or) Multiplicative Inverse is: Why does Acts not mention the deaths of Peter and Paul? 5 7 11 13 17 19 23 25 29 31 35 Try it for yourself! Which cracking method should a code cracker use. Determining the bad keys for a given alphabet length M is a perfect task for a computer. Parts of Long Multiplication 2 5 6 Multiplicand 3 2 Multiplier + 5 1 2 Partial Product + 7 6 8 Partial Product = 8 1 9 Sphero Up to 1 Hour Grades: 5 to 8. To find the multiplicative inverse of a real number, simply divide 1 by that number. 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. It surely acquires this simple form for any number of primes or prime powers. If you are able to invent a fast factoring algorithm, you will not have to worry about a future job. Our ultimate goal is not to develop a formula for the number of bad keys but rather for the number of good keys. 4) ((n*m) = ((n) * ((m) when n and m are relatively prime. 1. Each character is multiplied with this key and the corresponding letter is substituted. This is it. 15 Consider an alphabet length of M=35: the bad key a=5 (why?) GitHub - Mehul2205/Cryptography-Assignments: These are the lab Notice, that property 3) became useless for the calculation process since factors that are relative prime are separated via property 4). 15 The first time the loop passes the line cout << cl; the translated plain letter pl that was read in as cin >> pl; before the while loop is output as its cipher letter cl. Remember that the first 3 ciphers are meant to familiarize you with basic encryption systems. Even though this cipher seems to be more complex than the Caesar cipher, it is not more secure. For instance, we encoded with a=3, then the encryption function was C=3*P mod 26. The 14 as the possible cipher E then tells him to test the keys a=10 and a=23. The determinant of the matrix should not be equal to zero, and, additionally, the determinant of the matrix should have a modular multiplicative inverse. Example: D = 3, so $ 3 \times 17 \mod 26 \equiv 25 $ and the letter at rank 25 is Z. 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. Example3: Doing arithmetic MOD 7, the inverse of a=3 is a-1 = 5 because a * a-1 = 3*5 = 15 = 1 MOD 7. 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. The following steps take place: In the example, an overflow has occurred in the third letter, so that modulo |L| = 4 is calculated. Reminder : dCode is free to use. //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). Example: If we use the encoding key a=3, we find that the decoding key a-1 is 9 as the 1 occurs in the J- or 9-column telling us additionally that the plain letter J (=9) encrypts to the cipher letter b (=1). Modulus m. if the letter e (the most frequent letter in the English language) occurs 20 times in the plain text its replacement letter will appear 20 times in the cipher text. You now understand why cryptographers have an affection for prime numbers. Is there a generic term for these trajectories? Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. It describes the multiplicative property of (. https://de.wikipedia.org/wiki/Alphabet_(Kryptologie). So which ones do? An extreme example would be when a=0: all plain letters are translated into 0s which are all as so that no decryption is possible. In this lab, you'll learn about the multiplication cipher, a monoalphabetic cipher. 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. Tool to decrypt/encrypt with multiplicative encryption, a substitution cipher based on a multiplication operation. Online calculator: Modular arithmetic - PLANETCALC 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. margin-bottom: 16px; 10 the commonly used RSA Cipher is based on the relative slowness of such factoring programs. Example2: For M=9=32 we have u(9) = 32 - 31 = 9 3 = 6 which are the 6 good keys a=1,2,4,5,7,8. Modular Multiplicative Inverse Calculator - High accuracy calculation Additionally, you will learn that the RSA Cipher uses prime numbers as well. For example if we use "abcdefghijklmnopqrstuvwxyz" and a multiplier of 3, gives "adgjmpsvybehknqtwzcfilorux". If a = 1, the Affine cipher is equivalent of a Caesar 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?
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