DOCSLIB.ORG

A Novel Feistel Cipher Involving a Bunch of Keys Supplemented with XOR Operation

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Novel Feistel Cipher Involving a Bunch of Keys Supplemented with XOR Operation (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 3, No. 12, 2012 A Novel Feistel Cipher Involving a Bunch of Keys Supplemented with XOR Operation V.U.K Sastry K. Anup Kumar Dean R&D, Department of Computer Science and Associate Professor, Department of Computer Science Engineering, Sreenidhi Institute of Science & Tech. and Engineering, SNIST, Hyderabad, India Hyderabad, India Abstract—In this investigation, we have developed a novel block In order to satisfy (1.5), we chose ejk as an odd integer, cipher by modifying classical Feistel cipher. In this, we have used which lies in the interval [1-255], and thus we obtain djk also as a key bunched wherein each key has a multiplicative inverse. The an odd integer lying in the interval [1-255]. cryptanalysis carried out in this investigation clearly shows that this cipher cannot be broken by any attack. Here also we adopt an iterative procedure, and make use of the permutation process that consists of the interchange of the Keywords-encryption; decryption; cryptanalysis; avalanche effect; two halves of the plaintext , of course, represented in the form multiplicative inverse. of a pair of matrices. I. INTRODUCTION In the present analysis, our objective is to modify the Feistel cipher by including a bunch of keys. Here our interest is The study of the Feistel cipher [1-2] laid the foundation for to see how the different keys, occurring in the key bunch, the development of cryptography in the seventies of the last would influence the strength of the cipher. century. In the classical Feistel cipher the block size is 64 bits, and it is divided into two halves wherein each half is containing In what follows, we present the plan of the paper. In section 32 bits. The number of rounds in the iteration process is 16. 2, we introduce the development of the cipher and present the The basic equations governing the Feistel cipher can be written flowcharts and the algorithms corresponding to the cipher, in in the form section 3, we illustrate the cipher with an example and examine the avalanche effect. After that, we carry out the cryptanalysis Pi = Qi-1, (1.1) i i-1 i-1 i in section 4. Finally we present numerical computation and Q = P F (Q , K ), (1.2) draw conclusions. and II. DEVELOPMENT OF THE CIPHER Qi-1 = Pi, (1.3) i-1 i i i P = Q F (P , K ), (1.4) 2 i i th We consider a plaintext P containing 2m characters. On where P and Q are the blocks of the plaintext in the i using the EBCIDIC code this is written in terms of numbers round of the iteration process, F is a function chosen i th which are in the interval [0-255]. Now we write this in the form appropriately, and K is the key in the i round. In this analysis, of a pair of square matrices P0 and Q0, wherein each matrix is the XOR operation and the permutation that is performed by of size m. interchanging two halves of the data in the iteration process play a vital role in deciding the strength of the cipher. The basic equations governing the encryption of this block cipher are given by In the recent years, Sastry et al. [3-12] have offered several modifications to the Feistel cipher, and have studied various i i-1 [ Pjk ]= [ ejk Qjk ] mod 256, (2.1) aspects of this cipher, including different types of permutations and and substitutions. In all these investigations we have divided i i-1 i-1 the plaintext into a pair of matrices of equal size, and the key is [ Q ]= [e P ] mod 256 [Q ] , (2.2) taken in the form of a matrix. jk jk jk jk where j= 1 to m, k = 1 to m and i =1 to n, in which n is In the process of encryption, we take the key bunch as E, the number of rounds. and represent it in the form of a matrix given by E = [ejk]. The corresponding key bunch in the process of decryption is taken The corresponding equations of decryption are in the form, i-1 i as D = [djk]. Here for a given value of the key ejk, used in the [ Qjk ]= [ djk Pjk ] mod 256, (2.3) encryption, we determine the corresponding key djk, by using and the relation i-1 i i-1 [ Pjk ]=[djk( [Qjk ] [Qjk ] ) ] mod 256 (2.4) ( ejk x djk ) mod 256 =1, (1.5) where dkl is the multiplicative inverse of ekl, where j= 1 to m, k = 1 to m and i = n to 1, 92 | P a g e www.ijacsa.thesai.org (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 3, No. 12, 2012 i i th th here Pjk and Qjk are the j row k column elements of the left and right portions of the plaintext matrix, respectively, in Read Ciphertext C th the i round of the iteration process. and Key D On using the basic relations (2.1) - (2.4), governing the encryption and the decryption, the corresponding flowcharts for the encryption and the decryption can be written as shown Pn Qn below. Read Plaintext P and Key E for i = n to 1 for j =1 to m for k = 1 to m P0 Q0 i Pjk i for i = 1 to n Qjk i for j = 1 to m [djk Pjk ] mod 256 for k = 1 to m i-1 Pjk i-1 Q i-1 i-1 jk [e jk Pjk ] mod 256 [Qjk ] i-1 Q jk i i-1 [djk( [Qjk ] [Qjk ] ) ] mod 256 i-1 Pjk i-1 [ ejk Qjk ] mod 256 i i i P , Q Pjk i Q 0 0 jk P = P || Q Figure 2. The process of Decryption The algorithms for the encryption and the decryption are i i written as shown below. P , Q n n A. Algorithm for Encryption C = P || Q 1. Read P, E, and n 0 Figure 1. The Process of Encryption 2. P = Left half of P. Q0 = Right half of P. 3. for i = 1 to n 93 | P a g e www.ijacsa.thesai.org (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 3, No. 12, 2012 begin for j = 1 to m 066 114 111 116 begin 032 087 104 101 for k = 1 to m 0 begin P = (3.3) i i-1 032 119 101 114 [ Pjk ]= [ ejk Qjk ] mod 256, i i-1 i-1 [ Qjk ]= [ejk Pjk ] mod 256 [Qjk ] , 114 121 032 112 end end and end 6. C = Pn Qn /* represents concatenation */ 104 101 114 033 7. Write(C) 110 032 119 101 0 B. Algorithm for Decryption Q = (3.4) 1. Read C, D, and n. 101 032 118 101 n 2. P = Left half of C Qn = Right half of C 111 111 114 044 3. for i = n to 1 begin Let us take the encryption key bunch matrix E in the form for j = 1 to m 071 053 011 061 begin for k = 1 to m begin 117 069 057 051 i-1 i E = (3.5) [Qjk ] = [ djk Pjk ] mod 256, 121 139 101 043 i-1 i i-1 [Pjk ]=[djk ([Qjk ] [Qjk ]] mod 256 099 095 111 035 end and end end 6. P = P0 Q0 /* represents concatenation */ 119 029 163 021 7. Write (P) 221 141 009 251 In what follows we illustrate the cipher with a suitable example. D = (3.6) 201 035 109 131 III. ILLUSTRATION OF THE CIPHER Consider the plaintext given below. 075 159 143 139 Brother! When we were very poor, by looking at some On using the algorithm for encryption, given in section 2, corrupt politicians and employees who earned crores and we get the ciphertext C in the form crores, we use to think how to come up in life. Though you were a graduate having technical skills, you joined naxalites 088 166 064 218 222 060 064 088 thinking that only unethical rich are totally responsible for the ruination of our country. After the death of our father, I joined 140 078 014 104 028 204 176 036 as a police, our uncle started liquor business! He has earned C = (3.7) crores and crores. Though I have become a police inspector, I 088 094 002 182 244 188 202 108 am helpless. I am not able to control anything! I do not know when India will change! Write a letter. Do come back. (3.1) 240 120 038 118 208 224 146 196 Let us focus our attention on the first 32 characters of the plaintext (3.1). This is given by On using the keys in D, and applying the decryption algorithm on (3.6), we get back the original plaintext P given Brother! When we were very poor, (3.2) by (3.2) On using EBCIDIC code, we write (3.2) in the form of a Let us now study the avalanche effect. On changing the first pair of square matrices given by row , second column element of P0 from 114 to 115, we get a change of one binary bit in the plaintext. 94 | P a g e www.ijacsa.thesai.org (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 3, No. 12, 2012 On applying the encryption algorithm on this modified 2 (2.4m ) -7 plaintext, using the same key bunch matrix E, we get the 2 ciphertext C in the form 10 x 10 (2.4 m -15) ---------------------- years = 3.12 x 10 years 104 144 028 204 176 122 222 228 365 x 24 x 60 x 60 172 244 236 162 210 024 158 030 In this analysis, we have taken m=4.
Load more

Recommended publications
  • Block Ciphers and the Data Encryption Standard
    Lecture 3: Block Ciphers and the Data Encryption Standard Lecture Notes on “Computer and Network Security” by Avi Kak ([email protected]) January 26, 2021 3:43pm ©2021 Avinash Kak, Purdue University Goals: To introduce the notion of a block cipher in the modern context. To talk about the infeasibility of ideal block ciphers To introduce the notion of the Feistel Cipher Structure To go over DES, the Data Encryption Standard To illustrate important DES steps with Python and Perl code CONTENTS Section Title Page 3.1 Ideal Block Cipher 3 3.1.1 Size of the Encryption Key for the Ideal Block Cipher 6 3.2 The Feistel Structure for Block Ciphers 7 3.2.1 Mathematical Description of Each Round in the 10 Feistel Structure 3.2.2 Decryption in Ciphers Based on the Feistel Structure 12 3.3 DES: The Data Encryption Standard 16 3.3.1 One Round of Processing in DES 18 3.3.2 The S-Box for the Substitution Step in Each Round 22 3.3.3 The Substitution Tables 26 3.3.4 The P-Box Permutation in the Feistel Function 33 3.3.5 The DES Key Schedule: Generating the Round Keys 35 3.3.6 Initial Permutation of the Encryption Key 38 3.3.7 Contraction-Permutation that Generates the 48-Bit 42 Round Key from the 56-Bit Key 3.4 What Makes DES a Strong Cipher (to the 46 Extent It is a Strong Cipher) 3.5 Homework Problems 48 2 Computer and Network Security by Avi Kak Lecture 3 Back to TOC 3.1 IDEAL BLOCK CIPHER In a modern block cipher (but still using a classical encryption method), we replace a block of N bits from the plaintext with a block of N bits from the ciphertext.
    [Show full text]
  • 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.
    [Show full text]
  • Mirror Cipher Using Feistel Network
    Mirror Cipher using Feistel Network 1 2 3 Ihsan Muhammad Asnadi ​ Ranindya Paramitha ​ Tony ​ ​ ​ 123 ​ Informatics Department, Institut Teknologi Bandung, Bandung 40132, Indonesia 1 2 3 E-mail: 1​ [email protected] 1​ [email protected] 1​ [email protected] ​ ​ ​ ​ ​ Abstract. Mirror cipher is a cipher built by creativity which has a specific feature of mirrored round function. As ​ other ciphers, mirror cipher could be used to secure messages’ confidentiality and integrity. This cipher receives message and key inputs from its user. Then, it runs 9 rounds of feistel networks in ECB modes. Each round would run a round function which consists of 5 functions in mirrored order (9 function calls in total): s-box substitution, row substitution, column substitution, column cumulative xor, and round key addition. This cipher is implemented using Python and has been tested using several message and key combinations. Mirror cipher has applied Shanon’s diffusion and confusion property and proven to be secured from bruteforce and frequency analysis attack. 1. Introduction 1.1. Background In this modern world, data or messages are exchanged anytime and anywhere. To protect confidentiality and integrity of messages, people usually encrypt their messages before sending them, and then decrypt the received messages before reading them. These encryption and decryption practices and techniques are contained under the big concept of cryptography. There are many ciphers (encryption and decryption algorithms) that have been developed since the BC period. Ciphers are then divided into 2 kinds of ciphers, based on how it treats the message: stream cipher and block cipher.
    [Show full text]
  • 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
    [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]
  • Block Ciphers
    BLOCK CIPHERS MTH 440 Block ciphers • Plaintext is divided into blocks of a given length and turned into output ciphertext blocks of the same length • Suppose you had a block cipher, E(x,k) where the input plaintext blocks,x, were of size 5-bits and a 4-bit key, k. • PT = 10100010101100101 (17 bits), “Pad” the PT so that its length is a multiple of 5 (we will just pad with 0’s – it doesn’t really matter) • PT = 10100010101100101000 • Break the PT into blocks of 5-bits each (x=x1x2x3x4) where each xi is 5 bits) • x1=10100, x2= 01010, x3=11001, x4=01000 • Ciphertext: c1c2c3c4 where • c1=E(x1,k1), c2=E(x2,k2), c3=E(x3,k3), c4=E(x4,k4) • (when I write the blocks next to each other I just mean concatentate them (not multiply) – we’ll do this instead of using the || notation when it is not confusing) • Note the keys might all be the same or all different What do the E’s look like? • If y = E(x,k) then we’ll assume that we can decipher to a unique output so there is some function, we’ll call it D, so that x = D(y,k) • We might define our cipher to be repeated applications of some function E either with the same or different keys, we call each of these applications “round” • For example we might have a “3 round” cipher: y Fk x E((() E E x, k1 , k 2)), k 3 • We would then decipher via 1 x Fk (,, y) D((() D D y, k3 k 2) k 1) S-boxes (Substitution boxes) • Sometimes the “functions” used in the ciphers are just defined by a look up table that are often referred to “S- boxes” •x1 x 2 x 3 S(x 1 x 2 x 3 ) Define a 4-bit function with a 3-bit key 000
    [Show full text]
  • Meet-In-The-Middle Attacks on Reduced-Round XTEA*
    Meet-in-the-Middle Attacks on Reduced-Round XTEA⋆ Gautham Sekar⋆⋆, Nicky Mouha⋆ ⋆ ⋆, Vesselin Velichkov†, and Bart Preneel 1 Department of Electrical Engineering ESAT/SCD-COSIC, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001 Heverlee, Belgium. 2 Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium. {Gautham.Sekar,Nicky.Mouha,Vesselin.Velichkov, Bart.Preneel}@esat.kuleuven.be Abstract. The block cipher XTEA, designed by Needham and Wheeler, was published as a technical report in 1997. The cipher was a result of fixing some weaknesses in the cipher TEA (also designed by Wheeler and Needham), which was used in Microsoft’s Xbox gaming console. XTEA is a 64-round Feistel cipher with a block size of 64 bits and a key size of 128 bits. In this paper, we present meet-in-the-middle attacks on twelve vari- ants of the XTEA block cipher, where each variant consists of 23 rounds. Two of these require only 18 known plaintexts and a computational ef- fort equivalent to testing about 2117 keys, with a success probability of 1−2 −1025. Under the standard (single-key) setting, there is no attack re- ported on 23 or more rounds of XTEA, that requires less time and fewer data than the above. This paper also discusses a variant of the classical meet-in-the-middle approach. All attacks in this paper are applicable to XETA as well, a block cipher that has not undergone public analysis yet. TEA, XTEA and XETA are implemented in the Linux kernel. Keywords: Cryptanalysis, block cipher, meet-in-the-middle attack, Feis- tel network, XTEA, XETA.
    [Show full text]
  • Applications of Search Techniques to Cryptanalysis and the Construction of Cipher Components. James David Mclaughlin Submitted F
    Applications of search techniques to cryptanalysis and the construction of cipher components. James David McLaughlin Submitted for the degree of Doctor of Philosophy (PhD) University of York Department of Computer Science September 2012 2 Abstract In this dissertation, we investigate the ways in which search techniques, and in particular metaheuristic search techniques, can be used in cryptology. We address the design of simple cryptographic components (Boolean functions), before moving on to more complex entities (S-boxes). The emphasis then shifts from the construction of cryptographic arte- facts to the related area of cryptanalysis, in which we first derive non-linear approximations to S-boxes more powerful than the existing linear approximations, and then exploit these in cryptanalytic attacks against the ciphers DES and Serpent. Contents 1 Introduction. 11 1.1 The Structure of this Thesis . 12 2 A brief history of cryptography and cryptanalysis. 14 3 Literature review 20 3.1 Information on various types of block cipher, and a brief description of the Data Encryption Standard. 20 3.1.1 Feistel ciphers . 21 3.1.2 Other types of block cipher . 23 3.1.3 Confusion and diffusion . 24 3.2 Linear cryptanalysis. 26 3.2.1 The attack. 27 3.3 Differential cryptanalysis. 35 3.3.1 The attack. 39 3.3.2 Variants of the differential cryptanalytic attack . 44 3.4 Stream ciphers based on linear feedback shift registers . 48 3.5 A brief introduction to metaheuristics . 52 3.5.1 Hill-climbing . 55 3.5.2 Simulated annealing . 57 3.5.3 Memetic algorithms . 58 3.5.4 Ant algorithms .
    [Show full text]
  • Impossible Differential Cryptanalysis of the Lightweight Block Ciphers TEA, XTEA and HIGHT
    Impossible Differential Cryptanalysis of the Lightweight Block Ciphers TEA, XTEA and HIGHT Jiazhe Chen1;2;3?, Meiqin Wang1;2;3??, and Bart Preneel2;3 1 Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, School of Mathematics, Shandong University, Jinan 250100, China 2 Department of Electrical Engineering ESAT/SCD-COSIC, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001 Heverlee, Belgium 3 Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium [email protected] Abstract. TEA, XTEA and HIGHT are lightweight block ciphers with 64-bit block sizes and 128-bit keys. The round functions of the three ci- phers are based on the simple operations XOR, modular addition and shift/rotation. TEA and XTEA are Feistel ciphers with 64 rounds de- signed by Needham and Wheeler, where XTEA is a successor of TEA, which was proposed by the same authors as an enhanced version of TEA. HIGHT, which is designed by Hong et al., is a generalized Feistel cipher with 32 rounds. These block ciphers are simple and easy to implement but their diffusion is slow, which allows us to find some impossible prop- erties. This paper proposes a method to identify the impossible differentials for TEA and XTEA by using the weak diffusion, where the impossible differential comes from a bit contradiction. Our method finds a 14-round impossible differential of XTEA and a 13-round impossible differential of TEA, which result in impossible differential attacks on 23-round XTEA and 17-round TEA, respectively. These attacks significantly improve the previous impossible differential attacks on 14-round XTEA and 11-round TEA given by Moon et al.
    [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]
  • Design and Analysis of Lightweight Block Ciphers : a Focus on the Linear
    Design and Analysis of Lightweight Block Ciphers: A Focus on the Linear Layer Christof Beierle Doctoral Dissertation Faculty of Mathematics Ruhr-Universit¨atBochum December 2017 Design and Analysis of Lightweight Block Ciphers: A Focus on the Linear Layer vorgelegt von Christof Beierle Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften an der Fakult¨atf¨urMathematik der Ruhr-Universit¨atBochum Dezember 2017 First reviewer: Prof. Dr. Gregor Leander Second reviewer: Prof. Dr. Alexander May Date of oral examination: February 9, 2018 Abstract Lots of cryptographic schemes are based on block ciphers. Formally, a block cipher can be defined as a family of permutations on a finite binary vector space. A majority of modern constructions is based on the alternation of a nonlinear and a linear operation. The scope of this work is to study the linear operation with regard to optimized efficiency and necessary security requirements. Our main topics are • the problem of efficiently implementing multiplication with fixed elements in finite fields of characteristic two. • a method for finding optimal alternatives for the ShiftRows operation in AES-like ciphers. • the tweakable block ciphers Skinny and Mantis. • the effect of the choice of the linear operation and the round constants with regard to the resistance against invariant attacks. • the derivation of a security argument for the block cipher Simon that does not rely on computer-aided methods. Zusammenfassung Viele kryptographische Verfahren basieren auf Blockchiffren. Formal kann eine Blockchiffre als eine Familie von Permutationen auf einem endlichen bin¨arenVek- torraum definiert werden. Eine Vielzahl moderner Konstruktionen basiert auf der wechselseitigen Anwendung von nicht-linearen und linearen Abbildungen.
    [Show full text]
  • Block Ciphers And
    BlockBlock CiphersCiphers andand DESDES Plain Text Block 1 Block 2 Block 3 Raj Jain Washington University in Saint Louis Saint Louis, MO 63130 [email protected] Audio/Video recordings of this lecture are available at: http://www.cse.wustl.edu/~jain/cse571-14/ Washington University in St. Louis CSE571S ©2014 Raj Jain 3-1 OverviewOverview 1. Block Cipher Principles 2. Data Encryption Standard (DES) 3. Differential and Linear Cryptanalysis 4. Block Cipher Design Principles These slides are based partly on Lawrie Brown’s slides supplied with William Stalling’s book “Cryptography and Network Security: Principles and Practice,” 6th Ed, 2013. Washington University in St. Louis CSE571S ©2014 Raj Jain 3-2 BlockBlock vs.vs. StreamStream CiphersCiphers Stream: Bits and bytes are processed as they arrive Example: RC4 Block: Messages are broken into blocks of 64-bit, 512-bit, … Example: DES, AES Washington University in St. Louis CSE571S ©2014 Raj Jain 3-3 ShannonShannon’’ss SS--PP NetworksNetworks Claude Shannon introduced idea of substitution- permutation (S-P) networks in his 1949 paper Two primitive cryptographic operations: Substitution (S-box) = Replace n-bits by another Plaintext n-bits Diffusion: Dissipate statistical structure of plaintext over bulk of ciphertext. One bit change in plaintext changes many bits in ciphertext. Ciphertext Can not do frequency analysis. Permutation (P-box) = Bits are rearranged. No bits are added/removed. Confusion: Make relationship between ciphertext and key as complex as possible Combination S-P = Product cipher Washington University in St. Louis CSE571S ©2014 Raj Jain 3-4 FeistelFeistel CipherCipher StructureStructure A practical implementation of Shanon’s S-P Networks Partitions input block in 2 halves Perform a substitution on left data half based on a function of right half & subkey (Round Function or Mangler function) Then permutation by swapping halves Repeat this “round” of S-P many times Invertible Washington University in St.
    [Show full text]