1. Cryptography II Jagdish S. Gangolly School of Business
State University of New York at Albany
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

2. Cryptography II: Topics
Substitutions
Complexity of substitution encryption/decryption
One-time pad (Vignere tableau)
Vernam and book ciphers
Transpositions (or Permutations)
Digrams, Trigrams, n-grams
Shannon’s characteristics of “Good” ciphers
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

3. Cryptography II: Topics (Continued)
Data Encryption Standard) DES, Double DES and Triple DES
Advanced Encryption Standard (AES)
Certificates: Trust & Certificates
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

4. Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly
Substitutions
Complexity: Since it takes constant time to substitute a character, the complexity of the algorithms is n; i.e., a message twice as long takes twice the time to encrypt.
Cryptanalysis: Substitution ciphers can be attacked by guessing, using short words, repeated characters, statistical analysis of character frequencies, using dictionaries, n-gram analysis.
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

5. Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly
One-Time Pads
A synchronized sequence of non-repeating keys, similar to those in Vignere cipher.
Key management (generation, synchronization, distribution, storage) is a problem.
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

6. Vernam and Book Ciphers
Characters in plain text combined with arbitrarily long non-repeating sequence of numbers.
Vernam ciphers immune to most cryptanalytic attacks.
In book ciphers, a book commonly agreed upon is used as a source of “random numbers (e.g., telephone book or any other book)
If the book so used is known, it is easier to cryptanalyze the ciphertext.
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

7. Digrams, Trigrams, n-grams
Statistical analysis of frequency of characteristic patterns of letter sequences.
Study of conditional probabilities.
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

8. Transpositions (Permutations)
Rearrangement of the letters (or bits) of the plaintext. The aim is to confuse the cryptanalyst.
Requires large storage (since the entire plaintext message must be stored for columnar permutation).
Involves delay in decrypting since the entire ciphertext needs to be entered in storage before it can be deciphered.
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

9. Shannon’s characteristics of “Good” ciphers
The amount of secrecy needed should determine the amount of labour appropriate for the encryption and decryption
The set of keys and the enciphering algorithm should be free from complexity
The implementation of the system should be as simple as possible
The errors in ciphering should not propagate and cause corruption of further information in the message
The size of the enciphered text should be no larger than the text of the original message
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

10. Data Encryption Standard) DES, Double DES and Triple DES
DES (Developed by IBM based on the Lucifer algorithm, original name is Data Encryption Algorithm or DEA):
Uses 16 iterations of substitution (confusion) and permutation (diffusion)
Block cipher, block size being 64 bits
Uses key 64 bits long (can be any 56 bit number, the remaining 8 bits often used as check digits
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

11. Data Encryption Standard) DES, Double DES and Triple DES (Continued)
message m, two keys k1 and k2, ciphertext c
c = E(k2, E(k1,m))
Double DES Cryptanalysis:
Suppose you have two plaintext messages P1 and P2, and their corresponding ciphertext messages C1 and C2
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

12. Double DES Cryptanalysis (Continued)
Step 1: For each of the 256 possible keys k, compute
P1´= E(k,P1)
Step 2: For each of the 256 possible keys k, compute
P1´´= D(k,C1)
Step 3: Find the key pair k´ and k´´ for which
P1´= P1´´
Step 4: Check the match using P2 and C2.
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

13. Double DES Cryptanalysis (Continued)
Merkle-Hellman result: Computing P1´ requires 256 steps. Computing backward from C1 to obtain P1´´ requires 256 steps. Therefore the total number of steps required to identify the key pair k1 and k2 is 2* 256 steps, which is equivalent to using a 57 bit key. Hence doubling the encryption only doubles the effort required of an cryptanalyst.
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

14. Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly
Triple DES
Consider a message m, two keys k1 and k2, ciphertext C, and the encryption scheme
C = E(k1,D(k2,E(k1,m)))
Even though triple DES only doubles the key length from 56 to 112 bits (and is the same as double DES), it is effective against all feasible known attacks.
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

15. Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly
Advanced DES
Based on the Rijndael-Daemen algorithm. Each round (cycle) consists of
byte substitution (confusion step): substitution of each byte of a 128-bit block using a table,
shift row (transposition, also confusion step),
mix column (confusion and diffusion step), and
add sub key (confusion step).
Selected by as a Federal Information Processing standard in 2001.
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

16. DES Comparison (Source: Pfleeger & Pfleeger)
AES
Date
1976
1999
Block size
64 bits
128 bits
Key length
56 bits (effective)
128, 192, 256,…
Encryption primitives
Substitution, Permutation
Substitution, Row shifts, bit mixing
Cryptographic primitives
Confusion, Diffusion
Design
Open
Design Rationale
Closed
Selection Process
Secret
Secret, but accepted open public comment
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

17. Certificates: Trust & Certificates
Need for establishment of trust when the two parties to a transaction do not know each other
Hierarchical relationships as a basis for trust
The function of digital certificates in the establishment of trust, and in the maintenance of the integrity of public keys
Need for trust at the top level in the hierarchy
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly

18. Trust & Certificates (Continued)
Trust infrastructure in the internet
Root certification authorities
C&W, HKT, SecureNet, Verisign, Baltimore Technologies, Deutsche Telecom, Societa Interbancaria per l’Automatzione di Milano, Entrust, Certiposte,…
Certificate path and its role in the establishment of trust in e-commerce carried through the web
11/24/2018
Acc 661 Auditing of Adv Acctg Sys (Spring 2003) Gangolly