DOCSLIB.ORG

Crittografia Contemporanea (Simmetrica)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Crittografia Contemporanea (Simmetrica) Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Crittografia contemporanea Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Classificazione dei sistemi crittografici contemporanei • Il criterio di distinzione più importante per i sistemi crittografici contemporanei riguarda il tipo e numero di chiavi usate: nei sistemi a chiave simmetrica viene utilizzata una sola chiave, nei sistemi a chiave asimmetrica ogni utente dispone di due chiavi, una pubblica e una privata. • Secondariamente, i sistemi crittografici possono essere distinti in base al tipo di dati su cui lavorano: i sistemi a blocchi elaborano i dati in blocchi di dimensione fissa (ad es. 64 bit), i sistemi a flusso elaborano i dati un byte (o bit, o altra unità di informazione) per volta. 2 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Sistemi a chiave simmetrica • In questa lezione parleremo di sistemi a chiave simmetrica (e principalmente di sistemi a blocchi). X: messaggio in chiaro, Y: messaggio cifrato, K: chiave. X’, K’: stime di X e K da parte di un attaccante 3 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Problemi della cifratura a chiave simmetrica • Il problema principale della cifratura a chiave simmetrica consiste nella diffusione della chiave • Se n persone devono comunicare tra di loro mediante messaggi crittati, sono necessarie n(n-1)/2 chiavi diverse (ordine di grandezza quadratico!). Ognuna di queste chiavi deve essere concordata tra mittente e destinatario su un canale sicuro… • Vedremo nelle prossime lezioni come questo problema possa essere mitigato dai sistemi a chiave asimmetrica 4 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Caratteristica fondamentale dell’algoritmo di cifratura • Essere facilmente computabile ed invertibile se la chiave è nota • Essere difficilmente invertibile in assenza della chiave • In questo contesto, “facile” e “difficile” si riferiscono alla fattibilità pratica di effettuare una data computazione in tempi ragionevoli con le tecnologie disponibili attualmente o che potranno essere disponibili in un prossimo futuro (sicurezza computazionale). 5 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Principio di Kerckhoffs • un crittosistema deve essere sicuro anche se il suo funzionamento è di pubblico dominio, con l'eccezione della chiave • In altre parole l’algoritmo non deve essere segreto. Al contrario, renderlo noto al pubblico contribuisce a garantire la sua robustezza in quanto può essere analizzato dalla comunità crittanalitica. 6 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea OTP e cifrari a flusso 7 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea One-Time Pad • OTP (o cifrario di Vernam ) è un cifrario di Vigenère con chiave lunga quanto il testo (senza ripetizioni), totalmente casuale e utilizzabile una volta sola • Il testo cifrato non ha più alcuna relazione con quello originario: questa cifratura è inviolabile se l’attaccante ha accesso al solo testo cifrato (sicurezza incondizionata contro attacchi passivi) 8 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Sicurezza di OTP (dim. intuitiva) • Dimostrazione intuitiva dell’inviolabilità di OTP: • Dato un testo cifrato, per qualsiasi testo in chiaro della stessa lunghezza esiste una chiave (unica ed equiprobabile ) che lo genera. Esempio: testo cifrato DREMUFCA chiave i j l t g o u a testo in chiaro v i t t o r i a Esercizio: scrivere un testo cifrato casuale, e trovare almeno due chiavi che lo trasformino in parole di chiave o d s x q u q m senso compiuto testo in chiaro p o m p e l m o 9 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Sicurezza di OTP (dim. formale) • Shannon: un cifrario è sicuro se il testo cifrato non rivela alcuna informazione riguardo al testo in chiaro. • Formalmente, si richiede che: Pr ̿ ͟, ͤ͡ Ɣ ͗ Ɣ Pr ̿ ͟, ͥ͡ Ɣ ͗ ∀͗ ∈ č, ∀ ͤ͡, ͥ͡ ∈ ė, ͤ͡ Ɣ |ͥ͡| • Nel caso di OTP, dato un messaggio m e un testo cifrato c, e ipotizzando che le chiavi siano casuali (distribuite uniformemente su ĕ): #& /.. &,( Ͱ ͥ Pr ̿ ͟, ͡ Ɣ ͗ Ɣ Ɣ (costante ∀ ͡) ĕ ĕ č: insieme dei testi cifrati, ĕ: insieme delle chiavi, ė: insieme dei testi in chiaro ̿ʚ͟, ͡ʛ: algoritmo di cifratura applicato sul messaggio m con chiave k 10 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea One-Time Pad / 3 • Ricordiamo che le chiavi devono essere casuali, uniche per ogni messaggio e lunghe (almeno) quanto il messaggio stesso. – Se la chiave non è lunga quanto il messaggio, l’algoritmo è vulnerabile ad un attacco di Kasiski (già visto per Vigenère) – Se una stessa chiave viene usata per cifrare più messaggi, si ricade nel caso precedente – Se la chiave non è casuale, allora alcune chiavi sono più probabili di altre: questo ci permette di discriminare tra due output 11 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea One-Time Pad / 3 • Due problemi principali limitano l’uso di OTP in pratica: – Difficoltà di creare chiavi davvero casuali – Necessità di condivisione delle chiavi tra mittente e destinatario • Il problema di trasmettere il messaggio non è stato risolto, ma solo trasformato nel problema di condividere una chiave altrettanto lunga. • Unico vantaggio: condivisione della chiave e trasmissione del messaggio possono avvenire in istanti diversi (es: condivisione iniziale sicura della chiave per proteggere la successiva trasmissione del messaggio su canale insicuro) 12 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Richiamo sull’operatore XOR • L’operatore exclusive-or (XOR, ⊕) è un operatore booleano che assume valore 1 quando due bit sono diversi, e 0 quando sono uguali p q p⊕⊕⊕q Esempio: 0 0 0 110101001 ⊕ 1 0 1 010011011 = 0 1 1 100110010 1 1 0 Proprietà fondamentali: • A ⊕ A = 0 • A ⊕ 0 = A • A ⊕ ( B ⊕ C ) = ( A ⊕ B ) ⊕ C 13 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea OTP binario • Se volessimo applicare OTP a dati binari? • L’alfabeto è composto da due soli simboli: 0, 1 • La tabella di Vigenère si semplifica: 0 1 In altre parole, l’operatore binario di XOR 0 0 1 1 1 0 • Quindi si può realizzare una cifratura OTP su dati binari combinandoli in XOR con una sequenza casuale di bit CIFRATURA: C = M ⊕ K DECIFRAUTRA: M = C ⊕ K ( C ⊕ K = M ⊕ K ⊕ K = M ) 14 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Riutilizzo delle chiavi con OTP binario • OTP binario ci permette di capire meglio perché la chiave OTP non può essere riutilizzata: • C1 = M1 ⊕ K • C2 = M2 ⊕ K M1, M2 testi in chiaro, K chiave, C1, C2 testi cifrati • C1 ⊕ C2 = M1 ⊕ K ⊕ M2 ⊕ K = M1 ⊕ M2 Lo XOR di due testi cifrati è uguale allo XOR dei rispettivi testi in chiaro. Permette ad esempio di identificare immediatamente porzioni di testo uguali (in quanto il risultato dello XOR è una sequenza di 0) 15 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Esempio visuale ⊕⊕⊕ = M1 K C1 ⊕⊕⊕ ⊕⊕⊕ = M2 K C2 16 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Altri attacchi a OTP • «sicurezza incondizionata» significa che non è possibile decifrare un messaggio cifrato con OTP avendo a disposizione solamente il testo cifrato, perché ogni decifrazione è ugualmente probabile e quindi indistinguibile (sicurezza rispetto agli attacchi passivi ) • Esistono tuttavia altri attacchi possibili a OTP, ad esempio sfruttando la sua malleabilità • Un cifrario è malleabile se è possibile alterare il testo cifrato in modo da ottenere un risultato specifico in seguito alla decifratura ( attacco attivo ) 17 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Malleabilità di OTP Cifratura: C = M ⊕ K Un attaccante intercetta C e lo sostituisce con C’ = C ⊕ N decifratura: M’ = C’ ⊕ K = M ⊕ K ⊕ N ⊕ K = M ⊕ N Se l’attaccante conosce M, può scegliere un opportuno N tale che, in fase di decifratura, il testo in chiaro originario M sia sostituito da un testo arbitrario M’, scelto dall’attaccante 18 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea OTP e cifrari a flusso • L’idea di OTP binario è alla base di molti cifrari a flusso , in cui i bit da cifrare sono elaborati indipendentemente l’uno dall’altro, senza la necessità di suddividerli in blocchi di dimensioni fisse • In questo caso i cifrari a flusso sono basati sull’uso di PRG (pseudo- random generators), generatori di sequenze di bit apparentemente casuali • Naturalmente questi algoritmi non sono delle vere implementazioni di OTP, in quanto la sequenza di bit non è davvero casuale (è pur sempre generata da algoritmi deterministici… ) • E’ tuttavia sufficiente che tale sequenza sembri casuale da un punto di vista statistico (ovvero, in assenza del seed iniziale è impossibile fare delle previsioni sulla sequenza generata dall’algoritmo) 19 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Cifrari a flusso Chiave casuale OTP ⊕ Testo in chiaro Ɣ Testo cifrato chiave PRG Cifrario a flusso basato su PRG sequenza pseudo-casuale ⊕ Testo in chiaro Ɣ Testo cifrato 20 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea Cifrari a blocchi 21 Sicurezza nelle applicazioni multimediali: lezione 3, crittografia contemporanea I concetti di confusione
Load more

Recommended publications
  • Stage De Master 2R
    STAGE DE MASTER 2R SYSTEMES ELECTRONIQUES ET GENIE ELECTRIQUE PARCOURS SYSTEMES ELECTRONIQUES ANNEE UNIVERSITAIRE 2006/2007 CRYPTO-COMPRESSION BASED ON CHAOS OF STILL IMAGES FOR THE TRANSMISSION YIN XU École Polytechnique de l’Université de Nantes Laboratoire IREENA Encadrants du stage : Safwan EL ASSAD Vincent RICORDEL Stage effectué du (05/02/2007) au (09/07/2007) Acknowledgments I would like to express my gratitude to my supervisors Professor Safwan EL ASSAD and Professor Vincent RICORDEL, who have been giving me direction with great patience. As the tutor of the first part of my internship, Prof. RICORDEL coached me on the study of JPEG 2000 systems and I benefited a lot from his tutorials. His constructive suggestions on my research and careful correction of my submitted materials are deeply appreciated. And as the tutor of the second part of my internship, Prof. EL ASSAD pointed out a clear direction of the subject that I should follow, which spare me from the potential wasting of time. He was always encouraging me and thus providing me with more confidence to achieve the objects of the internship. Doctor. Abir AWAD helped me a lot on the program-performance comparisons of C++ and MATLAB and she also gave me many useful materials on my subject. I am really thankful. I would also give my thankfulness to Professor Joseph SAILLARD and Professor Patrick LE CALLET for attending my final defense as a member of the jury despite the busy occupation of their own work. Of course also send great thankfulness to my two supervisors Prof. EL ASSAD and Prof.
    [Show full text]
  • 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.
    [Show full text]
  • Network Security H B ACHARYA
    Network Security H B ACHARYA NETWORK SECURITY Day 2 NETWORK SECURITY Encryption Schemes NETWORK SECURITY Basic Problem ----- ----- ? Given: both parties already know the same secret How is this achieved in practice? Goal: send a message confidentially Any communication system that aims to guarantee confidentiality must solve this problem NETWORK SECURITY slide 4 One-Time Pad (Vernam Cipher) ----- 10111101… ----- = 10111101… 10001111… = 00110010… 00110010… = Key is a random bit sequence as long as the plaintext Decrypt by bitwise XOR of ciphertext and key: ciphertext key = (plaintext key) key = Encrypt by bitwise XOR of plaintext (key key) = plaintext and key: plaintext ciphertext = plaintext key Cipher achieves perfect secrecy if and only if there are as many possible keys as possible plaintexts, and every key is equally likely (Claude Shannon, 1949) NETWORK SECURITY slide 5 Advantages of One-Time Pad Easy to compute ◦ Encryption and decryption are the same operation ◦ Bitwise XOR is very cheap to compute As secure as theoretically possible ◦ Given a ciphertext, all plaintexts are equally likely, regardless of attacker’s computational resources ◦ …if and only if the key sequence is truly random ◦ True randomness is expensive to obtain in large quantities ◦ …if and only if each key is as long as the plaintext ◦ But how do the sender and the receiver communicate the key to each other? Where do they store the key? NETWORK SECURITY slide 6 Problems with One-Time Pad Key must be as long as the plaintext ◦ Impractical in most realistic
    [Show full text]
  • “Network Security” Omer Rana Cryptography Components
    “Network Security” Omer Rana CM0255 Material from: Cryptography Components Sender Receiver Ciphertext Plaintext Plaintext Encryption Decryption Encryption algorithm: Plaintext Ciphertext • Cipher: encryption or decryption algorithms (or categories of algorithms) • Key: a number (set of numbers) – that the cipher (as an algorithm) operates on. • To encrypt a message: – Encryption algorithm – Encryption key Ciphertext – Plaintext 1 Three types of keys: Symmetric -key Secret Key Cryptography Public Key shared secret key Alice Bob Private Key Plaintext Ciphertext Plaintext Encryption Decryption •Same key used by both parties •Key used for both encryption and decryption •Keys need to be swapped beforehand using a secure mechanism Asymmetric -key To everyone (public) Bob’s public Cryptography key Alice Bob Bob’s private key Ciphertext Plaintext Plaintext Encryption Decryption Differentiate between a public key and a private key Symmetric-Key Cryptography • Traditional ciphers: – Character oriented – Two main approaches: • Substitution ciphers or • Transposition Ciphers • Substitution Ciper: – Substitute one symbol with another – Mono-alphabetic : a character (symbol) in plaintext is changed to the same character (symbol) in ciphertext regardless of its position in the text If L O, every instance of L will be changed to O Plaintext: HELLO Ciphertext: KHOOR – Poly-alphabetic : each occurrence can have a different substitute. Relationship between a character in plaintext to ciphertext is one-to-many (based on position being in beginning, middle
    [Show full text]
  • 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.
    [Show full text]
  • COS433/Math 473: Cryptography Mark Zhandry Princeton University Spring 2017 Previously
    COS433/Math 473: Cryptography Mark Zhandry Princeton University Spring 2017 Previously Pseudorandom Functions and Permutaitons Modes of Operation Pseudorandom Functions Functions that “look like” random functions Syntax: • Key space {0,1}λ • Domain X (usually {0,1}m, m may depend on λ) • Co-domain/range Y (usually {0,1}n, may depend on λ) • Function F:{0,1}λ × XàY Pseudorandom Permutations (also known as block ciphers) Functions that “look like” random permutations Syntax: • Key space {0,1}λ • Domain X (usually {0,1}n, n usually depends on λ) • Range X • Function F:{0,1}λ × XàX • Function F-1:{0,1}λ × XàX Correctness: ∀k,x, F-1(k, F(k, x) ) = x Pseudorandom Permutations Security: λ b Challenger x∈X y b’ Pseudorandom Permutations Security: λ b=0 Challenger k ß Kλ x∈X y y ß F(k,x) b’ PRF-Exp0( , λ) Pseudorandom Permutations Security: λ b=1 Challenger HßPerms(X,X) x∈X y y = H(x) b’ PRF-Exp1( , λ) Theorem: A PRP (F,F-1) is secure iff F is a secure as a PRF Theorem: There are secure PRPs (F,F-1) where (F-1,F) is insecure Strong PRPs λ b=0 Challenger k ß K x∈X λ y y ß F(k,x) x∈X ß -1 y y F (k,x) b’ PRF-Exp0( , λ) Strong PRPs λ b=1 Challenger x∈X HßPerms(X,X) y y ß H(x) x∈X ß -1 y y H (x) b’ PRF-Exp1( , λ) Theorem: If (F,F-1) is a strong PRP, then so is (F-1,F) PRPs vs PRFs In practice, PRPs are the central building block of most crypto • Also PRFs • Can build PRGs • Very versatile Today Constructing PRPs Today, we are going to ignore negligible, and focus on concrete parameters • E.g.
    [Show full text]
  • Introduction to Modern Symmetric-Key Ciphers Objectives
    Introduction to Modern Symmetric-key Ciphers Objectives ❏ To distinguish between traditional and modern symmetric-key ciphers. ❏ To introduce modern block ciphers and discuss their characteristics. ❏ To explain why modern block ciphers need to be designed as substitution ciphers. ❏ To introduce components of block ciphers such as P-boxes and S-boxes. Objectives (Continued) ❏ To discuss product ciphers and distinguish between two classes of product ciphers: Feistel and non-Feistel ciphers. ❏ To discuss two kinds of attacks particularly designed for modern block ciphers: differential and linear cryptanalysis. ❏ To introduce stream ciphers and to distinguish between synchronous and nonsynchronous stream ciphers. ❏ To discuss linear and nonlinear feedback shift registers for implementing stream ciphers. MODERN BLOCK CIPHERS A symmetric-key modern block cipher encrypts an n-bit block of plaintext or decrypts an n-bit block of ciphertext. The encryption or decryption algorithm uses a k-bit key. 1 Substitution or Transposition 2 Block Ciphers as Permutation Groups 3 Components of a Modern Block Cipher 4 Product Ciphers 5 Two Classes of Product Ciphers 6 Attacks on Block Ciphers Figure A modern block cipher Example How many padding bits must be added to a message of 100 characters if 8-bit ASCII is used for encoding and the block cipher accepts blocks of 64 bits? Solution Encoding 100 characters using 8-bit ASCII results in an 800- bit message. The plaintext must be divisible by 64. If | M | and |Pad| are the length of the message and the length of the padding, Substitution or Transposition A modern block cipher can be designed to act as a substitution cipher or a transposition cipher.
    [Show full text]
  • An Efficient VHDL Description and Hardware Implementation of The
    An Efficient VHDL Description and Hardware Implementation of the Triple DES Algorithm A thesis submitted to the Graduate School of the University of Cincinnati In partial fulfillment of the requirements for the degree of Master of Science In the Department of Electrical and Computer Engineering Of the College of Engineering and Applied Sciences June 2014 By Lathika SriDatha Namburi B.Tech, Electronics and Communications Engineering, Jawaharlal Nehru Technological University, Hyderabad, India, 2011 Thesis Advisor and Committee Chair: Dr. Carla Purdy ABSTRACT Data transfer is becoming more and more essential these days with applications ranging from everyday social networking to important banking transactions. The data that is being sent or received shouldn’t be in its original form but must be coded to avoid the risk of eavesdropping. A number of algorithms to encrypt and decrypt the data are available depending on the level of security to be achieved. Many of these algorithms require special hardware which makes them expensive for applications which require a low to medium level of data security. FPGAs are a cost effective way to implement such algorithms. We briefly survey several encryption/decryption algorithms and then focus on one of these, the Triple DES. This algorithm is currently used in the electronic payment industry as well as in applications such as Microsoft OneNote, Microsoft Outlook and Microsoft system center configuration manager to password protect user content and data. We implement the algorithm in a Hardware Description Language, specifically VHDL and deploy it on an Altera DE1 board which uses a NIOS II soft core processor. The algorithm takes input encoded using a software based Huffman encoding to reduce its redundancy and compress the data.
    [Show full text]
  • Cryptanalysis of Block Ciphers
    Cryptanalysis of Block Ciphers Jiqiang Lu Technical Report RHUL–MA–2008–19 30 July 2008 Royal Holloway University of London Department of Mathematics Royal Holloway, University of London Egham, Surrey TW20 0EX, England http://www.rhul.ac.uk/mathematics/techreports CRYPTANALYSIS OF BLOCK CIPHERS JIQIANG LU Thesis submitted to the University of London for the degree of Doctor of Philosophy Information Security Group Department of Mathematics Royal Holloway, University of London 2008 Declaration These doctoral studies were conducted under the supervision of Prof. Chris Mitchell. The work presented in this thesis is the result of original research carried out by myself, in collaboration with others, whilst enrolled in the Information Security Group of Royal Holloway, University of London as a candidate for the degree of Doctor of Philosophy. This work has not been submitted for any other degree or award in any other university or educational establishment. Jiqiang Lu July 2008 2 Acknowledgements First of all, I thank my supervisor Prof. Chris Mitchell for suggesting block cipher cryptanalysis as my research topic when I began my Ph.D. studies in September 2005. I had never done research in this challenging ¯eld before, but I soon found it to be really interesting. Every time I ¯nished a manuscript, Chris would give me detailed comments on it, both editorial and technical, which not only bene¯tted my research, but also improved my written English. Chris' comments are fantastic, and it is straightforward to follow them to make revisions. I thank my advisor Dr. Alex Dent for his constructive suggestions, although we work in very di®erent ¯elds.
    [Show full text]
  • COS433/Math 473: Cryptography Mark Zhandry Princeton University Fall 2020 Announcements/Reminders
    COS433/Math 473: Cryptography Mark Zhandry Princeton University Fall 2020 Announcements/Reminders HW2 due Today • Submit through Gradescope PR1 Due October 6 Previously on COS 433… Confusion/Diffusion Paradigm Confusion/Diffusion Paradigm Third Attempt: Repeat multiple times! f1 f2 f3 f4 f5 f6 Round π1 f7 f8 f9 f10 f11 f12 π2 Confusion/Diffusion Paradigm While single round is insecure, we’ve made progress • Each bit affects 8 output bits With repetition, hopefully we will make more and more progress Confusion/Diffusion Paradigm With 2 rounds, • Each bit affects 64 output bits With 3 rounds, all 128 bits are affected Repeat a few more times for good measure Limitations Describing subs/perms requires many bits • Key size for r rounds is approximately 28×λ×r • Ideally want key size to be 128 (or 256) Idea: instead, fix subs/perms • But then what’s the key? Substitution Permutation Networks Variant of previous construction • Fixed public permutations for confusion (called a substitution box, or S-box) • Fixed public permutation for diffusion (called a permutation box, or P-box) • XOR “round key” at beginning of each round Substitution Permutation Networks ⊕ ⊕ ⊕ ⊕ ⊕ ⊕ Round key Round s1 s2 s3 s4 s5 s6 π Substitution Permutation Networks ⊕ ⊕ ⊕ ⊕ ⊕ ⊕ Round key Round s1 s2 s3 s4 s5 s6 π Potentially ⊕ ⊕ ⊕ ⊕ ⊕ ⊕ different s1 s2 s3 s4 s5 s6 π Substitution Permutation Networks ⊕ ⊕ ⊕ ⊕ ⊕ ⊕ Round key Round s1 s2 s3 s4 s5 s6 π Potentially ⊕ ⊕ ⊕ ⊕ ⊕ ⊕ different s1 s2 s3 s4 s5 s6 π Final key ⊕ ⊕ ⊕ ⊕ ⊕ ⊕ mixing Substitution Permutation Networks To specify
    [Show full text]
  • Research Article Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation
    Hindawi Complexity Volume 2020, Article ID 8868884, 16 pages https://doi.org/10.1155/2020/8868884 Research Article Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation Musheer Ahmad 1 and Eesa Al-Solami 2 1Department of Computer Engineering, Jamia Millia Islamia, New Delhi 110025, India 2Department of Information Security, University of Jeddah, Jeddah 21493, Saudi Arabia Correspondence should be addressed to Musheer Ahmad; [email protected] Received 30 September 2020; Revised 7 December 2020; Accepted 11 December 2020; Published 23 December 2020 Academic Editor: Jesus M. Muñoz-Pacheco Copyright © 2020 Musheer Ahmad and Eesa Al-Solami. *is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. *is paper proposes to present a novel method of generating cryptographic dynamic substitution-boxes, which makes use of the combined effect of discrete hyperchaos mapping and algebraic group theory. Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour in terms of large Lyapunov exponents, excellent bifurcation, phase attractor, high entropy, and unpredictability. Secondly, a hyperchaotic key-dependent substitution-box generation process is designed, which is based on the bijectivity-preserving effect of multiplication with permutation matrix to obtain satisfactory configuration of substitution-box matrix over the enormously large problem space of 256!. Lastly, the security strength of obtained S-box is further elevated through the action of proposed algebraic group structure. *e standard set of performance parameters such as nonlinearity, strict avalanche criterion, bits independent criterion, differential uniformity, and linear approximation probability is quantified to assess the security and robustness of proposed S-box.
    [Show full text]
  • Cryptography Glossary
    Cryptography Glossary A5/1 A stream cipher used in GSM mobile phone communication. 36 Active Attack A cryptanalysis attack that relies on actively disrupting communication 44 or forcefully getting access to data. Adaptive chosen-ciphertext Attack Similar to chosen-ciphertext attack but Eve can choose subsequent ci- 44 phertexts based on information learnt from previous encryptions. Adaptive chosen-plaintext Attack Similar to chosen-plaintext attack but Eve can choose subsequent plain- 44 texts based on information learnt from previous encryptions. AddRoundKey The round key addition operation used during AES encryption and de- 28 cryption. AES The advanced encryption standard that is the successor of DES. 26 Alice The sender of an encrypted message. 11 Asymmetric Cipher Cipher that uses different (not trivially related) keys for encryption and 11, 54 decryption. Asymmetric Cryptography The study of algorithms and protocols for asymmetric ciphers. 54 Birthday Paradox A probability theoretical fact stating that in a random group of ¢¡ people 47 the likelihood that two of them will have the same birthday is more than £¥¤§¦ Block A fixed-length group of bits. 11 Block Cipher A symmetric key cipher, which operates on fixed-length groups of bits, 11 named blocks. Bob The intended receiver of an encrypted message. Bob is assumed to have 11 the key to decrypt it. C2 Short for Cryptomeria. 24 CA Short for Certification Authority. 71 Caesar Cipher Shift cipher with fixed shift of ¡ . 6 © § ¨ © !¨ Carmichael Number A number ¨ for which for all but that is 64 nevertheless composite. CBC Short for Cipher Block Chaining 20 CBC-MAC A method to produce a MAC from a block cipher.
    [Show full text]