15-853:Algorithms in the Real World Cryptography Outline Cryptography
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
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 -
Chapter 3 – Block Ciphers and the Data Encryption Standard
Symmetric Cryptography Chapter 6 Block vs Stream Ciphers • Block ciphers process messages into blocks, each of which is then en/decrypted – Like a substitution on very big characters • 64-bits or more • Stream ciphers process messages a bit or byte at a time when en/decrypting – Many current ciphers are block ciphers • Better analyzed. • Broader range of applications. Block vs Stream Ciphers Block Cipher Principles • Block ciphers look like an extremely large substitution • Would need table of 264 entries for a 64-bit block • Arbitrary reversible substitution cipher for a large block size is not practical – 64-bit general substitution block cipher, key size 264! • Most symmetric block ciphers are based on a Feistel Cipher Structure • Needed since must be able to decrypt ciphertext to recover messages efficiently Ideal Block Cipher Substitution-Permutation Ciphers • in 1949 Shannon introduced idea of substitution- permutation (S-P) networks – modern substitution-transposition product cipher • These form the basis of modern block ciphers • S-P networks are based on the two primitive cryptographic operations we have seen before: – substitution (S-box) – permutation (P-box) (transposition) • Provide confusion and diffusion of message Diffusion and Confusion • Introduced by Claude Shannon to thwart cryptanalysis based on statistical analysis – Assume the attacker has some knowledge of the statistical characteristics of the plaintext • Cipher needs to completely obscure statistical properties of original message • A one-time pad does this Diffusion -
A Tutorial on the Implementation of Block Ciphers: Software and Hardware Applications
A Tutorial on the Implementation of Block Ciphers: Software and Hardware Applications Howard M. Heys Memorial University of Newfoundland, St. John's, Canada email: [email protected] Dec. 10, 2020 2 Abstract In this article, we discuss basic strategies that can be used to implement block ciphers in both software and hardware environments. As models for discussion, we use substitution- permutation networks which form the basis for many practical block cipher structures. For software implementation, we discuss approaches such as table lookups and bit-slicing, while for hardware implementation, we examine a broad range of architectures from high speed structures like pipelining, to compact structures based on serialization. To illustrate different implementation concepts, we present example data associated with specific methods and discuss sample designs that can be employed to realize different implementation strategies. We expect that the article will be of particular interest to researchers, scientists, and engineers that are new to the field of cryptographic implementation. 3 4 Terminology and Notation Abbreviation Definition SPN substitution-permutation network IoT Internet of Things AES Advanced Encryption Standard ECB electronic codebook mode CBC cipher block chaining mode CTR counter mode CMOS complementary metal-oxide semiconductor ASIC application-specific integrated circuit FPGA field-programmable gate array Table 1: Abbreviations Used in Article 5 6 Variable Definition B plaintext/ciphertext block size (also, size of cipher state) κ number -
Symmetric Key Ciphers Objectives
Symmetric Key Ciphers Debdeep Mukhopadhyay Assistant Professor Department of Computer Science and Engineering Indian Institute of Technology Kharagpur INDIA -721302 Objectives • Definition of Symmetric Types of Symmetric Key ciphers – Modern Block Ciphers • Full Size and Partial Size Key Ciphers • Components of a Modern Block Cipher – PBox (Permutation Box) – SBox (Substitution Box) –Swap – Properties of the Exclusive OR operation • Diffusion and Confusion • Types of Block Ciphers: Feistel and non-Feistel ciphers D. Mukhopadhyay Crypto & Network Security IIT Kharagpur 1 Symmetric Key Setting Communication Message Channel Message E D Ka Kb Bob Alice Assumptions Eve Ka is the encryption key, Kb is the decryption key. For symmetric key ciphers, Ka=Kb - Only Alice and Bob knows Ka (or Kb) - Eve has access to E, D and the Communication Channel but does not know the key Ka (or Kb) Types of symmetric key ciphers • Block Ciphers: Symmetric key ciphers, where a block of data is encrypted • Stream Ciphers: Symmetric key ciphers, where block size=1 D. Mukhopadhyay Crypto & Network Security IIT Kharagpur 2 Block Ciphers Block Cipher • A symmetric key modern cipher encrypts an n bit block of plaintext or decrypts an n bit block of ciphertext. •Padding: – If the message has fewer than n bits, padding must be done to make it n bits. – If the message size is not a multiple of n, then it should be divided into n bit blocks and the last block should be padded. D. Mukhopadhyay Crypto & Network Security IIT Kharagpur 3 Full Size Key Ciphers • Transposition Ciphers: – Involves rearrangement of bits, without changing value. – Consider an n bit cipher – How many such rearrangements are possible? •n! – How many key bits are necessary? • ceil[log2 (n!)] Full Size Key Ciphers • Substitution Ciphers: – It does not transpose bits, but substitutes values – Can we model this as a permutation? – Yes. -
Network Security Chapter 8
Network Security Chapter 8 Network security problems can be divided roughly into 4 closely intertwined areas: secrecy (confidentiality), authentication, nonrepudiation, and integrity control. Question: what does non-repudiation mean? What does “integrity” mean? • Cryptography • Symmetric-Key Algorithms • Public-Key Algorithms • Digital Signatures • Management of Public Keys • Communication Security • Authentication Protocols • Email Security -- skip • Web Security • Social Issues -- skip Revised: August 2011 CN5E by Tanenbaum & Wetherall, © Pearson Education-Prentice Hall and D. Wetherall, 2011 Network Security Security concerns a variety of threats and defenses across all layers Application Authentication, Authorization, and non-repudiation Transport End-to-end encryption Network Firewalls, IP Security Link Packets can be encrypted on data link layer basis Physical Wireless transmissions can be encrypted CN5E by Tanenbaum & Wetherall, © Pearson Education-Prentice Hall and D. Wetherall, 2011 Network Security (1) Some different adversaries and security threats • Different threats require different defenses CN5E by Tanenbaum & Wetherall, © Pearson Education-Prentice Hall and D. Wetherall, 2011 Cryptography Cryptography – 2 Greek words meaning “Secret Writing” Vocabulary: • Cipher – character-for-character or bit-by-bit transformation • Code – replaces one word with another word or symbol Cryptography is a fundamental building block for security mechanisms. • Introduction » • Substitution ciphers » • Transposition ciphers » • One-time pads -
Outline Block Ciphers
Block Ciphers: DES, AES Guevara Noubir http://www.ccs.neu.edu/home/noubir/Courses/CSG252/F04 Textbook: —Cryptography: Theory and Applications“, Douglas Stinson, Chapman & Hall/CRC Press, 2002 Reading: Chapter 3 Outline n Substitution-Permutation Networks n Linear Cryptanalysis n Differential Cryptanalysis n DES n AES n Modes of Operation CSG252 Classical Cryptography 2 Block Ciphers n Typical design approach: n Product cipher: substitutions and permutations n Leading to a non-idempotent cipher n Iteration: n Nr: number of rounds → 1 2 Nr n Key schedule: k k , k , …, k , n Subkeys derived according to publicly known algorithm i n w : state n Round function r r-1 r n w = g(w , k ) 0 n w : plaintext x n Required property of g: ? n Encryption and Decryption sequence CSG252 Classical Cryptography 3 1 SPN: Substitution Permutation Networks n SPN: special type of iterated cipher (w/ small change) n Block length: l x m n x = x(1) || x(2) || … || x(m) n x(i) = (x(i-1)l+1, …, xil) n Components: π l → l n Substitution cipher s: {0, 1} {0, 1} π → n Permutation cipher (S-box) P: {1, …, lm} {1, …, lm} n Outline: n Iterate Nr times: m substitutions; 1 permutation; ⊕ sub-key; n Definition of SPN cryptosytems: n P = ?; C = ?; K ⊆ ?; n Algorithm: n Designed to allow decryption using the same algorithm n What are the parameters of the decryption algorithm? CSG252 Classical Cryptography 4 SPN: Example n l = m = 4; Nr = 4; n Key schedule: n k: (k1, …, k32) 32 bits r n k : (k4r-3, …, k4r+12) z 0 1 2 3 4 5 6 7 8 9 A B C D E F π S(z) E 4 D 1 2 F B 8 3 A 6 C -
Symmetric Key Cryptosystems Definition
Symmetric Key Cryptosystems Debdeep Mukhopadhyay IIT Kharagpur Definition • Alice and Bob has the same key to encrypt as well as to decrypt • The key is shared via a “secured channel” • Symmetric Ciphers are of two types: – Block : The plaintext is encrypted in blocks – Stream: The block length is 1 • Symmetric Ciphers are used for bulk encryption, as they have better performance than their asymmetric counter-part. 1 Block Ciphers What we have learnt from history? • Observation: If we have a cipher C1=(P,P,K1,e1,d1) and a cipher C2 (P,P,K2,e2,d2). • We define the product cipher as C1xC2 by the process of first applying C1 and then C2 • Thus C1xC2=(P,P,K1xK2,e,d) • Any key is of the form: (k1,k2) and e=e2(e1(x,k1),k2). Likewise d is defined. Note that the product rule is always associative 2 Question: • Thus if we compute product of ciphers, does the cipher become stronger? – The key space become larger –2nd Thought: Does it really become larger. • Let us consider the product of a 1. multiplicative cipher (M): y=ax, where a is co-prime to 26 //Plain Texts are characters 2. shift cipher (S) : y=x + k Is MxS=SxM? • MxS: y=ax+k : key=(a,k). This is an affine cipher, as total size of key space is 312. • SxM: y=a(x+k)=ax+ak – Now, since gcd(a,26)=1, this is also an affine cipher. – key = (a,ak) – As gcd(a,26)=1, a-1 exists. There is a one-one relation between ak and k. -
Data Encryption Standard (DES)
6 Data Encryption Standard (DES) Objectives In this chapter, we discuss the Data Encryption Standard (DES), the modern symmetric-key block cipher. The following are our main objectives for this chapter: + To review a short history of DES + To defi ne the basic structure of DES + To describe the details of building elements of DES + To describe the round keys generation process + To analyze DES he emphasis is on how DES uses a Feistel cipher to achieve confusion and diffusion of bits from the Tplaintext to the ciphertext. 6.1 INTRODUCTION The Data Encryption Standard (DES) is a symmetric-key block cipher published by the National Institute of Standards and Technology (NIST). 6.1.1 History In 1973, NIST published a request for proposals for a national symmetric-key cryptosystem. A proposal from IBM, a modifi cation of a project called Lucifer, was accepted as DES. DES was published in the Federal Register in March 1975 as a draft of the Federal Information Processing Standard (FIPS). After the publication, the draft was criticized severely for two reasons. First, critics questioned the small key length (only 56 bits), which could make the cipher vulnerable to brute-force attack. Second, critics were concerned about some hidden design behind the internal structure of DES. They were suspicious that some part of the structure (the S-boxes) may have some hidden trapdoor that would allow the National Security Agency (NSA) to decrypt the messages without the need for the key. Later IBM designers mentioned that the internal structure was designed to prevent differential cryptanalysis. -
Algorithms and Mechanisms Historical Ciphers
Algorithms and Mechanisms Cryptography is nothing more than a mathematical framework for discussing the implications of various paranoid delusions — Don Alvarez Historical Ciphers Non-standard hieroglyphics, 1900BC Atbash cipher (Old Testament, reversed Hebrew alphabet, 600BC) Caesar cipher: letter = letter + 3 ‘fish’ ‘ilvk’ rot13: Add 13/swap alphabet halves •Usenet convention used to hide possibly offensive jokes •Applying it twice restores the original text Substitution Ciphers Simple substitution cipher: a=p,b=m,c=f,... •Break via letter frequency analysis Polyalphabetic substitution cipher 1. a = p, b = m, c = f, ... 2. a = l, b = t, c = a, ... 3. a = f, b = x, c = p, ... •Break by decomposing into individual alphabets, then solve as simple substitution One-time Pad (1917) Message s e c r e t 18 5 3 17 5 19 OTP +15 8 1 12 19 5 7 13 4 3 24 24 g m d c x x OTP is unbreakable provided •Pad is never reused (VENONA) •Unpredictable random numbers are used (physical sources, e.g. radioactive decay) One-time Pad (ctd) Used by •Russian spies •The Washington-Moscow “hot line” •CIA covert operations Many snake oil algorithms claim unbreakability by claiming to be a OTP •Pseudo-OTPs give pseudo-security Cipher machines attempted to create approximations to OTPs, first mechanically, then electronically Cipher Machines (~1920) 1. Basic component = wired rotor •Simple substitution 2. Step the rotor after each letter •Polyalphabetic substitution, period = 26 Cipher Machines (ctd) 3. Chain multiple rotors Each rotor steps the next one when a full -
Cryptographic Analysis of All 4 × 4-Bit S-Boxes
Cryptographic Analysis of All 4 × 4-Bit S-Boxes Markku-Juhani O. Saarinen REVERE SECURITY 4500 Westgrove Drive, Suite 335, Addison, TX 75001, USA. [email protected] Abstract. We present cryptanalytic results of an exhaustive search of all 16! bijective 4-bit S-Boxes. Previously affine equivalence classes have been exhaus- tively analyzed in 2007 work by Leander and Poschmann. We extend on this work by giving further properties of the optimal S-Box linear equivalence classes. In our main analysis we consider two S-Boxes to be cryptanalytically equivalent if they are isomorphic up to the permutation of input and output bits and a XOR of a constant in the input and output. We have enumerated all such equivalence classes with respect to their differential and linear properties. These equivalence classes are equivalent not only in their differential and linear bounds but also have equiv- alent algebraic properties, branch number and circuit complexity. We describe a “golden” set of S-boxes that have ideal cryptographic properties. We also present a comparison table of S-Boxes from a dozen published cryptographic algorithms. Keywords: S-Box, Differential cryptanalysis, Linear cryptanalysis, Exhaustive permutation search. 1 Introduction Horst Feistel introduced the Lucifer cipher, which can be considered to be the first modern block cipher, some 40 years ago. Feistel followed closely the prin- ciples outlined by Claude Shannon in 1949 [36] when designing Lucifer. We quote from Feistel’s 1971 patent text [20]: Shannon, in his paper, presents further developments in the art of cryp- tography by introducing the product cipher. That is, the successive ap- plication of two or more distinctly different kinds of message symbol transformations. -
A Brief Outlook at Block Ciphers
A Brief Outlook at Block Ciphers Pascal Junod Ecole¶ Polytechnique F¶ed¶eralede Lausanne, Suisse CSA'03, Rabat, Maroc, 10-09-2003 Content F Generic Concepts F DES / AES F Cryptanalysis of Block Ciphers F Provable Security CSA'03, 10 septembre 2003, Rabat, Maroc { i { Block Cipher P e d P C K K CSA'03, 10 septembre 2003, Rabat, Maroc { ii { Block Cipher (2) F Deterministic, invertible function: e : {0, 1}n × K → {0, 1}n d : {0, 1}n × K → {0, 1}n F The function is parametered by a key K. F Mapping an n-bit plaintext P to an n-bit ciphertext C: C = eK(P ) F The function must be a bijection for a ¯xed key. CSA'03, 10 septembre 2003, Rabat, Maroc { iii { Product Ciphers and Iterated Block Ciphers F A product cipher combines two or more transformations in a manner intending that the resulting cipher is (hopefully) more secure than the individual components. F An iterated block cipher is a block cipher involving the sequential repeti- tion of an internal function f called a round function. Parameters include the number of rounds r, the block bit size n and the bit size k of the input key K from which r subkeys ki (called round keys) are derived. For invertibility purposes, the round function f is a bijection on the round input for each value ki. CSA'03, 10 septembre 2003, Rabat, Maroc { iv { Product Ciphers and Iterated Block Ciphers (2) P K f k1 f k2 f kr C CSA'03, 10 septembre 2003, Rabat, Maroc { v { Good and Bad Block Ciphers F Flexibility F Throughput F Estimated Security Level CSA'03, 10 septembre 2003, Rabat, Maroc { vi { Data Encryption Standard (DES) F American standard from (1976 - 1998). -
Symmetric Cryptography: DES And
Modern Symmetric Ciphers Symmetric Cryptography: Symmetric Cryptography: z We will now look at two examples of modern symmetric key DES and RC4 ciphers: –DES – RC4 z These will serve as the basis for later discussion z We will also discuss modes of operation z Other popular ciphers: AES (Rijndael), RC5 Block vs Stream Ciphers Block Cipher Principles z There are two main classes of symmetric ciphers: z Most symmetric block ciphers are based on a Feistel Cipher – Block Ciphers: Break message into blocks and operate on a block- Structure by-block basis – This structure is desirable as it is easily reversible, allowing for – Stream Ciphers: Process messages bit-by-bit or byte-by-byte as easy encryption and decryption data arrives. Just reuse the same code, essentially! – Feistel structures allow us to break the construction of an z Typically, block ciphers may be modified to run in a “stream encryption/decryption algorithm into smaller, manageable building mode” blocks z We will examine two of ciphers: z Goal of a block cipher: – DES: The basic block cipher (building block for 3DES) – Mix and permute message bits in a way that is parameterized by – RC4: A popular example of a stream cipher an encryption key – Output should be “statistically” uncorrelated with the key and input message 1 Substitution & Permutation Ciphers Confusion and Diffusion z In 1949 Claude Shannon introduced idea of substitution- z Cipher needs to completely obscure statistical properties of permutation (S-P) networks original message – modern substitution-transposition