multiplicative cipher calculatorghana lotto prediction

What 1 formula is used for the Affine Cipher Calculator? a bug ? 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 0 15 First we need to calculate the modular multiplicative inverse of keyA. . Our good-key-criterion declares those integers to be good keys that are relative prime to 27. However, there are some additional integers that are not prime (i.e. Vice versa, the cost of detecting the most frequent cipher letter in the first approach is at the gain of producing only one plain text provided that the most frequent cipher letter turns out to be unique. The encryption process is done by multiplying the numerical value of each letter in the plaintext by the key and then taking the result modulo the key. An affine cipher is a cipher belonging to the group of monoalphabetic substitution ciphers. Reminder : dCode is free to use. Therefore, no matter how he decides to crack the cipher text, it wont take long. In fact, the security of i.e. Information Security Stack Exchange is a question and answer site for information security professionals. Try to explain this, than continue reading! These calculations were correct but almost required a calculator. It is not difficult to understand that the length of such numbers requires the usage of computers. That is, . There are several way to implement the inversion and the affine transformation described in the AES to get the final SBox. Equivalently stated, 105 divided by 26 leaves a remainder of 1. Thank you! All symbols to be encrypted must belong to alphabet, Everyone who receives the link will be able to view this calculation, Copyright PlanetCalc Version: For example, Caesar cipher using a left rotation of three places, equivalent to a right shift of 23 as given below. Why are players required to record the moves in World Championship Classical games? 8 Alternatively, the non-alphabet letters in the key and the plain text can also be filtered out to increase the security. They seem to not follow any apparent pattern. 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. Even though this cipher seems to be more complex than the Caesar cipher, it is not more secure. a=4 is inverse to itself modulo 5 since a * a-1 = 4 * 4 = 16 = 1 MOD 5. What is the symbol (which looks similar to an equals sign) called? Encrypt and decrypt any cipher created in a Playfair cipher. 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? Calculate the value of each letter as follows (where a and b are the keys of the password): E (x)= (ax + b) mod m 3. where c is the modular multiplicative inverse of a. The key should be changed frequently to prevent cryptographic attacks. 23 What is the inverse of 5 MOD 11? So are 2 and 3, 2 and 5, 3 and 10, 26 and 27, 45 and 16. 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. Each letter is associated with its rank $ c $ in the alphabet (starting from 0). gcd(k,36)=1. In the detailed representation of the alphabets (click on the "" -button), the alphabets can be edited in the short-write mode. Subsequently, that difference is multiplied by the good key a=5 which I defined as such in int a=5. 2) If M is a prime power, M=pn: Now lets look back at M=27 as an example where we only have the one prime factor p=3, such that M=33. If a single character is encrypted by E(C) = (c * k) % 36 then possible keys k are numbers that are coprime to 36, ie. 2) u(pn)= pn - pn-1, if M is a power of a prime M= pn. First of all, you need to know which one of the 12 good keys was used. https://de.wikipedia.org/wiki/Alphabet_(Kryptologie). This brute force approach will work fast enough for integers M that have 10 digits or less. affine cipher If you are able to invent a fast factoring algorithm, you will not have to worry about a future job. Does the increase of our alphabet length by 1 increase the number of unique encryptions obtained? 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? 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. Lab 2. See the image attached below for a better understanding. We denote 5-1 the inverse of 5. Remember that the first 3 ciphers are meant to familiarize you with basic encryption systems. Just as the regular multiplication of two integers is commutative (i.e. By using this website, you agree with our Cookies Policy. This means that the cipher E does not equal 7. 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. Options: Multiplier: filter whitespace characters group 5 characters filter non-alphabet characters convert to first alphabet 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. The modular multiplicative inverse of a modulo m can be found with the Extended Euclidean algorithm. 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! So, we are left with determining the decoding key a-1 knowing the original encoding key a. 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 handling of non-alphabet characters (convert, skip, ) can be set in the options - but this is not a function of the actual encryption process itself. 26, 52, 78, ) have its equivalent key in a=0, a very bad key, since 26=52=78=0 MOD 26. By using our site, you 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. Network Security: Multiplicative InverseTopics discussed:1) Explanation on the basics of Multiplicative Inverse for a given number.2) Explanation on the basi. As you can see on the wiki, decryption function for affine cipher for the following encrytption function: E (input) = a*input + b mod m is defined as: D (enc) = a^-1 * (enc - b) mod m The only possible problem here can be computation of a^-1, which is modular multiplicative inverse. 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. background-image: none; Example: D = 3, so $ 3 \times 17 \mod 26 \equiv 25 $ and the letter at rank 25 is Z. Since 625=24*26+1 which means that 625 leaves a remainder of 1 when divided by 26, we have 625 = 1 MOD 26 and altogether 25 * 25 = 625 = 1 MOD 26. Multiplying such answers yields the number of good keys for any given alphabet length. And, for this to happen, we need to have a modular inverse of the key matrix in - ring of integers modulo m. If source vector B is multiplied by matrix A to get vector C, then to restore vector B from vector C (decrypt text), one needs to multiply it by the modular inverse of the matrix. For the same reason, an alphabet length of M=31 produces u=30 unique encryptions. A reciprocal is one of a pair of numbers that when multiplied with another number equals the number 1. Please enable JavaScript to use all functions of this website. It describes the multiplicative property of (. rev2023.5.1.43405. Modulo Arithmetic & Ciphers. Technically 1 too, but this would be no change from plaintext. Introduction to Monotonic Stack - Data Structure and Algorithm Tutorials. You should have realized that decoding means to undo the original multiplication. Example4: For M= 34 =81, we get u(81) = 34 - 33 = 81 27 = 54. 19 The key should not be easily guessable or should not be easily cracked. To have the solution, the right part of the linear diophantine equation should be a multiple of the . 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. Of course, you dont want to receive any more ambiguous messages. In fact, I always have to subtract 101 from each entered lower case plain letter to get its corresponding number. The bad key a=2 yields an ambiguous message as we saw in the introductory example: each A turns into 0 (=a) since 2*0 = 0 MOD 26 just as each N turns into 0 since 2*13 = 26 = 0 MOD 26. Examples for property 2): 8 and 25 are prime powers. 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. This is important because even if a key is secure when it is first chosen, it can become less secure over time as technology and methods for breaking encryption increase. 13 All we need to know are the prime divisors of M, but we dont even need to know how often a prime number divides M. However, it turns out to be indispensable when M is not the product of two primes, but say a product of a prime and a prime power. Option 2: Cracking the cipher code using trial and error (brute force) Knowing that there are just 12 possible unique encryptions MOD 26, the journalist produces the corresponding 12 rows in the 26 x 26 multiplication table and cracks the code easily. For the M, 12*3=36 would result. That are those that dont have a common divisor with 26. I.e., for M=27 we just need to know that 3 is a prime divisor of 27 but not how often it divides 27. Try to understand as much as possible first, then continue reading. We wont have to do it that way again since there is a much more straightforward method. This is not a useful encryption system since it may yield ambiguous messages. WAP to implement Additive cipher(key=20), Multiplicative cipher(key=15)and affine cipher(key=15,20). What is the inverse of 7 MOD 11? The multiplicative cipher is a special case of the Affine cipher where B is 0. Cipher textanromrjukahhouha=1ANROMRJUKAHHOUHa=3ANXWEXDYMALLWYLa=5ANTISTHECARRIERa=7ANVCYVFOUABBCOBa=9ANZQKZBIEAVVQIVa=11ANLGULPQIADDGQDa=15ANPUGPLKSAXXUKXa=17ANBKQBZSWAFFKSFa=19ANFYCFVMGAZZYMZa=21ANHSIHTWYAJJSWJa=23ANDEWDXCOAPPECPa=25ANJMOJRGQATTMGT MS Excel as a simple encryption and decryption tool: I created the following table in MS Excel with the CHAR and the MOD function: Cipher textanromrjukahhouhaa-101317141217920100771420739ANXWEXDYMALLWYL521ANTISTHECARRIER715ANVCYVFOUABBCOB93ANZQKZBIEAVVQIV1119ANLGULPQIADDGQD157ANPUGPLKSAXXUKX1723ANBKQBZSWAFFKSF1911ANFYCFVMGAZZYMZ215ANHSIHTWYAJJSWJ2317ANDEWDXCOAPPECP2525ANJMOJRGQATTMGT For example, I created the T in the row a=5 using the Excel-formula =CHAR(65+MOD(E$2*$B4,26)) where the cell E$2 contains 17 and the cell $B4 contains 21 as the decoding key a-1. Thus, property 4) yields nothing new if our alphabet length is the product of two primes. For the fraction a/b, the multiplicative inverse is b/a. I want to show you an example where we used it already. Say, we want to encrypt the plain letter C=67. 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. Multiplicative encryption uses a key $ k $ (an integer) and an alphabet. Are the used 12 unique encryptions a set number? One of the major goals of current Mathematics research is to design faster factoring algorithms as todays are fairly slow. That means the key should not have any common factors with the alphabet or plaintext except for 1. (Identification), How to decipher Multiplicative cipher without key? margin-bottom: 16px; Now, lets look at examples for MOD arithmetic: Example2: The inverse of a=3 is a-1 = 2 MOD 5 because a * a-1 = 3*2 = 6 = 1 MOD 5. In order to create a n x n size matrix, keyphrase length should be square of an integer, i.e., 4, 9, 16. WAP to find the solutions of equations: a.14x=12mod 18 b.3x+4=6 mod 132. For illustration purposes we use the message "GEHEIMNIS" and the key 3. Why is that? I will couple the Multiplication Cipher with the Caesar Cipher (which produces 26 unique encryptions) to obtain a super encryption that will allow 12*26=312 possible unique encryptions. Are they the odd numbers between 1 and 25? 3 This is the reason why a=2 yields an ambiguous decryption. Thus they have the following restrictions: . How to encrypt using Multiplicative cipher? 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). 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. 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. 5 7 11 13 17 19 23 25 29 31 35 It has to be placed after the cout command as in: cout << setw(2) << j*factor. For larger integers, however, dividing by every integer less than M slows the program down enormously. Verify this now! Each character of the used alphabet is assigned to a value. Parabolic, suborbital and ballistic trajectories all follow elliptic paths. Or can we even increase the mere 12 unique encryptions for the Multiplication Cipher by varying the alphabet length? Notice that we found the good keys indirectly. However, converting 19 to its character does not yield the desired T. The T is stored as 84 which you could see by entering the Excel formula =CODE("T"). If you choose to do so, dont forget to also redefine the corresponding decoding key in int a=5, ainverse=21; . Please, check our dCode Discord community for help requests!NB: for encrypted messages, test our automatic cipher identifier! 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.) } This, however, limits readability. 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. A summary of our explorations for the number of good keys shows: 1) u(p) = p - 1, if M is prime M=p. 1 You can find the reciprocal quite easily. 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. CRITERION FOR GOOD KEYS A key a produces a unique encryption, if the greatest common divisor of 26 and a equals 1, which we write as: gcd(26, a)=1 Convince yourself that 26 has a greatest common divisor equal to 1 with each of these good keys a = 1,3,5,7,9,11,15,17,19,21,23,25. 1. 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. Hey, this shows a great way to produce more unique encryptions which of course makes life harder for an eavesdropper: Recommendation for more security: Choose the alphabet length M to be a prime number to make cracking the cipher text more difficult. Example 1: For M=27=33: Inserting 3 for p and 3 for n in pn - pn-1 yields u(27) = 33 - 32 = 27-9 = 18 which is just what we wanted. If a is a good key, that is if a is relatively prime to 26, then f produces a one-to-one relationship between plain and cipher letters, which therefore permits a unique encryption. Notice in all three equations that because a=2 turns the 13 (=N) into 0 in 2*13 = 0, all the multiples of a=2 translate the N into 0 (=a). Firstly I have no idea how they derived this formula, but I think I have a general idea. 3) ((p*q) = (p-1)*(q-1) for two distinct primes p and q. 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. Counter examples are: 45 and 18 are not relative prime since gcd(45,18)=9 and not 1. How to recognize a Multiplicative ciphertext? Determining the bad keys for a given alphabet length M is a perfect task for a computer. Examples for property 3): 15 and 21 are products of two primes. Cryptoanalysis - Cracking the Multiplication Cipher Just like the Cipher Caesar Cipher, the Multiplication is not secure at all. Before considering such encoding techniques, we go ahead and check if the other frequent number, 20, is the cipher E. Checking the E column, we can see that the possible two keys are the bad one a=18 and the good one a=5. Thus, dividing is performed slightly different: instead of dividing by 5 or multiplying by 1/5, we first write 5-1 (instead of 1/5) where 5-1 now equals an integer and multiply both sides by that integer 5-1. The algorithm memorizes the alphabet with which it has determined the number of the plaintext. The letter A remains unchanged ans id always encoded A. The monoalphabetic cipher family has one very important feature, namely one letter of the open alphabet corresponds to exactly one letter of the secret alphabet. Similarly, the multiples of a=7 will translate an F (=5) into an 0 (=a) because 7 does so. We just had to multiply each cipher letter by a-1. If multiplication is used to convert to cipher text, it is called a wrap-around situation. 24 Which was the first Sci-Fi story to predict obnoxious "robo calls"? 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) <. Since we are performing MOD 26 arithmetic, we use the MOD-operator % that guarantees us the product (a*(pl -'a'))%26; to be between 0 and 25. This website would like to use cookies for Google Analytics. //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). That is why the English alphabet in the calculator above is expanded with space, comma, and dot up to 29 symbols; 29 is a prime integer. 15 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. Remember that a function, per definition, assigns to each x-value one particular y-value. In the process you'll become comfortable with modular arithmetic and begin to understand its importance to modern cryptography. } 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. The answer is a simple No: Only those encryption systems that withstand all possible attacks are secure and thus useful. How many multiples of 3 will not produce a unique encryption? As 29 is prime, it has no divisors except for 1 and 29 and thus there are no multiples as bad keys. In order to be able to use the command setw() we have to include the iomanip.h library in #include . Ubuntu won't accept my choice of password. However, it yields the original text. However, it is not a secure method of encryption and can be easily broken too. 343 and 14 are not relative prime since gcd(343,14)=7. ((5)=_____ as 1,2,3,4 are relative prime to 5. The Multiplicative Cipher is an Affine cipher (ax+b) with the value b null (equal to 0), so a multiplication by $ a $. Code Learn how PLANETCALC and our partners collect and use data. How could it be broken? 2) Lastly, I want to explain the trick how I manage to encode not only a letter but a whole word or sentence if necessary. He obtains: Cipher textanromrjukahhouh013171412179201007714207 013116711232140151519215PLAIN TEXTANLGHLXCOAPPTCP That message does not reveal a virus carrier. div#home a:visited { Step 3: Now, apply the formula which is mentioned above. It is possible to distinguish between 2 types of actions in the plain text: uppercase letters [A-Z] and digits [0-9]. 7 5 for the RSA encryption. 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. What would you do? Method 2: Merged: In the alphabet, mod 22 is calculated because the alphabet contains 22 elements. Each character is multiplied with this key and the corresponding letter is substituted. This means that the key should be a large, random number that is difficult to guess or factor. When a letter occurs in several alphabets, the first of these alphabets is used. Multiply It! Therefore, we first have to add 65 to the 19 in order to translate the 84 eventually into the desired T using =CHAR(65+MOD(E$2*$B4,26)). We then write them in the form (1-1/p), multiply them and that product by M yielding ((M). It only takes a minute to sign up. 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. We obtain ((2*13) = ((2) *((13).

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