Enhancing the Security of Caesar Cipher Substitution Method Using a Randomized Approach for More Secure Communication
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Introduction to Cryptography Teachers' Reference
Introduction to Cryptography Teachers’ Reference Dear Teachers! Here I have mentioned some guidelines for your good self so that your students can benefit form these modules. I am very hopeful that you will enjoy conducting the session. After Module-1 1. Scytale Decryption In your class ask your students to devise a method to decrypt the message just been encrypted using Scytale. Encourage them to look around to find a decryption tool. Ask your students to cut a strip of paper some 4mm wide, 32cm long and light pencil lines drawn on it at 4mm distance. To give it the following shape. Now write cipher text on the paper strip in the following way. t i t i r s a e e e e e b h y w i t i l r f d n m g o e e o h v n t t r a a e c a g o o w d m h Encourage them once again to find a tool around them to decrypt it. Ask them to look for a very familiar thing they must have been using right from their early school days to do their work. Now many of them must have figured out that you are asking for a pencil. Now ask them to use the pencil to decrypt the cipher text by using pencil and the only reasonable way would be to wrap the paper strip around the strip. The plain text will be visible along the six side faces of the pencil. Encourage them to reason that how did it work? There is a connection between six rows of the table in which the plain text was filled and the six faces of the pencil. -
Simple Substitution and Caesar Ciphers
Spring 2015 Chris Christensen MAT/CSC 483 Simple Substitution Ciphers The art of writing secret messages – intelligible to those who are in possession of the key and unintelligible to all others – has been studied for centuries. The usefulness of such messages, especially in time of war, is obvious; on the other hand, their solution may be a matter of great importance to those from whom the key is concealed. But the romance connected with the subject, the not uncommon desire to discover a secret, and the implied challenge to the ingenuity of all from who it is hidden have attracted to the subject the attention of many to whom its utility is a matter of indifference. Abraham Sinkov In Mathematical Recreations & Essays By W.W. Rouse Ball and H.S.M. Coxeter, c. 1938 We begin our study of cryptology from the romantic point of view – the point of view of someone who has the “not uncommon desire to discover a secret” and someone who takes up the “implied challenged to the ingenuity” that is tossed down by secret writing. We begin with one of the most common classical ciphers: simple substitution. A simple substitution cipher is a method of concealment that replaces each letter of a plaintext message with another letter. Here is the key to a simple substitution cipher: Plaintext letters: abcdefghijklmnopqrstuvwxyz Ciphertext letters: EKMFLGDQVZNTOWYHXUSPAIBRCJ The key gives the correspondence between a plaintext letter and its replacement ciphertext letter. (It is traditional to use small letters for plaintext and capital letters, or small capital letters, for ciphertext. We will not use small capital letters for ciphertext so that plaintext and ciphertext letters will line up vertically.) Using this key, every plaintext letter a would be replaced by ciphertext E, every plaintext letter e by L, etc. -
FROM JULIUS CAESAR to the BLOCKCHAIN: a BRIEF HISTORY of CRYPTOGRAPHY by Côme JEAN JARRY & Romain ROUPHAEL, Cofounders of BELEM
Corporate identity in the digital era #9 JANUARY 2017 FROM JULIUS CAESAR TO THE BLOCKCHAIN: A BRIEF HISTORY OF CRYPTOGRAPHY By Côme JEAN JARRY & Romain ROUPHAEL, cofounders of BELEM 22 The world’s most important asset is information. Now message was inscribed lengthwise. Once the parchment more than ever. With computer theft and hacking was unrolled, the letters of the message were mixed becoming a common threat, protecting information up and the message meaningless. The receiver would is crucial to ensure a trusted global economy. need an identical stick to decipher the text. The E-commerce, online banking, social networking or scytale transposition cipher relied on changing the emailing, online medical results checking, all our order of the letters, rather than the letters themselves. transactions made across digital networks and This cryptographic technique still prevails today. insecure channels of communication, such as the Internet, mobile phones or ATMs, are subjected to vulnerabilities. Our best answer is cryptography. And THE ART OF SUBSTITUTION it has always been. As a science and as an art, it is Julius Caesar was also known to use encryption to an essential way to protect communication. convey messages to his army generals posted in the Cryptography goes back to older times, as far back as war front. The Caesar cipher is a simple substitution the Ancient World. cipher in which each letter of the plaintext is rotated left or right by some number of positions down the alphabet. The receiver of the message would then Early cryptography was solely concerned with shift the letters back by the same number of positions concealing and protecting messages. -
Index-Of-Coincidence.Pdf
The Index of Coincidence William F. Friedman in the 1930s developed the index of coincidence. For a given text X, where X is the sequence of letters x1x2…xn, the index of coincidence IC(X) is defined to be the probability that two randomly selected letters in the ciphertext represent, the same plaintext symbol. For a given ciphertext of length n, let n0, n1, …, n25 be the respective letter counts of A, B, C, . , Z in the ciphertext. Then, the index of coincidence can be computed as 25 ni (ni −1) IC = ∑ i=0 n(n −1) We can also calculate this index for any language source. For some source of letters, let p be the probability of occurrence of the letter a, p be the probability of occurrence of a € b the letter b, and so on. Then the index of coincidence for this source is 25 2 Isource = pa pa + pb pb +…+ pz pz = ∑ pi i=0 We can interpret the index of coincidence as the probability of randomly selecting two identical letters from the source. To see why the index of coincidence gives us useful information, first€ note that the empirical probability of randomly selecting two identical letters from a large English plaintext is approximately 0.065. This implies that an (English) ciphertext having an index of coincidence I of approximately 0.065 is probably associated with a mono-alphabetic substitution cipher, since this statistic will not change if the letters are simply relabeled (which is the effect of encrypting with a simple substitution). The longer and more random a Vigenere cipher keyword is, the more evenly the letters are distributed throughout the ciphertext. -
CPSC 467B: Cryptography and Computer Security
Outline Perfect secrecy One-time pad Cryptanalysis CPSC 467b: Cryptography and Computer Security Michael J. Fischer Lecture 3 January 15, 2010 Michael J. Fischer CPSC 467b 1/40 Outline Perfect secrecy One-time pad Cryptanalysis 1 Perfect secrecy Caesar cipher Loss of perfection 2 One-time pad 3 Cryptanalysis Caesar cipher Brute force attack Manual attacks Michael J. Fischer CPSC 467b 2/40 Outline Perfect secrecy One-time pad Cryptanalysis Caesar cipher Loss of perfection Caesar cipher Recall: Base Caesar cipher: Ek (m) = (m + k) mod 26 Dk (c) = (c − k) mod 26: Full Caesar cipher: r Ek (m1 ::: mr ) = Ek (m1) ::: Ek (mr ) r Dk (c1 ::: cr ) = Dk (c1) ::: Dk (cr ): Michael J. Fischer CPSC 467b 3/40 Outline Perfect secrecy One-time pad Cryptanalysis Caesar cipher Loss of perfection Simplified Caesar cipher A probabilistic analysis of the Caesar cipher. Simplify by restricting to a 3-letter alphabet. M = C = K = f0; 1; 2g Ek (m) = (m + k) mod 3 Dk (m) = (m − k) mod 3. A priori message probabilities: m pm 0 1=2 1 1=3 2 1=6 Michael J. Fischer CPSC 467b 4/40 Outline Perfect secrecy One-time pad Cryptanalysis Caesar cipher Loss of perfection Joint message-key distribution Each key has probability 1/3. Joint probability distribution: k z }| { 0 1 2 8 0 1=6 1=6 1=6 < m 1 1=9 1=9 1=9 : 2 1=18 1=18 1=18 Michael J. Fischer CPSC 467b 5/40 Outline Perfect secrecy One-time pad Cryptanalysis Caesar cipher Loss of perfection Conditional probability distribution Recall P[m = 1] = 1=3. -
The Enigma Cipher Machine
The Enigma Cipher Machine Anna Hurlbut 2018-11-27 Abstract The Enigma cipher machine was invented in the early 1920s to help businesses protect commercial secrets, but the German military soon saw its potential application to military communications. By the mid-1930s, every branch of the German military was using Enigma for nearly all their encrypted communications. The electromechanical cipher machine works using a system of wires, rotors, a reflector and a plugboard to send an electrical signal from the keyboard to the lampboard, encrypting each message letter by letter. Enigma masterfully balances ease of use and security, the opposing forces of any cryptosystem. The key space is ap- proximately 15 million million million, and it could be compared to a Vigen´erecipher with a key length of 16900. Though it seemed infallible, the infamous machine eventually failed. While the cryptosystem did have inherent technical flaws, its defeat was mainly a result of errors in human operation. British intelligence at Bletchley Park was able to find patterns in German messages and used these patterns as cracks to break into the entire system. Enigma represents a vital moment in the field of cryptogra- phy. It initiated the transition from by-hand methods to automated and mechanized methods and acted as a catalyst for the development of com- puters. Additionally, Enigma's ultimate failure illustrated the inadequacy of security through obscurity and pointed the future of cryptography to- wards more advanced methods. 1 Contents 1 Historical Context 3 2 Cryptography Basics and Simple Substitution Ciphers 4 2.1 Caesar Cipher . 6 3 The Vigen´ereCipher 6 3.1 Vigen´ereCryptanalysis . -
Grade 6 Math Circles Cryptography Solutions Atbash Cipher Caesar Cipher
Faculty of Mathematics Centre for Education in Waterloo, Ontario N2L 3G1 Mathematics and Computing Grade 6 Math Circles November 5/6 2019 Cryptography Solutions Hello World Khoor Zruog Hello Zruog Khoor Khoor Zruog World 1. Person A encrypts plaintext 2. Person B receives ciphertext 3. Person B decrypts ciphertext back into ciphertext into plaintext Atbash Cipher Examples 1. Encrypt \Math Circles" using the Atbash cipher. Nzgs Xrixovh 2. Decrypt \ORLM PRMT" using the Atbash cipher. LION KING Caesar Cipher Examples: Encrypt or decrypt the following messages using the shift number given in parentheses: a) Welcome to Math Circles! (5) Bjqhtrj yt Rfym Hnwhqjx! plaintext A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ciphertext F G H I J K L M N O P Q R S T U V W X Y Z A B C D E 1 b) Ljw hxd anjm cqrb? (9) Can you read this? plaintext A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ciphertext J K L M N O P Q R S T U V W X Y Z A B C D E F G H I c) What if I did a Caesar Shift of 26 units on \Welcome to Math Circles!"? A Caesar shift of 26 would be shifting by the length of the alphabet. For example I would be shifting A 26 letters to the right. -
Shift Cipher Substitution Cipher Vigenère Cipher Hill Cipher
Lecture 2 Classical Cryptosystems Shift cipher Substitution cipher Vigenère cipher Hill cipher 1 Shift Cipher • A Substitution Cipher • The Key Space: – [0 … 25] • Encryption given a key K: – each letter in the plaintext P is replaced with the K’th letter following the corresponding number ( shift right ) • Decryption given K: – shift left • History: K = 3, Caesar’s cipher 2 Shift Cipher • Formally: • Let P=C= K=Z 26 For 0≤K≤25 ek(x) = x+K mod 26 and dk(y) = y-K mod 26 ʚͬ, ͭ ∈ ͔ͦͪ ʛ 3 Shift Cipher: An Example ABCDEFGHIJKLMNOPQRSTUVWXYZ 0 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 • P = CRYPTOGRAPHYISFUN Note that punctuation is often • K = 11 eliminated • C = NCJAVZRCLASJTDQFY • C → 2; 2+11 mod 26 = 13 → N • R → 17; 17+11 mod 26 = 2 → C • … • N → 13; 13+11 mod 26 = 24 → Y 4 Shift Cipher: Cryptanalysis • Can an attacker find K? – YES: exhaustive search, key space is small (<= 26 possible keys). – Once K is found, very easy to decrypt Exercise 1: decrypt the following ciphertext hphtwwxppelextoytrse Exercise 2: decrypt the following ciphertext jbcrclqrwcrvnbjenbwrwn VERY useful MATLAB functions can be found here: http://www2.math.umd.edu/~lcw/MatlabCode/ 5 General Mono-alphabetical Substitution Cipher • The key space: all possible permutations of Σ = {A, B, C, …, Z} • Encryption, given a key (permutation) π: – each letter X in the plaintext P is replaced with π(X) • Decryption, given a key π: – each letter Y in the ciphertext C is replaced with π-1(Y) • Example ABCDEFGHIJKLMNOPQRSTUVWXYZ πBADCZHWYGOQXSVTRNMSKJI PEFU • BECAUSE AZDBJSZ 6 Strength of the General Substitution Cipher • Exhaustive search is now infeasible – key space size is 26! ≈ 4*10 26 • Dominates the art of secret writing throughout the first millennium A.D. -
Classic Crypto
Classic Crypto Classic Crypto 1 Overview We briefly consider the following classic (pen and paper) ciphers o Transposition ciphers o Substitution ciphers o One-time pad o Codebook These were all chosen for a reason o We see same principles in modern ciphers Classic Crypto 2 Transposition Ciphers In transposition ciphers, we transpose (scramble) the plaintext letters o The scrambled text is the ciphertext o The transposition is the key Corresponds to Shannon’s principle of diffusion (more about this later) o This idea is widely used in modern ciphers Classic Crypto 3 Scytale Spartans, circa 500 BC Wind strip of leather around a rod Write message across the rod T H E T I M E H A S C O M E T H E W A L R U S S A I D T O T A L K O F M A N Y T H I N G S When unwrapped, letters are scrambled TSATAHCLONEORTYTMUATIESLHMTS… Classic Crypto 4 Scytale Suppose Alice and Bob use Scytale to encrypt a message o What is the key? o How hard is it for Trudy to break without key? Suppose many different rod diameters are available to Alice and Bob… o How hard is it for Trudy to break a message? o Can Trudy attack messages automatically—without manually examining each putative decrypt? Classic Crypto 5 Columnar Transposition Put plaintext into rows of matrix then read ciphertext out of columns For example, suppose matrix is 3 x 4 o Plaintext: SEETHELIGHT o Ciphertext: SHGEEHELTTIX Same effect as Scytale o What is the key? Classic Crypto 6 Keyword Columnar Transposition For example o Plaintext: CRYPTOISFUN o Matrix 3 x 4 and keyword MATH o Ciphertext: -
Substitution Ciphers
Foundations of Computer Security Lecture 40: Substitution Ciphers Dr. Bill Young Department of Computer Sciences University of Texas at Austin Lecture 40: 1 Substitution Ciphers Substitution Ciphers A substitution cipher is one in which each symbol of the plaintext is exchanged for another symbol. If this is done uniformly this is called a monoalphabetic cipher or simple substitution cipher. If different substitutions are made depending on where in the plaintext the symbol occurs, this is called a polyalphabetic substitution. Lecture 40: 2 Substitution Ciphers Simple Substitution A simple substitution cipher is an injection (1-1 mapping) of the alphabet into itself or another alphabet. What is the key? A simple substitution is breakable; we could try all k! mappings from the plaintext to ciphertext alphabets. That’s usually not necessary. Redundancies in the plaintext (letter frequencies, digrams, etc.) are reflected in the ciphertext. Not all substitution ciphers are simple substitution ciphers. Lecture 40: 3 Substitution Ciphers Caesar Cipher The Caesar Cipher is a monoalphabetic cipher in which each letter is replaced in the encryption by another letter a fixed “distance” away in the alphabet. For example, A is replaced by C, B by D, ..., Y by A, Z by B, etc. What is the key? What is the size of the keyspace? Is the algorithm strong? Lecture 40: 4 Substitution Ciphers Vigen`ere Cipher The Vigen`ere Cipher is an example of a polyalphabetic cipher, sometimes called a running key cipher because the key is another text. Start with a key string: “monitors to go to the bathroom” and a plaintext to encrypt: “four score and seven years ago.” Align the two texts, possibly removing spaces: plaintext: fours corea ndsev enyea rsago key: monit orsto gotot hebat hroom ciphertext: rcizl qfkxo trlso lrzet yjoua Then use the letter pairs to look up an encryption in a table (called a Vigen`ere Tableau or tabula recta). -
Hill Cipher: a Cryptosystem Using Linear Algebra
The Hill Cipher: A Cryptosystem Using Linear Algebra Robyn N. Taylor Mentor: Gerard LaVarnway Norwich University Northfield, VT April 6, 2013 Classic Cryptology Classic cryptology refers to methods of encipherment from antiquity to the middle of the 20th century Hudson River Undergraduate Mathematics Conference The Central Problem of Classic Cryptology Alice Eve Bob Communication channel Key channel Hudson River Undergraduate Mathematics Conference Polygraphic Substitution Ciphers polygraphic substitution cipher: blocks of plaintext characters are replaced by blocks of ciphertext characters Hudson River Undergraduate Mathematics Conference Lester Hill of Hunter College first introduced his “system” in an article in 1929 published in the American Mathematical Monthly entitled “Cryptology in an Algebraic Alphabet” Hudson River Undergraduate Mathematics Conference Lester Hill’s Cipher Machine Hudson River Undergraduate Mathematics Conference Principle Idea Group plaintext letters into blocks (size of 2,3,4 …) Encipher blocks as other equal length blocks plaintext ciphertext MI EQ SS GC Hudson River Undergraduate Mathematics Conference Block size Hill worked in three letter blocks We will work in two letter blocks Restrict alphabet to capital letters: A, B, C, D, ….Z Hudson River Undergraduate Mathematics Conference Monoalphabetic Substitution How many two letter blocks can we form from the letters A…Z? 26 X 26 = 676 Therefore, we can think of Hill’s system as a monoalphabetic substitution cipher on a 676 character alphabet. Hudson River Undergraduate Mathematics Conference Y Axmod26 Y is a 2 x 1 matrix of ciphertext numerical equivalents A is a 2 x 2 matrix x is a 2 x1 matrix of plaintext numerical equivalents. yx11 ab mod 26 yx22 cd Hudson River Undergraduate Mathematics Conference The Key The key to the encryption scheme is the coefficient matrix A. -
Vigenere Cryptography
Fall 2006 Chris Christensen MAT/CSC 483 Cryptography of the Vigenère Cipher Cryptanalysis is based upon finding the ghosts of patterns of the plaintext. We have seen that an important technique of doing this is frequency analysis. So, cryptographers try to develop ciphers that are not easily attacked by frequency analysis. There are two basic ways to do this: use more than one ciphertext alphabet or encrypt more than one letter in a block. First, we will consider using more than one cipher text alphabet. Simple substitution ciphers, Caesar ciphers, multiplicative ciphers, and affine ciphers are all examples of monoalphabetic ciphers – only one ciphertext alphabet is used. Even if the original word lengths are concealed and the substitution alphabet is random, it is possible to find a solution by using frequency data, repetition patterns and information about the way letters combine with one another. What makes the solution possible is the fact that a given plain language letter is always represented by the same cipher letter. As a consequence, all the properties of plain language such as frequencies and combinations are carried over into the cipher and may be utilized for solution. In effect we could say that all such properties are invariant except that the names of the letters have been changed. It would seem then that one way to obtain greater security would be to use more than one alphabet in enciphering a message. The general system could be one that uses a number of different alphabets for encipherment, with an understanding between correspondents of the order in which the alphabets are to be used.