A polyalphabetic substitution cipher is similar to a monoalphabetic substitution except that the cipher alphabet is changed periodically while enciphering the message. keys With so many keys, might think the system is secure But would be !!!WRONG!!! Homework 2 Submit solution to problem 2.18. The algorithm m plaintext letter substitution cipher text m ,numerical value(a=0,b=1,….z=25) c1=(k11p1+k12p2+k13p3)mod 26 c2=(k21p1+k22p2+k23p3)mod 26 c3=(k31p1+k32p2+k33p3)mod 26 the column of vectors: c1 k11 k12 k13 p1 c2 k21 k22 k23 p2 mod 26 c3 k31 k32 k33 p3 12. Hill cipher works as follows: Assign the number to each alphabet in the plain text. Answer: 12 mod 9 3 or 12 3 mod 9 Definition: Let a, r, m (where is a set of all 5. Another example of the polyalphabetic ciphers is the Vigenère cipher. The Hill cipher algorithm is one of the symmetric key algorithms that have several advantages in data encryption. While using Caesar cipher technique, encrypting and decrypting symbols involves converting the values into numbers with a simple basic procedure of addition or subtraction. Note that this example is no more secure than using a simple Caesar substitution cipher, but it serves to illustrate a simple example of the mechanics of RSA encryption. Share yours for free! 12 Example: Playfair Cipher Program file for this chapter: This project investigates a cipher that is somewhat more complicated than the simple substitution cipher of Chapter 11. For each letter, look at the letter of the keyword above it (if it was 'M', then you would go to the row that starts with an 'M'), and find that row in the Vigenere table. Known plaintext – The cryptanalyst has a copy of the cipher text and the corresponding plaintext. In order to encipher by Vigenère cipher, you need two things: a keyword and the Vigenère square, below. – Hill Cipher – Cryptography is the art of protecting information by transforming it into a format that is not directly readable, called cipher text. Let's say we want to encipher the following sentence,"THE PROFESSOR IS EVIL", into ciphertext. Chosen plaintext – The cryptanalysts gains temporary access to the encryption machine. • The number of all possible encryption functions (bijections) is 2b! Pick a keyword (for our example, the keyword will be "MEC"). Vigenère Cipher. • Example – substitution cipher • Consider a block cipher: blocks of size b bits, and key of size k • The number of all possible functions mapping b bits to b bits is (2b)2b Necessary Condition (cont.) The first thing we do is to group the letters into pairs of 2 letters. The Playfair Cipher Decryption Algorithm: The Algorithm consistes of 2 steps: Generate the key Square(5×5) at the receiver’s end: The key square is a 5×5 grid of alphabets that acts as the key for encrypting the plaintext. Other encryption methods at that time also utilized special coding machines. • Keyless Cipher – a cipher that does not require the use of a key • key cannot be changed If the encryption algorithm should fall into the interceptor ’s hands, future messages can still be kept secret because the interceptor will not know the key value. The Vigenère cipher was published in 1586 by the French diplomat Blaise de Vigenère. Learn new and interesting things. Even though it is a type of classical and historical cryptography method, it has a special place in my heart because of strong math background and easy adaptation. Examples: Caesar cipher (1 letter substitution), Playfair (2-letter), Hill (multiple letters), Vigenere (poly-alphabetic). Consider the letters and the associated numbers to be used as shown below − The numbers will be used for multiplication procedure •Hv ufe fh kar karvedrh vu pfkarpfkdlh fer fivnk erfmdkz, karz fer svk lrekfds; hv ufe fh karz fer lrekfds, karz fer svk fivnk erfmdkz.– Fmirek Rdshkrds. In playfair cipher, initially a key table is created. View Caesar Cipher PPTs online, safely and virus-free! This makes block ciphers popular today. 7. • c=kp mod … In the process of encrypting hill chipper require help table to encode letters or Abjat are arranged in a sequence of letters or Abjat "A" to "Z". Vigenère Cipher CR 22 plaintext (x) key (k) (x + k) mod 26 ciphertext |keyspace| = 26 m (where m is the length of the key) Cryptanalysis of Vigenère Cipher • Frequency analysis more difficult (but not impossible) • Attack has two steps CR 23. The first L is encrypted as N; the second as Z. Example: C=7=0111 Another example: B=011011, C=? DES Key Generation (K1–K16) 19 64 bit key (including parity-check bits) 28 bits 28 bits Matrix PC-1 and PC-2 are givenby the standard (see nextslide) Ci=LS i(C i-1) Di=LS i(D i-1) Ki=PC-2(CiDi) LS=LeftShift-shift one position if i=1,2,9 or 16-shift two positions otherwise 48 bits. Hill’s method was considered sophisticated and powerful in its time and is one of many methods influencing techniques in use today. I need to encrypt a file (such as .doc, .ppt, .jpeg, etc), and not just the contents of file. Actually, it was the first one appearing in the history. Multiple stages of substitution and transposition can be used to form strong ciphers. Chiper hill is an example of a polyalphabetic cipher that employs modulus and linear algebra techniques. 30. Have here the rules for filling in the 5x5 matrix, L to R, top to bottom, first with keyword after duplicate letters have been removed, and then with the remain letters, with I/J used as a single letter. The matrix must be invertible for use in decrypting. The next two examples, playfair and Vigenere Cipher are polyalphabetic ciphers. How this Cipher Works. Presentations_PPT_Unit-1_27042019051856AM.pptx - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. Note 30. A = 0, B= 1….z = 25; Organize the plain text message as a matrix of numbers base on the above step that is in number format. So for example, a 64-bit block cipher will take in 64 bits of plaintext and encrypt it into 64 bits of ciphertext. • The number of encryption functions in our cipher is at most 2k. On the other hand, cryptoanalysis is still partially hard. Majority of the symmetric ciphers used today are actually block ciphers. Monoalphabetic ciphers •Our examples of the permutation, shift, decimation, and affine ciphers were monoalphabetic ciphers, that is every letter was replaced by the same letter each time. Prime numbers play important roles in various encryption schemes. If multiplication is used to convert to cipher text, it is called a wrap-around situation. Hill cipher works on the multiple alphabets at the same time. Hill's cipher machine, from figure 4 of the patent. * The shift cipher is sometimes referred to as the Caesar cipher. In this example, the letter e in the plaintext is variably encrypted to S and V, and in the ciphertext W is, in different places, the result of a plaintext f, t, and r. This variability makes attacking the ciphertext by the frequency of letters in English much more difficult. HILL CIPHER .The multiletter cipher hill cipher developed by the mathematician Lester hill in 1929. . Monoalphabetic Cipher Security Now have a total of 26! Hill Cipher Please email your Mathematica file to tleise@amherst.edu by 4pm on Monday. The resultant matrix is … Remember that calculating m e mod n is easy, but calculating the inverse c-e mod n is very difficult, well, for large n's anyway. * Use the shift cipher with key = 15 to encrypt the message “HELLO.” Solution We encrypt one character at a time. Hill Cipher. The following discussion assumes an elementary knowledge of matrices Examples of encryption: Shift cipher, substitution, Transformation A matrix can be used as a cipher to encrypt a message. 2.18. Playfair cipher is an example of doing this. If we would do a Hill 3-cipher, we would group the letters in groups of 3 letters and use a 3 x 3 transformation matrix, but in this example we're using a Hill 2-cipher. Encryption Abjat and this letter serves as a conversion of plaintext (messages or data) and key that you want to encrypt and decrypt. Hill devised a mechanical encryption machine to help with the mathematics; his machine relied on gears and levers, but never gained widespread use. Summary of Application in Linear Algebra Cipher matrix can be as sample as a 3x3 matrix composed of Radom integers. Get ideas for your own presentations. Hill ciphers are quite simple, while other methods are much more sophisticated, like RSA public key encryption that involves two very large prime numbers and is used for internet security. Playfair Cipher. 2-18 Washington University in St. Louis CSE571S ©2011 Raj Jain. Hill cipher is a polygraphic substitution cipher based on linear algebra. Example 30.2 Solution The cipher is not monoalphabetic because each occurrence of L is encrypted by a different character. Some Number Theory Modulo Operation: Question: What is 12 mod 9? The Playfair Cipher was first described by Charles Wheatstone in 1854, and it was the first example of a Digraph Substitution Cipher. The key table is a 5×5 grid of alphabets that acts as the key for encrypting the plaintext. The basic idea of this cipher is to use a number of monoalphabetic ciphers in turn. The Vigenère cipher is an example of a polyalphabetic substitution cipher. Many are downloadable. Thus, it does not hide all features of the image which reveals patterns in the plaintext. However, a main drawback of this algorithm is that it encrypts identical plaintext blocks to identical ciphertext blocks and cannot encrypt images that contain large areas of a single color. – Example : VigenereCipher, Hill Cipher 21. Hill cipher is a kind of a block cipher method. Cipher text only – A copy of cipher text alone is known to the cryptanalyst. I already searched on the Internet, but I didn't find much research that focuses on file encryption. When it was first put to the British Foreign Office as a cipher, it was rejected due to its perceived complexity. In this scheme, pairs of letters are encrypted, instead of single letters as in the case of simple substitution cipher. As we know, Hill cipher is a classic cipher in cryptography and is mostly used for encrypting text. Description. View L2.ppt from CSE 402 at JK Lakshmipat University. In cases where bits of plaintext is shorter than the block size, padding schemes are called into play. Write your keyword across the top of the text you want to encipher, repeating it as many times as necessary. It is named after Lord Playfair, who heavily promoted the use of the cipher to the military. In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra.Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once.. 16 Conclusion The Hill 2-cipher is a great example of how mathematics can change the way we communicate. •In a decimation cipher A always represents itself The cipher is conceptually like using multiple different mono-alphabetic cipher keys in sequence.