1. Lecture 3 Feistel based algorithms

2. Today 1.Block ciphers - basis 2.Feistel cipher 3.DES 4.DES variations 5.IDEA 5.NEWDES

3. Ideal Block Cipher

4. Source text Ciphered text SP - network

5. Feistel cipher structure

6. DES In 1972, the National Institute of Standards and Technology (called the National Bureau of Standards at the time) decided that a strong cryptographic algorithm was needed to protect non-classified information. In 1974 IBM submitted the Lucifer algorithm, which appeared to meet most of NIST's design requirements. NIST enlisted the help of the National Security Agency to evaluate the security of Lucifer. DES is classic Feistel cipher with the n=64 bits. Unfortunately even that n is not real. In fact the algorithm use only 56 bits as key. The official explanation was that the 8-th bit from each byte is needed for parity check. One of the greatest worries was that the key length, originally 128 bits, was reduced to just 56 bits by NSA request, weakening it significantly. The modified Lucifer algorithm was adopted by NIST as a federal standard (see FIPS 46–2) on November 23, 1976. Its name was changed to the Data Encryption Standard (DES).

7. (a) twisted ladder (b) untwisted ladder Li = R i-1 Ri = L i-1  f (R i-1, K i )

9. Using DES CBC In CBC mode (Cypher Block Chaining Mode), each ciphertext block β i is combined using a XOR with the next input block α i+1. The following scheme is used: We define a block with initial value V I = β 0, and then the blocks are ciphered using the following equation β i = e K (β i−1 ⊕ α i ),(i ≥ 1)

10. using DES Usually OFB and CFB is used for 64 bits blocks but there is no problem in applying on the variable length k bits blocks where (1 ≤ k ≤ 64). All four modes have both advantages and disadvantages. A ECB and OFB changing a block from unencrypted input text α i will drive to modifications only to one encrypted output block β i. As we expected this may be a weakness from cryptanalytic point of view especially because the OFB modes is often used in securing satellite communication channels.

11. Using DES to MAC Designing a MAC using CBC. We begin with an initial block filled with zeroes Then the encrypted text β 1, β 2,..., β n is constructed using key K, ın CBC mode, The MAC is represented by β n block as is presented in the figure. After that Alice will sent the message α 1, α 2,..., α n, associated with the β n MAC. When Bob receive the message α 1, α 2,..., α n, and also generate a β 1,..., β n using secret key K and checks if the resulted β n is identical with the message MAC. It is clear that without having the secret key it is almost impossible to generate the correct MAC The following figure sketches the computation of the CBC-MAC of a message comprising blocks using a secret key k and a block cipher E:

12. Triple DES (3DES) Triple DES also known as 3DES or sometimes as DES − ede, is an system based by DES. It was proposed by Walter Tuchman (the former chief of the Intel team that develop the DES) Was published in FIPS Pub 46−3. The idea is simple and use the following formula where: m unencrypted pain text (64 bits), c is the encrypted result, k 1, k 2, k 3 are DES keys (de 56 bits), DES k : DES encrypt using key k, DES k −1 : DES decript using key k.

14. schema

16. References http://crypto.stackexchange.com/questions/245/does-unbalancing-a-feistel-cipher- always-improve-security-does-it-improve-securihttp://crypto.stackexchange.com/questions/245/does-unbalancing-a-feistel-cipher- always-improve-security-does-it-improve-securi http://www.itl.nist.gov/fipspubs/fip81.htm http://www.cacr.math.uwaterloo.ca/hac/http://www.cacr.math.uwaterloo.ca/hac/http://www.cacr.math.uwaterloo.ca/hac/ http://williamstallings.com/OS4e.htmlhttp://williamstallings.com/OS4e.htmlhttp://williamstallings.com/OS4e.html William Stallings, Cryptography and Network Security, Fourth Edition, 2005, Prentice Hall http://www.computersciencestudent.com/ http://williamstallings.com/Crypto/Crypto4e-inst.html http://www.tropsoft.com/strongenc/des.htm http://cryptodox.com/NewDES http://en.wikipedia.org/wiki/Meet-in-the-middle_attack Xuejia Lai and James L. Massey, A Proposal for a New Block Encryption Standard, EUROCRYPT 1990, pp389–404A Proposal for a New Block Encryption Standard EUROCRYPT Bruce Schneier, Applied Cryptography Second Edition John, Cryptography, Second Edition - John Wiley & Sons http://top- topics.thefullwiki.org/Broken_block_ciphers

17. Who knows? … about the real security of an algorithm!