Grade 6 Math Circles Cryptography Introduction to Cryptography
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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. -
Enhancing the Security of Caesar Cipher Substitution Method Using a Randomized Approach for More Secure Communication
International Journal of Computer Applications (0975 – 8887) Volume 129 – No.13, November2015 Enhancing the Security of Caesar Cipher Substitution Method using a Randomized Approach for more Secure Communication Atish Jain Ronak Dedhia Abhijit Patil Dept. of Computer Engineering Dept. of Computer Engineering Dept. of Computer Engineering D.J. Sanghvi College of D.J. Sanghvi College of D.J. Sanghvi College of Engineering Engineering Engineering Mumbai University, Mumbai, Mumbai University, Mumbai, Mumbai University, Mumbai, India India India ABSTRACT communication can be encoded to prevent their contents from Caesar cipher is an ancient, elementary method of encrypting being disclosed through various techniques like interception plain text message into cipher text protecting it from of message or eavesdropping. Different ways include using adversaries. However, with the advent of powerful computers, ciphers, codes, substitution, etc. so that only the authorized there is a need for increasing the complexity of such people can view and interpret the real message correctly. techniques. This paper contributes in the area of classical Cryptography concerns itself with four main objectives, cryptography by providing a modified and expanded version namely, 1) Confidentiality, 2) Integrity, 3) Non-repudiation for Caesar cipher using knowledge of mathematics and and 4) Authentication. [1] computer science. To increase the strength of this classical Cryptography is divided into two types, Symmetric key and encryption technique, the proposed modified algorithm uses Asymmetric key cryptography. In Symmetric key the concepts of affine ciphers, transposition ciphers and cryptography a single key is shared between sender and randomized substitution techniques to create a cipher text receiver. The sender uses the shared key and encryption which is nearly impossible to decode. -
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. -
A Cipher Based on the Random Sequence of Digits in Irrational Numbers
https://doi.org/10.48009/1_iis_2016_14-25 Issues in Information Systems Volume 17, Issue I, pp. 14-25, 2016 A CIPHER BASED ON THE RANDOM SEQUENCE OF DIGITS IN IRRATIONAL NUMBERS J. L. González-Santander, [email protected], Universidad Católica de Valencia “san Vicente mártir” G. Martín González. [email protected], Universidad Católica de Valencia “san Vicente mártir” ABSTRACT An encryption method combining a transposition cipher with one-time pad cipher is proposed. The transposition cipher prevents the malleability of the messages and the randomness of one-time pad cipher is based on the normality of "almost" all irrational numbers. Further, authentication and perfect forward secrecy are implemented. This method is quite suitable for communication within groups of people who know one each other in advance, such as mobile chat groups. Keywords: One-time Pad Cipher, Transposition Ciphers, Chat Mobile Groups Privacy, Forward Secrecy INTRODUCTION In cryptography, a cipher is a procedure for encoding and decoding a message in such a way that only authorized parties can write and read information about the message. Generally speaking, there are two main different cipher methods, transposition, and substitution ciphers, both methods being known from Antiquity. For instance, Caesar cipher consists in substitute each letter of the plaintext some fixed number of positions further down the alphabet. The name of this cipher came from Julius Caesar because he used this method taking a shift of three to communicate to his generals (Suetonius, c. 69-122 AD). In ancient Sparta, the transposition cipher entailed the use of a simple device, the scytale (skytálē) to encrypt and decrypt messages (Plutarch, c. -
Secret Wri0ng Steganography
Secret wring LIVITCSWPIYVEWHEVSRIQMXLEYVEOIEWHRXEXIP FEMVEWHKVSTYLXZIXLIKIIXPIJVSZEYPERRGERI MWQLMGLMXQERIWGPSRIHMXQEREKIETXMJTPRGEV EKEITREWHEXXLEXXMZITWAWSQWXSWEXTVEPMRXR SJGSTVRIEYVIEXCVMUIMWERGMIWXMJMGCSMWXSJ OMIQXLIVIQIVIXQSVSTWHKPEGARCSXRWIEVSWII BXVIZMXFSJXLIKEGAEWHEPSWYSWIWIEVXLISXLI VXLIRGEPIRQIVIIBGIIHMWYPFLEVHEWHYPSRRFQ MXLEPPXLIECCIEVEWGISJKTVWMRLIHYSPHXLIQI MYLXSJXLIMWRIGXQEROIVFVIZEVAEKPIEWHXEAM WYEPPXLMWYRMWXSGSWRMHIVEXMSWMGSTPHLEVHP FKPEZINTCMXIVJSVLMRSCMWMSWVIRCIGXMWYMX CSCI 470: Web Science • Keith Vertanen • Copyright © 2014 Overview • Secret wri+ng – Steganography – Cryptography • Keys, plaintext, ciphertext • Codes vs. Ciphers • Transposi+on ciphers • Subs+tu+on ciphers 2 Steganography vs. Cryptography • Steganography – "concealed wri+ng" – Hide messages to keep secret – Does not aract aen+on (iF not Found). • Cryptography – "hidden wring" – Scramble messages so unintelligible – Screams: "Please try and decode me!" • But not mutually exclusive: – e.g. Scrambled message in "invisible" ink 3 Physical hiding • Ancient Chinese – Write message on very thin silk sheet – Rolled up, covered in wax, and ingested by messenger • 480 BC – His+aeus wants Aristagoras oF Miletus to revolt against the Persian King • Shaves head oF messenger, taoos message on scalp • Wait For hair to grow back • Sends messenger to Aristagoras 4 Physical hiding • 480 BC – Demaratus, Greek ex-pat living in Persia – No+ces build up For aack on Greece – Sent secret messages: • Scraped wax oF tablet • Wrote on wood • Covered up with wax – Persian ships -
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. -
A Hybrid Cryptosystem Based on Vigenère Cipher and Columnar Transposition Cipher
International Journal of Advanced Technology & Engineering Research (IJATER) www.ijater.com A HYBRID CRYPTOSYSTEM BASED ON VIGENÈRE CIPHER AND COLUMNAR TRANSPOSITION CIPHER Quist-Aphetsi Kester, MIEEE, Lecturer Faculty of Informatics, Ghana Technology University College, PMB 100 Accra North, Ghana Phone Contact +233 209822141 Email: [email protected] / [email protected] graphy that use the same cryptographic keys for both en- Abstract cryption of plaintext and decryption of cipher text. The keys may be identical or there may be a simple transformation to Privacy is one of the key issues addressed by information go between the two keys. The keys, in practice, represent a Security. Through cryptographic encryption methods, one shared secret between two or more parties that can be used can prevent a third party from understanding transmitted raw to maintain a private information link [5]. This requirement data over unsecured channel during signal transmission. The that both parties have access to the secret key is one of the cryptographic methods for enhancing the security of digital main drawbacks of symmetric key encryption, in compari- contents have gained high significance in the current era. son to public-key encryption. Typical examples symmetric Breach of security and misuse of confidential information algorithms are Advanced Encryption Standard (AES), Blow- that has been intercepted by unauthorized parties are key fish, Tripple Data Encryption Standard (3DES) and Serpent problems that information security tries to solve. [6]. This paper sets out to contribute to the general body of Asymmetric or Public key encryption on the other hand is an knowledge in the area of classical cryptography by develop- encryption method where a message encrypted with a reci- ing a new hybrid way of encryption of plaintext. -
Enigma Cryptanalysis - Beginnings
Enigma Cryptanalysis - Beginnings Gaurish Korpal∗ [email protected] July 15, 2015 Abstract Any message may be hidden in two basic ways. The methods of steganography conceal the very existence of the message, for example invisible inks and microdots. The methods of cryptography, on the other hand, do not conceal the presence of a secret message but render it unintelligible as ciphertext, to outsiders by various transformations of the plaintext. Breaking ciphers require ingenuity, creativity and a little math. In this article our focus will be on breaking Enigma ciphers. The skill involved in breaking ciphers is called cryptanalysis. Keywords. Enigma, cryptanalysis, cypher, Caesar, Vigen`ere,Rejewski, Zygalski, Bomba, Bombe 1 Cipher not Code A code is a mapping from some meaningful unit (word, sentence, phrase) into something else (usually a shorter group of symbols). A code requires a codebook, it is simply a list of these mappings. For example we could make up a code where the word Apple is written as 67, historical example of this is \Zimmermann Telegram Code" for more details refer [7]. Ciphers do not involve meaning. Instead they are mechanical operations (known as algorithms) which are performed on the individual or small chunks of letters. A code is stored as a mapping in a codebook, while ciphers transform individual symbols according to an algorithm. It was definitively stated in 1883 by the Dutch linguist Auguste Kerckhoffs von Nieuwenhof in his book La Cryptographie militaire: Kerckhoffs' Principle: The security of a cryptosystem must not depend on keeping secret the crypto-algorithm. The security depends only on keeping secret the key. -
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. -
Q.1 What Is Cryptography? Ans. Cryptographic
WWW.UPTUNOTES.COM Q.1 What is cryptography? Ans. Cryptographic systems are generally classified along 3 independent dimensions: Type of operations used for transforming plain text to cipher text All the encryption algorithms are based on two general principles: substitution, in which each element in the plaintext is mapped into another element, and transposition, in which elements in the plaintext are rearranged. The number of keys used are: 1. If the sender and receiver uses same key then it is said to be symmetric key (or) single key (or) conventional encryption. 2. If the sender and receiver use different keys then it is said to be public key encryption. Q.2 Explain the Cryptanalysis? Ans. The process of attempting to discover X or K or both is known as cryptanalysis. The strategy used by the cryptanalysis depends on the nature of the encryption scheme and the information available to the cryptanalyst. Q.3 Write down the various types of cryptanalytic attacks? Ans. There are various types of cryptanalytic attacks based on the amount of information known to the cryptanalyst. 1. Cipher Text Only – A copy of cipher text alone is known to the cryptanalyst. 2. Known Plaintext – The cryptanalyst has a copy of the cipher text and the corresponding plaintext. 3. Chosen Plaintext – The cryptanalysts gains temporary access to the encryption machine. They cannot open it to find the key, however; they can encrypt a large number of suitably chosen plaintexts and try to use the resulting cipher texts to deduce the key. 4. Chosen Cipher Text – The cryptanalyst obtains temporary access to the decryption machine, uses it to decrypt several string of symbols, and tries to use the results to deduce the key.