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## Class Assignment

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**Double Transposition Encryption**Encrypt and decrypt the message we are all together using a double transposition cipher with the following key: matrix 4×4, row permutation (1,2,3,4) → (2,4,1,3) and Column permutation (1,2,3,4) → (3,1,2,4). Class Assignment Home Assignment**http://usmantariq.org/support/**Student Help Desk**INTRODUCTION**The Data Encryption Standard (DES) is a symmetric-key block cipher published by the National Institute of Standards and Technology (NIST). Symmetric-key encryption are secret-key, single-key, shared-key, one-key, and private-key encryption.**History**In 1973, NIST published a request for proposals for a national symmetric-key cryptosystem. A proposal from IBM, a modification 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).**Overview**DES is a block cipher, as shown in Figure. Encryption and decryption with DES**It is a symmetric key cipher operating on fixed-length**groups of bits, called blocks, with an unvarying transformation. Encryption A block cipher encryption algorithm might take (for example) a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext. The exact transformation is controlled using a second input — the secret key. Decryption Decryption is similar: the decryption algorithm takes, in this example, a 128-bit block of ciphertext together with the secret key, and yields the original 128-bit block of plaintext. Block ciphers Rr ÅF(kr,Lr) =Rr ÅF(kr,Rr-1) =Rr Å(Rr ÅLr-1) =Lr-1.**As there are over 70,000,000,000,000,000 (seventy**quadrillion) possible keys of 56 bits, the feasibility of deriving a particular key in this way is extremely unlikely in typical threat environments Why 56 bit key?**DES Structure**• The encryption process is made of two permutations (P-boxes), which we call • initial and final permutations, • and sixteen Feistel rounds. Permutation: A particular order in which things are arranged.**Permutationisan operation performed by a function,**which moves an element at place j to the place k. The key-dependentcomputation can be simply defined in terms of a function f, called the cipher function, and a function KS, called the key schedule. Permutation ?**Continue**General structure of DES Eight bits are used solely for checking parity, and are thereafter discarded. Every 8th bit of the selected key is discarded, i.e. positions 8, 16, 24, 32, 40, 48, 56, 64 are removed from the 64 bit key leaving behind only the 56 bit key. In mathematics, parity refers to the evenness or oddness of an integer, which for a binary number is determined only by the least significant bit.**Example:**Transmission sent using even parity**Initial and Final Permutations**Figure Initial and finalpermutation steps in DES**Continue**Table Initial and final permutation tables**Rounds**DES uses 16 rounds. Each round of DES is a Feistel cipher. Figure A round in DES (encryption site)**block size**increasing size improves security, but slows cipher key size increasing size improves security, makes exhaustive key searching harder, but may slow cipher number of rounds increasing number improves security, but slows cipher subkey generation greater complexity can make analysis harder, but slows cipher round function greater complexity can make analysis harder, but slows cipher fast software en/decryption & ease of analysis are more recent concerns for practical use and testing Feistel Cipher Design Principles**Continued**DES Function The heart of DES is the DES function. The DES function applies a 48-bit key to the rightmost 32 bits to produce a 32-bit output. Figure DES function**8 S-boxes**Each S-Box mapps 6 to 4 bits outer bits 1 & 6 (row bits) select the row inner bits 2-5 (col bits) select the column For example, in S1, for input 011001, the row is 01 (row 1) the column is 1100 (column 12). The value in row 1, column 12 is 9 The output is 1001. result is 8 X 4 bits, or 32 bits Substitution Boxes**Continue**Expansion P-box Since RI−1 is a 32-bit input and KI is a 48-bit key, we first need to expand RI−1 to 48 bits. Figure Expansion permutation**Continue**• Whitener (XOR) • After the expansion permutation, DES uses the XOR operation on the expanded right section and the round key. • Note that both the right section and the key are 48-bits in length. • Also note that the round key is used only in this operation.**Continue**S-Boxes The S-boxes do the real mixing (confusion). DES uses 8 S-boxes, each with a 6-bit input and a 4-bit output. See Figure Figure S-boxes**Continue**Figure 6.8 S-box rule**Continue**Table 6.3 shows the permutation for S-box 1 Table 6.3 S-box 1**Continued**Example 6.3 The input to S-box 1 is 100011. What is the output? Solution If we write the first and the sixth bits together, we get 11 in binary, which is 3 in decimal. The remaining bits are 0001 in binary, which is 1 in decimal. We look for the value in row 3, column 1, in Table. The result is 12 in decimal, which in binary is 1100. So the input 100011 yields the output 1100.**Continued**Example 6.4 The input to S-box 8 is 000000. What is the output? Solution If we write the first and the sixth bits together, we get 00 in binary, which is 0 in decimal. The remaining bits are 0000 in binary, which is 0 in decimal. We look for the value in row 0, column 0, in Table . The result is 14 in decimal, which is 1110 in binary. So the input 000000 yields the output 1110.**56-bit keys have 256 = 7.2 x 1016 values**brute force search looks hard recent advances have shown is possible in 1997 on Internet in a few months in 1998 on dedicated hardware (EFF) in a few days in 1999 above combined in 22hrs! still must be able to recognize plaintext now considering alternatives to DES Strength of DES – Key Size**6.2.3 Cipher and Reverse Cipher**Note Using mixers and swappers, we can create the cipher and reverse cipher, each having 16 rounds. First Approach To achieve this goal, one approach is to make the last round (round 16) different from the others; it has only a mixer and no swapper. In the first approach, there is no swapper in the last round.**6.2.3Continued**Figure 6.9 DES cipher and reverse cipher for the first approach**6.2.3Continued**Algorithm 6.1 Pseudocode for DES cipher**6.2.3Continued**Algorithm 6.1 Pseudocode for DES cipher (Continued)**6.2.3Continued**Algorithm 6.1 Pseudocode for DES cipher (Continued)**6.2.3Continued**Algorithm 6.1 Pseudocode for DES cipher (Continued)**6.2.3Continued**Alternative Approach We can make all 16 rounds the same by including one swapper to the 16th round and add an extra swapper after that (two swappers cancel the effect of each other). Key Generation The round-key generator creates sixteen 48-bit keys out of a 56-bit cipher key.**6.2.3Continued**Figure 6.10Key generation**6-3 DES ANALYSIS**Critics have used a strong magnifier to analyze DES. Tests have been done to measure the strength of some desired properties in a block cipher. Topics discussed in this section: 6.3.1 Properties6.3.2 Design Criteria 6.3.3 DES Weaknesses**6.3.1 Properties**Two desired properties of a block cipher are the avalanche effect and the completeness. The avalanche effect is evident if, when an input is changed slightly (for example, flipping a single bit) the output changes significantly Example To check the avalanche effect in DES, let us encrypt two plaintext blocks (with the same key) that differ only in one bit and observe the differences in the number of bits in each round.**6.3.1Continued**Example 6.7 Continued Although the two plaintext blocks differ only in the rightmost bit, the ciphertext blocks differ in 29 bits. This means that changing approximately 1.5 percent of the plaintext creates a hange of approximately 45 percent in the ciphertext. Table 6.17 Number of bit differences for Example 6.7**6.3.1Continued**Completeness effect Completeness effect means that each bit of the ciphertext needs to depend on many bits on the plaintext.**6.3.2 Design Criteria**S-Boxe The design provides confusion and diffusion of bits from each round to the next. P-Boxes They provide diffusion of bits. Number of Rounds DES uses sixteen rounds of Feistel ciphers. the ciphertext is thoroughly a random function of plaintext and ciphertext.**6.3.3 DES Weaknesses**During the last few years critics have found some weaknesses in DES. Weaknesses in Cipher Design 1. Weaknesses in S-boxes 2. Weaknesses in P-boxes 3. Weaknesses in Key**6.3.3Continued**Example 6.8 Let us try the first weak key in Table 6.18 to encrypt a block two times. After two encryptions with the same key the original plaintext block is created. Note that we have used the encryption algorithm two times, not one encryption followed by another decryption.**6.3.3Continued**Figure 6.11 Double encryption and decryption with a weak key**6.3.3Continued**Figure 6.12 A pair of semi-weak keys in encryption and decryption