Section 2: Basic Cryptography
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Chapter 3 – Block Ciphers and the Data Encryption Standard
Chapter 3 –Block Ciphers and the Data Cryptography and Network Encryption Standard Security All the afternoon Mungo had been working on Stern's Chapter 3 code, principally with the aid of the latest messages which he had copied down at the Nevin Square drop. Stern was very confident. He must be well aware London Central knew about that drop. It was obvious Fifth Edition that they didn't care how often Mungo read their messages, so confident were they in the by William Stallings impenetrability of the code. —Talking to Strange Men, Ruth Rendell Lecture slides by Lawrie Brown Modern Block Ciphers Block vs Stream Ciphers now look at modern block ciphers • block ciphers process messages in blocks, each one of the most widely used types of of which is then en/decrypted cryptographic algorithms • like a substitution on very big characters provide secrecy /hii/authentication services – 64‐bits or more focus on DES (Data Encryption Standard) • stream ciphers process messages a bit or byte at a time when en/decrypting to illustrate block cipher design principles • many current ciphers are block ciphers – better analysed – broader range of applications Block vs Stream Ciphers Block Cipher Principles • most symmetric block ciphers are based on a Feistel Cipher Structure • needed since must be able to decrypt ciphertext to recover messages efficiently • bloc k cihiphers lklook like an extremely large substitution • would need table of 264 entries for a 64‐bit block • instead create from smaller building blocks • using idea of a product cipher 1 Claude -
Feistel Like Construction of Involutory Binary Matrices with High Branch Number
Feistel Like Construction of Involutory Binary Matrices With High Branch Number Adnan Baysal1,2, Mustafa C¸oban3, and Mehmet Ozen¨ 3 1TUB¨ ITAK_ - BILGEM,_ PK 74, 41470, Gebze, Kocaeli, Turkey, [email protected] 2Kocaeli University, Department of Computer Engineering, Faculty of Engineering, Institute of Science, 41380, Umuttepe, Kocaeli, Turkey 3Sakarya University, Faculty of Arts and Sciences, Department of Mathematics, Sakarya, Turkey, [email protected], [email protected] August 4, 2016 Abstract In this paper, we propose a generic method to construct involutory binary matrices from a three round Feistel scheme with a linear round function. We prove bounds on the maximum achievable branch number (BN) and the number of fixed points of our construction. We also define two families of efficiently implementable round functions to be used in our method. The usage of these families in the proposed method produces matrices achieving the proven bounds on branch numbers and fixed points. Moreover, we show that BN of the transpose matrix is the same with the original matrix for the function families we defined. Some of the generated matrices are Maximum Distance Binary Linear (MDBL), i.e. matrices with the highest achievable BN. The number of fixed points of the generated matrices are close to the expected value for a random involution. Generated matrices are especially suitable for utilising in bitslice block ciphers and hash functions. They can be implemented efficiently in many platforms, from low cost CPUs to dedicated hardware. Keywords: Diffusion layer, bitslice cipher, hash function, involution, MDBL matrices, Fixed points. 1 Introduction Modern block ciphers and hash functions use two basic layers iteratively to provide security: confusion and diffusion. -
Block Ciphers
Block Ciphers Chester Rebeiro IIT Madras CR STINSON : chapters 3 Block Cipher KE KD untrusted communication link Alice E D Bob #%AR3Xf34^$ “Attack at Dawn!!” message encryption (ciphertext) decryption “Attack at Dawn!!” Encryption key is the same as the decryption key (KE = K D) CR 2 Block Cipher : Encryption Key Length Secret Key Plaintext Ciphertext Block Cipher (Encryption) Block Length • A block cipher encryption algorithm encrypts n bits of plaintext at a time • May need to pad the plaintext if necessary • y = ek(x) CR 3 Block Cipher : Decryption Key Length Secret Key Ciphertext Plaintext Block Cipher (Decryption) Block Length • A block cipher decryption algorithm recovers the plaintext from the ciphertext. • x = dk(y) CR 4 Inside the Block Cipher PlaintextBlock (an iterative cipher) Key Whitening Round 1 key1 Round 2 key2 Round 3 key3 Round n keyn Ciphertext Block • Each round has the same endomorphic cryptosystem, which takes a key and produces an intermediate ouput • Size of the key is huge… much larger than the block size. CR 5 Inside the Block Cipher (the key schedule) PlaintextBlock Secret Key Key Whitening Round 1 Round Key 1 Round 2 Round Key 2 Round 3 Round Key 3 Key Expansion Expansion Key Key Round n Round Key n Ciphertext Block • A single secret key of fixed size used to generate ‘round keys’ for each round CR 6 Inside the Round Function Round Input • Add Round key : Add Round Key Mixing operation between the round input and the round key. typically, an ex-or operation Confusion Layer • Confusion layer : Makes the relationship between round Diffusion Layer input and output complex. -
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. -
Lecture Four
Lecture Four Today’s Topics . Historic Symmetric ciphers . Modern symmetric ciphers . DES, AES . Asymmetric ciphers . RSA . Next class: Protocols Example Ciphers . Shift cipher: each plaintext characters is replaced by a character k to the right. (When k=3, it’s a Caesar cipher). “Watch out for Brutus!” => “Jngpu bhg sbe Oehghf!” . Only 25 choices! Not hard to break by brute force. Substitution Cipher: each character in plaintext is replaced by a corresponding character of ciphertext. E.g., cryptograms in newspapers. plaintext code: a b c d e f g h i f k l m n o p q r s t u v w x y z ciphertext code: m n b v c x z a s d f g h j k l p o i u y t r e w q . 26! Possible pairs. Is is really that hard to break? Substitution ciphers . The Caesar cipher has a small key space, but doesn’t create a statistical independence between the plaintext and the ciphertext. The best ciphers allow no statistical attacks, thereby forcing a brute force, exhaustive search; all the security lies with the key space. As cryptographic algorithms matured, the statistical independence between the plaintext and cipher text increased. Ciphers . The caesar cipher, hill cipher, and playfair cipher all work with a single alphabet for doing substitutions . They are monoalphabetic substitutions. A more complex (and more robust) alternative is to use different substitution mappings on various portions of the plaintext. Polyalphabetic substitutions. More ciphers . Vigenère cipher: each character of plaintext is encrypted with a different a cipher key. -
Confusion and Diffusion
Confusion and Diffusion Ref: William Stallings, Cryptography and Network Security, 3rd Edition, Prentice Hall, 2003 Confusion and Diffusion 1 Statistics and Plaintext • Suppose the frequency distribution of plaintext in a human-readable message in some language is known. • Or suppose there are known words or phrases that are used in the plaintext message. • A cryptanalysist can use this information to break a cryptographic algorithm. Confusion and Diffusion 2 Changing Statistics • Claude Shannon suggested that to complicate statistical attacks, the cryptographer could dissipate the statistical structure of the plaintext in the long range statistics of the ciphertext. • Shannon called this process diffusion . Confusion and Diffusion 3 Changing Statistics (p.2) • Diffusion can be accomplished by having many plaintext characters affect each ciphertext character. • An example of diffusion is the encryption of a message M=m 1,m 2,... using a an averaging: y n= ∑i=1,k mn+i (mod26). Confusion and Diffusion 4 Changing Statistics (p.3) • In binary block ciphers, such as the Data Encryption Standard (DES), diffusion can be accomplished using permutations on data, and then applying a function to the permutation to produce ciphertext. Confusion and Diffusion 5 Complex Use of a Key • Diffusion complicates the statistics of the ciphertext, and makes it difficult to discover the key of the encryption process. • The process of confusion , makes the use of the key so complex, that even when an attacker knows the statistics, it is still difficult to deduce the key. Confusion and Diffusion 6 Complex Use of a Key(p.2) • Confusion can be accomplished by using a complex substitution algorithm. -
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. -
What You Should Know for the Final Exam
MATC16 Cryptography and Coding Theory G´abor Pete University of Toronto Scarborough What you should know for the final exam Principles and goals of cryptography: Kerckhoff’s principle. Shannon’s confusion and diffusion. Possible attack situations (cipher- text only, chosen plaintext, etc.). Possible goals of attacker, and the corresponding tasks of cryptography (confidentiality, data integrity, authentication, non-repudiation). [Chap- ter 1, plus page 38 and http://en.wikipedia.org/wiki/Confusion_and_diffusion for diffusion & confusion.] Classical cryptosystems: Number theory basics: infinitely many primes exist, basics of modular arithmetic, extended Euclidean algorithm, solving ax+by = d, inverting numbers and matrices (mod n). [Sections 3.1-3 and 3.8.] Shift and affine ciphers. Their ciphertext only and known plaintext attacks. Composition of two affine ciphers is again an affine cipher. [Sections 2.1-2.] Substitution ciphers in general. [Section 2.4] Vigen`ere cipher. Known plaintext attack. Ciphertext only: finding the key length, then frequency analysis. [Section 2.3.] Hill cipher. Known plaintext attack. [Section 2.7.] One-time pad. LFSR sequences. Known plaintext attack, finding the recursion. [Sections 2.9 and 11.] Basics of Enigma. [Section 2.12, up to middle of page 53.] The DES: Feistel systems, simplified and real DES (without the exact expansion functions and S-boxes and permutations, of course), how decryption works in these DES versions. How the extra parity check bits in the real DES key ensure error detection. How confusion and diffusion are fulfilled in DES. [Sections 4.1-2 and 4.4.] Double and Triple DES. Meet-in-the-middle attack. (I mentioned here that one can organize the two lists of length n and find a match between them in almost linear time (n log n) instead of the naive approach that would give only n2, and hence would ruin the attack completely. -
A Lightweight Encryption Algorithm for Secure Internet of Things
Pre-Print Version, Original article is available at (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 8, No. 1, 2017 SIT: A Lightweight Encryption Algorithm for Secure Internet of Things Muhammad Usman∗, Irfan Ahmedy, M. Imran Aslamy, Shujaat Khan∗ and Usman Ali Shahy ∗Faculty of Engineering Science and Technology (FEST), Iqra University, Defence View, Karachi-75500, Pakistan. Email: fmusman, [email protected] yDepartment of Electronic Engineering, NED University of Engineering and Technology, University Road, Karachi 75270, Pakistan. Email: firfans, [email protected], [email protected] Abstract—The Internet of Things (IoT) being a promising and apply analytics to share the most valuable data with the technology of the future is expected to connect billions of devices. applications. The IoT is taking the conventional internet, sensor The increased number of communication is expected to generate network and mobile network to another level as every thing mountains of data and the security of data can be a threat. The will be connected to the internet. A matter of concern that must devices in the architecture are essentially smaller in size and be kept under consideration is to ensure the issues related to low powered. Conventional encryption algorithms are generally confidentiality, data integrity and authenticity that will emerge computationally expensive due to their complexity and requires many rounds to encrypt, essentially wasting the constrained on account of security and privacy [4]. energy of the gadgets. Less complex algorithm, however, may compromise the desired integrity. In this paper we propose a A. Applications of IoT: lightweight encryption algorithm named as Secure IoT (SIT). -
Stream and Block Ciphers
Symmetric Cryptography Block Ciphers and Stream Ciphers Stream Ciphers K Seeded by a key K the stream cipher Stream ⃗z generates a random bit-stream z. Cipher A stream of plain-text bits p is XORed with the pseudo-random stream to obtain the cipher text stream c ⃗c=⃗p⊕⃗z and ⃗p=⃗c⊕⃗z ⃗c cipher text ⃗p plain text The same stream generator (using the same seed) ⃗z key stream used for both encryption and decryption Stream Ciphers K →¯zk ¯c=¯p⊕¯z k ¯ci=¯pi ⊕¯z k ¯c j=¯p j ⊕¯zk Attacker has access to ¯ci and ¯c j ¯ci⊕¯c j=(¯pi⊕¯zk )⊕(¯p j⊕¯z k)=¯pi⊕ ¯p j ● XORing two cipher-texts encrypted using the same seed results in XOR of corresponding plain-texts ● Redundancy in plain-text structure can be easily used to determine both plain- texts ● And hence, the key stream ● Never reuse seed? ● Impractical ● Extend seed using an initial value (IV) which can be sent in the clear ● Never reuse IV Block Ciphers ● C=E(P,K) ● P=D(C,K) ● E() and D() are algorithms ● P is a block of “plain text” (m bits) ● C is the corresponding “cipher text” (also m bits) ● K is the secret key (k bits long) ● (k,m) block cipher – k-bit keysize, m-bit blocksize ● (m+k)-bit input, m-bit output Desired Properties ● The most efficient attack should be the brute-force attack (complexity depends only on key length) ● Knowledge of any number of plain-cipher text pairs, still does not reveal any information regarding any bit of 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. -
Applied Cryptography and Data Security
Lecture Notes APPLIED CRYPTOGRAPHY AND DATA SECURITY (version 2.5 | January 2005) Prof. Christof Paar Chair for Communication Security Department of Electrical Engineering and Information Sciences Ruhr-Universit¨at Bochum Germany www.crypto.rub.de Table of Contents 1 Introduction to Cryptography and Data Security 2 1.1 Literature Recommendations . 3 1.2 Overview on the Field of Cryptology . 4 1.3 Symmetric Cryptosystems . 5 1.3.1 Basics . 5 1.3.2 A Motivating Example: The Substitution Cipher . 7 1.3.3 How Many Key Bits Are Enough? . 9 1.4 Cryptanalysis . 10 1.4.1 Rules of the Game . 10 1.4.2 Attacks against Crypto Algorithms . 11 1.5 Some Number Theory . 12 1.6 Simple Blockciphers . 17 1.6.1 Shift Cipher . 18 1.6.2 Affine Cipher . 20 1.7 Lessons Learned | Introduction . 21 2 Stream Ciphers 22 2.1 Introduction . 22 2.2 Some Remarks on Random Number Generators . 26 2.3 General Thoughts on Security, One-Time Pad and Practical Stream Ciphers 27 2.4 Synchronous Stream Ciphers . 31 i 2.4.1 Linear Feedback Shift Registers (LFSR) . 31 2.4.2 Clock Controlled Shift Registers . 34 2.5 Known Plaintext Attack Against Single LFSRs . 35 2.6 Lessons Learned | Stream Ciphers . 37 3 Data Encryption Standard (DES) 38 3.1 Confusion and Diffusion . 38 3.2 Introduction to DES . 40 3.2.1 Overview . 41 3.2.2 Permutations . 42 3.2.3 Core Iteration / f-Function . 43 3.2.4 Key Schedule . 45 3.3 Decryption . 47 3.4 Implementation . 50 3.4.1 Hardware .