Discrete Mathematics with Applications MATH236 Dr. Hung P. - PowerPoint PPT Presentation

Discrete Mathematics with Applications MATH236 Dr. Hung P. Tong-Viet School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal Pietermaritzburg Campus Semester 1, 2013 Tong-Viet (UKZN) MATH236 Semester 1, 2013 1 / 15

Table of contents Product Cryptosystems. DES and AES 1 ASCII 2 Feistel ciphers 3 Tong-Viet (UKZN) MATH236 Semester 1, 2013 2 / 15

Product Cryptosystems. DES and AES Product cryptosystems The first kinds of cryptosystems that we considered were simple substitution ciphers and permutation ciphers They are easily be attacked Tong-Viet (UKZN) MATH236 Semester 1, 2013 3 / 15

Product Cryptosystems. DES and AES Product cryptosystems The first kinds of cryptosystems that we considered were simple substitution ciphers and permutation ciphers They are easily be attacked We now consider a new kind of cryptosystem that is based on them but it is considerably more difficult to attack; Tong-Viet (UKZN) MATH236 Semester 1, 2013 3 / 15

Product Cryptosystems. DES and AES Product cryptosystems The first kinds of cryptosystems that we considered were simple substitution ciphers and permutation ciphers They are easily be attacked We now consider a new kind of cryptosystem that is based on them but it is considerably more difficult to attack; Most modern cryptosystems are of the type we now consider Tong-Viet (UKZN) MATH236 Semester 1, 2013 3 / 15

Product Cryptosystems. DES and AES Product cryptosystems The first kinds of cryptosystems that we considered were simple substitution ciphers and permutation ciphers They are easily be attacked We now consider a new kind of cryptosystem that is based on them but it is considerably more difficult to attack; Most modern cryptosystems are of the type we now consider A product cryptosystem is a block cipher that repeatedly perfoms substitutions and permutations, one after the other, to produce ciphertext Tong-Viet (UKZN) MATH236 Semester 1, 2013 3 / 15

Product Cryptosystems. DES and AES Product cryptosystems The first kinds of cryptosystems that we considered were simple substitution ciphers and permutation ciphers They are easily be attacked We now consider a new kind of cryptosystem that is based on them but it is considerably more difficult to attack; Most modern cryptosystems are of the type we now consider A product cryptosystem is a block cipher that repeatedly perfoms substitutions and permutations, one after the other, to produce ciphertext Tong-Viet (UKZN) MATH236 Semester 1, 2013 3 / 15

Product Cryptosystems. DES and AES Background In 1973, the US’s National Bureau of Standards (now NIST) called for the development of an ‘algorithm to be implemented in electronic hardware devices, to be used for cryptographic protection of computer data’ The proposal submitted by IBM was adopted in 1977 as the Data Encryption Standard or DES Tong-Viet (UKZN) MATH236 Semester 1, 2013 4 / 15

Product Cryptosystems. DES and AES Background In 1973, the US’s National Bureau of Standards (now NIST) called for the development of an ‘algorithm to be implemented in electronic hardware devices, to be used for cryptographic protection of computer data’ The proposal submitted by IBM was adopted in 1977 as the Data Encryption Standard or DES DES is based on an earlier cryptosystem called Lucifer, developed at IBM by Horst Feistel Tong-Viet (UKZN) MATH236 Semester 1, 2013 4 / 15

Product Cryptosystems. DES and AES Background In 1973, the US’s National Bureau of Standards (now NIST) called for the development of an ‘algorithm to be implemented in electronic hardware devices, to be used for cryptographic protection of computer data’ The proposal submitted by IBM was adopted in 1977 as the Data Encryption Standard or DES DES is based on an earlier cryptosystem called Lucifer, developed at IBM by Horst Feistel DES became the most widely used cryptosystem in the world Tong-Viet (UKZN) MATH236 Semester 1, 2013 4 / 15

Product Cryptosystems. DES and AES Background In 1973, the US’s National Bureau of Standards (now NIST) called for the development of an ‘algorithm to be implemented in electronic hardware devices, to be used for cryptographic protection of computer data’ The proposal submitted by IBM was adopted in 1977 as the Data Encryption Standard or DES DES is based on an earlier cryptosystem called Lucifer, developed at IBM by Horst Feistel DES became the most widely used cryptosystem in the world It is used to protect PIN’s (Personal Identification Numbers) of banking clients, telephonic transfers of money and communication over internet Tong-Viet (UKZN) MATH236 Semester 1, 2013 4 / 15

Product Cryptosystems. DES and AES Background In 1973, the US’s National Bureau of Standards (now NIST) called for the development of an ‘algorithm to be implemented in electronic hardware devices, to be used for cryptographic protection of computer data’ The proposal submitted by IBM was adopted in 1977 as the Data Encryption Standard or DES DES is based on an earlier cryptosystem called Lucifer, developed at IBM by Horst Feistel DES became the most widely used cryptosystem in the world It is used to protect PIN’s (Personal Identification Numbers) of banking clients, telephonic transfers of money and communication over internet Tong-Viet (UKZN) MATH236 Semester 1, 2013 4 / 15

Product Cryptosystems. DES and AES Background Every five years, the NIST reviewed DES to decide whether or not it was still considered to be safe against attack In October, 2000, a block cipher system called Rijndael was chosen as the Advanced Encryption Standard or AES Tong-Viet (UKZN) MATH236 Semester 1, 2013 5 / 15

Product Cryptosystems. DES and AES Background Every five years, the NIST reviewed DES to decide whether or not it was still considered to be safe against attack In October, 2000, a block cipher system called Rijndael was chosen as the Advanced Encryption Standard or AES After some minor modifications, it was adopted as a standard in November 2001 Tong-Viet (UKZN) MATH236 Semester 1, 2013 5 / 15

Product Cryptosystems. DES and AES Background Every five years, the NIST reviewed DES to decide whether or not it was still considered to be safe against attack In October, 2000, a block cipher system called Rijndael was chosen as the Advanced Encryption Standard or AES After some minor modifications, it was adopted as a standard in November 2001 DES is still in use, especially the variant of DES called triple-DES. Tong-Viet (UKZN) MATH236 Semester 1, 2013 5 / 15

Product Cryptosystems. DES and AES Background Every five years, the NIST reviewed DES to decide whether or not it was still considered to be safe against attack In October, 2000, a block cipher system called Rijndael was chosen as the Advanced Encryption Standard or AES After some minor modifications, it was adopted as a standard in November 2001 DES is still in use, especially the variant of DES called triple-DES. Tong-Viet (UKZN) MATH236 Semester 1, 2013 5 / 15

ASCII ASCII Both DES and AES are designed to operate on the binary alphabet Z 2 = { 0 , 1 } so any message we wish to encrypt with them must be first encoded as binary Tong-Viet (UKZN) MATH236 Semester 1, 2013 6 / 15

ASCII ASCII Both DES and AES are designed to operate on the binary alphabet Z 2 = { 0 , 1 } so any message we wish to encrypt with them must be first encoded as binary The most widely used convention is ASCII, the American Standard Code for Information interchange, which assigns an 8-digit binary number (a byte) to each symbol we wish to encrypt (see Table 6 . 2 page 123) Tong-Viet (UKZN) MATH236 Semester 1, 2013 6 / 15

ASCII ASCII Both DES and AES are designed to operate on the binary alphabet Z 2 = { 0 , 1 } so any message we wish to encrypt with them must be first encoded as binary The most widely used convention is ASCII, the American Standard Code for Information interchange, which assigns an 8-digit binary number (a byte) to each symbol we wish to encrypt (see Table 6 . 2 page 123) For example, the space, ‘a’ and ‘A’ are encoded by 00100000 , 0100001 and 01100001 , respectively Tong-Viet (UKZN) MATH236 Semester 1, 2013 6 / 15

ASCII ASCII Both DES and AES are designed to operate on the binary alphabet Z 2 = { 0 , 1 } so any message we wish to encrypt with them must be first encoded as binary The most widely used convention is ASCII, the American Standard Code for Information interchange, which assigns an 8-digit binary number (a byte) to each symbol we wish to encrypt (see Table 6 . 2 page 123) For example, the space, ‘a’ and ‘A’ are encoded by 00100000 , 0100001 and 01100001 , respectively We assume from now on that all the cryptosystems we consider operate on the binary alphabet Z 2 = { 0 , 1 } Tong-Viet (UKZN) MATH236 Semester 1, 2013 6 / 15

ASCII ASCII Both DES and AES are designed to operate on the binary alphabet Z 2 = { 0 , 1 } so any message we wish to encrypt with them must be first encoded as binary The most widely used convention is ASCII, the American Standard Code for Information interchange, which assigns an 8-digit binary number (a byte) to each symbol we wish to encrypt (see Table 6 . 2 page 123) For example, the space, ‘a’ and ‘A’ are encoded by 00100000 , 0100001 and 01100001 , respectively We assume from now on that all the cryptosystems we consider operate on the binary alphabet Z 2 = { 0 , 1 } Tong-Viet (UKZN) MATH236 Semester 1, 2013 6 / 15