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Topic: Hill cipher

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Classical cryptography

Simple substitution cipher

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	8 The Hill Cipher
		The Hill cipher works by viewing a group of letters as a vector, and encryption is done by matrix multiplication.
		In attempting to crack a Hill cipher, the usefulness of frequency analysis becomes vanishingly small as the size of the blocks of letters increases.
		Lester Hill and Louis Weisner were issued a patent for a ``Message Protector'' which mechanically implemented a Hill cipher acting on blocks of six letters at a time.
	www.math.sunysb.edu /~scott/papers/MSTP/crypto/8Hill_Cipher.html (604 words)

	NationMaster - Encyclopedia: Hill cipher (Site not responding. Last check: )
		Hill and a partner were awarded a patent (U.S. Patent 1,845,947) for this device, which performed a 6 × 6 matrix multiplication modulo 26 using a system of gears and chains.
		With the Hill cipher, each block of plaintext letters is encoded as a block of the same size of ciphertext letters.
		Enciphering in the Hill Cipher is the same as finding a and b given x and y, where x and y are numbers from 0 to 25 substituted for two letters of a digraph being enciphered, and deciphering is solving for x and y given a and b.
	www.nationmaster.com /encyclopedia/Hill-cipher (3474 words)

	The Hill Cipher
		This cipher was once implemented in the form of a machine using gears and chains like those used with bicycles.
		The Hill Cipher deals with modulo-26 arithmetic, and so in addition to zero, 13 and all the even numbers are disallowed for this manipulation.
		Enciphering in the Hill Cipher is the same as finding a and b given x and y, where x and y are numbers from 0 to 25 substituted for two letters of a digraph being enciphered, and deciphering is solving for x and y given a and b.
	www.quadibloc.com /crypto/ro020103.htm (593 words)

	Hill Cipher Encryption and Decryption - Wolfram Demonstration Project
		In a Hill cipher encryption, the plaintext message is broken up into blocks of length
		Each block of plaintext letters is then converted into a vector of numbers and is dotted with the matrix.
		"Hill Cipher Encryption and Decryption" from The Wolfram Demonstrations Project
	demonstrations.wolfram.com /HillCipherEncryptionAndDecryption (107 words)

	SSH - Support - Cryptography A-Z - Algorithms - Secret Key Cryptosystems
		OFB (output feedback): the cipher is used as a synchronous key-stream generator, whose output is XORed with the plaintext to obtain ciphertext, block by block.
		DES proved to be a very strong cipher and it took over a decade for any interesting cryptanalytical attacks against it to develop (not to underestimate the pioneering efforts that lead to this breakthrough).
		The Hill cipher uses matrices in clock arithmetic, and is highly suspectible to known plaintext attacks.
	www.ssh.com /support/cryptography/algorithms/symmetric.html (3707 words)

	Science Fair Projects - Classical cipher
		In general, classical ciphers operate on an alphabet of letters (such as "A-Z"), and are implemented by hand or with simple mechanical devices.
		In a substitution cipher, letters (or groups of letters) are systematically replaced throughout the message for other letters (or groups of letters).
		In a transposition cipher, the letters themselves are kept unchanged, but rather their order within the message is scrambled according to some well-defined scheme.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Classical_cipher (354 words)

	Substitution cipher - Term Explanation on IndexSuche.Com
		The simple substitution cipher is one in which each plaintext character is simply replaced by a corresponding one from a cipher alphabet.
		The cipher alphabet may be shifted or reversed (creating the Caesar cipher and atbash ciphers, respectively) or scrambled, in which case it is called a "mixed alphabet" or "deranged alphabet".
		Unfortunately, the Hill cipher is vulnerable to a known_plaintext attack because it is completely linear, so it must be combined with some non-linear step to defeat this attack.
	www.indexsuche.com /Substitution_cipher.html (2153 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		A monoalphabetic cipher uses fixed substitution over the entire message, whereas a polyalphabetic cipher uses a number of substitutions at different times in the messageâ”such as with homophones, where a unit from the plaintext is mapped to one of several possibilities in the ciphertext.
		The cipher alphabet may be shifted or reversed (creating the Caesar and Atbash ciphers, respectively) or scrambled in a more complex fashion, in which case it is called a mixed alphabet or deranged alphabet.
		Modern stream ciphers can also be seen, from a sufficiently abstract perspective, to be a form of polyalphabetic cipher in which all the effort has gone into making the keystream as long and unpredictable as possible.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=substitution_cipher (2642 words)

	[No title] (Site not responding. Last check: )
		Hill's Cipher could be carried out by hand probably without too much hardship for groups of letters up to five.
		To encipher a plaintext n-gram using the Hill Cipher, a nonsingular n x n matrix M is selected.
		It seems that Hill and a partner (Weisner) filed a patent (Message Protector, patent number 1,854,947) for a mechanical version of the Hill Cipher in 1929, which, according to Kahn [KAHN], used an involuntary matrix enciphering key so that the same machine could be used to both encipher and decipher.
	www.math.utoledo.edu /~codentha/Cryptanalysis/lanaki/lanaki08.txt (12651 words)

	Cryptology - The art of secret messages (Site not responding. Last check: )
		This paper is written for the purpose of demonstrating how linear algebra is used in encoding and deciphering a Hill Cipher where the text is manipulated in blocks of two letters.
		This is an introduction to the application of cryptography using the Hill Cipher.
		The Hill Cipher uses matrix multiplication to perform the transformation and multiplication by an inverse matrix to undo the operation and recover the text.
	oxygen.fvcc.edu /~dhicketh/Math201/studentprojects/fall2004/kristamartens/CryptologyPaper2.htm (1669 words)

	Programming Problems for Current year for Region 1 for ACM Asian Programming Contest (Site not responding. Last check: )
		The Hill cipher is a cipher using an * matrix as the key.
		Finally, the cipher text is obtained by mapping the numbers,,*, into capital letters: mapped to A, 1 mapped to B,..., 25 mapped to Z. Note that the method of transformation and the key will be the same for every block.
		In this problem, we assume that =3D3 in the Hill cipher, and that a pair of message and its cipher text are given.
	uweb.txstate.edu /~ch01/prob96ka.htm (1618 words)

	Hill Cipher - Karr.net (Site not responding. Last check: )
		Hill takes pictures of the children he has met through this work, he says.
		An opponent who intercepts n plaintext/ciphertext character pairs can set up a linear system which can (usually) be easily solved; if it happens that this system is indeterminate, it is only necessary to add a few more plaintext/ciphertext pairs.
		The net effect is that the effective keyspace of a basic Hill cipher is about 4.64n − 1.7.
	www.naturalresearch.com /encyclopedia/Hill_cipher (1020 words)

	Borys Bradel's n-Hill Cipher Applet Page
		Type in the encrypted cipher text and press the decrypt button to see what the original message was.
		The decryption matrix is multiplied by the vectors from the cipher text and the result is turned into the plain text.
		The ability to crack the cipher is based upon the idea that given plaintext converted into vectors p1,p2,etc. and ciphertext converted into vectors c1,c2,etc. so that P and C be defined such that
	www.eecg.toronto.edu /~bradel/projects/cryptography (724 words)

	[No title]
		A calculator to encipher and decipher using the Hill and RSA algorithms.
		Hill Cipher: Enter the coefficients for the Hill transformation in the cells a,b,c and d in the table.
		Deciphering: Enter numbers in the column labelled "cipher" and press the "decipher" button.
	www.math.unl.edu /~jorr1/gilbhatch/ciphercalc.html (192 words)

	mutasyon.net \| Teknoloji \| Kağıt-Kalem Kriptolojisi I (Affine and Hill Cipher)
		Hill şifreleme yöntemi Lester Hill tarafından bulunmuş ve 1929 yılında yayınlanmıştır.
		Bir mesajı Hill yöntemi ile belli bir düzen içinde şifrelememiz gerekir.
		Hill yönteminin en önemli özelliğini de burada görmüş oluruz.
	www.mutasyon.net /makaleoku.asp?id=781 (529 words)

	Crg Hill's poetry scorecard
		This will be the first time Hill and Huth have performed together since their performance in March of this year, so don't miss this east coast appearance.
		Crag Hill has been exploring the world through the prisms of verbal and visual language since his re-birth in the 1970s.
		Geof Huth is a writer of textual and visual poetry who has lived on most of the continents on earth.
	scorecard.typepad.com /crag_hills_poetry_score (1059 words)

	Cryptography
		The ciphers I will discuss are called Hill ciphers after Lester S. Hill who introduced them in two papers: "Cryptography in an Algebraic Alphabet," American Mathematical Monthly, 36, June-July 1929, pp.
		For Hill ciphers I assign numerical values to each plaintext and ciphertext letter so that A=1, B=2, C=2 and so on.
		The following procedure shows the simplest Hill ciphers (Hill 2-cipher), successive pairs of plaintext that are transformed into ciphertext by a 2 x 2 matrix A.
	www.math.washington.edu /~king/coursedir/m308a01/Projects/Cryptography.htm (1534 words)

	Cryptography-Research Digest #794
		The Hill cipher encrypts by multiples (mod i) the transform of a vector, P', by a non-singular matrix M: P'M = C' The vector C' is decrypted by multiplying it by the inverse of M, N: C'N = P' Given M, N can be computed.
		This tactic effectively hides those elements of P' are used in the series of table-lookups (that is, it hides which elements of P' are used each of the table-lookups, from the perspective of not being able to determine the characteristics of R).
		In view of the foregoing, would such a cipher system be secure as a public key (the series of tables being the public key) even if the general nature of the non-linear transform J and the interrelated matrix R were known (but not their particulars)?
	www.mail-archive.com /cryptography-research@senator-bedfellow.mit.edu/msg00015.html (419 words)

	Lanaki Lesson 8
		Hill's Cipher could be carried out by hand probably without too much hardship for groups of letters up to five.
		To encipher a plaintext n-gram using the Hill Cipher, a nonsingular n x n matrix M is selected.
		It seems that Hill and a partner (Weisner) filed a patent (Message Protector, patent number 1,854,947) for a mechanical version of the Hill Cipher in 1929, which, according to Kahn [KAHN], used an involuntary matrix enciphering key so that the same machine could be used to both encipher and decipher.
	www.fortunecity.com /skyscraper/coding/379/lesson8.htm (12614 words)

	[No title]
		The plaintext `friday’ is encrypted using the Hill cipher with m=2 to give the ciphertext `PQCFKU’.
		Find the the key K. (It is acceptable to write the key K as a product of two matrices without performing the multiplication or taking the inverse.) Suppose that you are informed that the plaintext `abccab’ has been encrypted with the Vigenere cipher and the corresponding ciphertext is `bbccab’.
		The Hill cipher is used with m=2, and the key is the 2-by-2 matrix K = (4 1) (3 1) Encrypt the message `1 2 3 4’.
	triton.towson.edu /~mzimand/aucrypto/practiceMidTerm.doc (765 words)

	Electrical and Mechanical Cipher Machines
		Using machinery to automate encryption permitted ciphers to be much more complicated than those which can reasonably be applied by hand without too many mistakes.
		And this was true even though machines had to be reliable and inexpensive, and this meant they could only carry out fairly simple operations.
		There are several types of cipher machine that we will examine in this section; and a few more that belong to another section, since they hint at the computer age to follow.
	www.quadibloc.com /crypto/roto02.htm (98 words)

	[No title]
		With the length of the file "somefile" and the difference of the Bytes after the removal of the highest bit in mind it is assumed, that the plaintext is a 7-bit ASCII text.
		Construction a Hill cipher that would result in a ciphertext with the mentioned attributes seemed too much trouble for something this obvious.
		Since the subtraction of 128 (deleting of the highest Bit) did not result in anything very meaningful, and the difference between the Bytes was to high to result in anything meaningful if subtractions with a Value significantly lesser or higher than 128 (except for a function of the form f:B->B x-> 256-x.
	www.honeynet.org /scans/scan16/som/som38.txt (1430 words)

	[No title]
		The cipher is worth 35 points and is due no >later than April 17.
		Then once the key was found applied it to the rest of the cipher text to decrypt the meassage.
		There was a bug in the code because a pair of the cipher pairs were too large when multiplied by 10325 to fit into an integer (I wrote it in C).
	www.cs.umbc.edu /~stephens/crypto/sol2.html (1740 words)

	CSC290: Introduction to Cryptology
		The core of Hill cipher is matrix manipulations.
		One simple way is to slide across the plain text and pick up m m-substrings, m being the block size of the Hill cipher.
		In fact, what 'ing' was encrypted may not appear in the cipher text at all.
	www.cs.rochester.edu /~bh/csc290/hill.html (899 words)

	Chris Christensen's Summer 2001 MAT115
		The Friedman test results provide evidence of that: the index of coincidence is 0.0408 (which suggests that the cipher is polyalphabetic) and the estimated length of the keyword is 9.4855.
		The Friedman test results are: the index of coincidence is 0.0749 (which suggest that the cipher is monoalphabetic) and the estimated length of the keyword (which is useless information for this exercise) is 0.7327.
		Here are the frequencies of individual letters (notice that these frequencies are similar to what we expect for plaintext) and of the trigraphs.
	www.nku.edu /~christensen/ccsa.html (693 words)

	www.apifinder.com - the essential directory for application programming interfaces
		The Caesar cipher is a substitution cipher that may have been used by Julius Caesar to communicate with his army.
		The Hill cipher is a polygraphic substitution cipher based on linear algebra.
		Vigenere, or Tritheim's system, is the most common polyalphabetic substitution cipher, a system in which letters are encoded based on their location in the text.
	www.apifinder.com /APIFinder/APIsByCategory/28880?catID=2525 (3024 words)

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