Error Propagation Effect of AES and Techniques to ward off the problem

INVESTIGATION OF ERROR
PROPAGATION EFFECT OF AES AND TO
FIND TECHNIQUES AND SOLUTION OF
THE PROBLEM
Dr. Bikramjit sarkar
Associate Professor
Dept. of Computer Science and Engineering
Techno India – Salt Lake
Kolkata, India
Email: sarkar.Bikramjit@gmail.com

Abstract
The Rijndael algorithm (Advanced Encryption Standard)
suffers from a major limitation owing to error
propagation in the encryption process. The salient
objective of our research is
To study different schemes for modified redundancy
based AES scheme,
To analyze the proposed schemes in terms of speed of
encryption /decryption and the level of security offered,
To finally design an error-free AES.

Advance Encryption Standard
Due to the several reports of failure of security or key
of DES (Data Encryption Standard), The NIST decided
to launch in 1997 a new standardization process, known
as Advanced Encryption Standard (AES).
The algorithm “Rijndael” was finally selected to
become the AES through an open contest where anyone
including even non-American citizen and companies
was invited to submit a candidate algorithm and to send
public comments on the other proposals.
The algorithm was named after its designers Daemen
and Rijmen.

Advance Encryption Standard contd..
The replacement has aimed to augment the level of
security mainly with higher key size. Besides the higher
level of security, AES has aimed to provide higher
efficiency and better flexibility by means of encryption
at different levels and with different block sizes.
The AES encryption is done at several rounds of
iteration. Each round of iteration has different input
data and different keys. The input data and the keys of
different rounds are all generated from the original
source data and the source key respectively. On the
basis of this theory the input data and the keys at
rounds follow a data path and key path respectively.

Advance Encryption Standard contd..

Error Propagation Effect of AES
AES is designed for flexibility and for implementing in
both Hardware and software. Due to its low memory
requirement, AES suitable for implementation in
devices like smart card etc. But the AES algorithm
suffers from a major limitation Error Propagation
Effect.
An error, if inflicted in any round, propagates through
the rest of the rounds and finally results in a large
number of errors in the cipher.

Error Propagation Effect of AES contd..
The effect of the Error Propagation has been observed
through an experiment carried out with the following
plain text (128 bits) and the cipher key (128 bits):
Plain text Cipher key

Now a one-bit error is forcibly injected in 8th bit
position of the intermediate cipher generated after 1st
round and then encrypt it through 9 more rounds of
AES encryption. As a consequence, an erroneous
cipher is generated at the output as follows:
Erroneous Cipher text Error free Cipher text

In this way, the experiment has been conducted on
deliberately injecting one-bit errors after different
rounds and consequently a number of erroneous ciphers
were generated. Upon decryption of these erroneous
ciphers, corresponding plaintexts have been received,
which, to a great extent, differ from the actual plain
text.
The result found in the above experiment is shown in
Table 1.

One-bit Errors injected in
8th bit positions of the
intermediate states
Number of errors in the cipher text
after injection of one bit error at
intermediate states
Number of corresponding errors in
the plain text after decrypting the
erroneous cipher
After 1st round 71 67
After 2nd round 67 55
After 3rd round 56 69
After 4th round 51 61
Table 1

Available Techniques to fight the Error
Propagation Effect of AES
the limitation of error propagation in AES leads to low
speed of encryption, more processing overhead and
higher complexity, because until and unless error free
encryption be achieved the transmission of the cipher
will be meaningless.
In order to tackle the error propagation of AES, two
techniques have been studied in literatures:
Redundancy Based Technique
Byte Based Parity Technique

Redundancy Based Technique
The Redundancy Based Technique needs both the
encryption module and decryption module for
producing error-free cipher at the transmitter. The
output cipher of the encryption module is decrypted by
the decryption module. The decrypted output is
compared with the plain text to check whether there is
any error at all. If they match, the cipher is considered
to be error-free. The dual process of encryption and
decryption by the technique make the encryption
process slow and costly as well. Although this
technique is suitable for both software and hardware
implementation.

Byte Based Parity Technique
The byte based parity technique makes use of parity
checking at each byte of plain text to combat error. Yet
it has the limitation of not being able to correct all type
of error vectors. Also the byte based parity technique is
not suitable for software implementation.

Selective AES
The performance of any cryptosystem is measured by
two parameters: level of security it provides and speed
of encryption and decryption. Selective AES is the
process of AES encryption of a fraction of message
keeping the remaining portions unencrypted, which
increases in the speed of encryption / decryption.

Error Propagation in Selective AES
The Error Propagation Effect has been observed in
Selective AES through an experiment conducted with
the following 640-bit message and 128-bit key:
Message = “ERROR PROPAGATION EFFECT OF
AES HAS THROWN A GREAT RESEARCH
CHALLENGE BEFORE US.”
Key = “BIKRAMJIT SARKAR”

Error Propagation in Selective AES contd..
First the entire message is divided into 5 blocks B1, B2,
B3, B4 and B5, each of which is of 128 bits, where,
B1 = “ERROR PROPAGATIO”,
B2 = “N EFFECT OF AES ”,
B3 = “HAS THROWN A GRE”,
B4 = “AT RESEARCH CHAL” and
B5 = “LENGE BEFORE US.”

The AES Encryption process has 10 rounds. And after
each round (1st to 9th) one intermediate state is found
and after the 10 rounds the final cipher text is
generated. So, each block, while being encrypted to
generate the final cipher, generates 9 intermediate
states.
Now after first round, the eighth bit of each
intermediate state generated from each block get
forcibly infected. The same thing is repeated for each of
the blocks after fifth and ninth rounds.

Now the erroneous ciphers are compared with the error
free cipher and accordingly the total number of errors at
the output ciphers for each of the cases is found. The
average number of errors occurred in the output cipher
when a single bit error has occurred in any of the
intermediate states generated during the encryption
process is also obtained and Table 2 is formed:
Block(s) Encrypted Percentage of Selection
Average number of errors occurred at the output after the
execution of the Encryption Module
B1 20 45.67
B1 & B2 40 88.67
B1, B2 & B3 60 133.67
B1, B2, B3 & B4 80 176.0
B1, B2, B3, B4 & B5 100 221.33
Table 2

From Table 2 it is clear that lesser is the percentage of
selection, lesser is the number of errors occurred at the
output. But the processing speed is inversely
proportional to the percentage of selection. So there
must be a tread off between the security level and the
processing speed since, the level of security is
proportional to the percentage of selection.

Redundancy Based Technique redefined
It is clear that the Redundancy Based Technique
requires the comparison of 128 bits since the plain text
taken is of 128 bits. Here the proposed algorithm SBM
1.1 proposes to modify the Redundancy Based
Technique that will reduce the overhead of comparison
to only 8 bits. The algorithm makes use of the
Longitudinal Redundancy Check (LRC) code.

Redundancy Based Technique redefined contd..
Proposed Algorithm: SBM 1.1
1. Input the plain text P of 128 bits
2. Generate an LRC code (8 bits), say L, out of P
3. Encrypt P with AES Encryptor to find the cipher
text, say C
4. Decrypt C with AES Decryptor to find P’
5. Generate an LRC code (8 bits), say L’, out of P’
6. L and L’ are now compared. If L and L’ are found to
be same, C is considered to be error-free and is
transmitted through the channel.

Block Diagram: SBM 1.1

Experimental Results:
Input Message P (128 bits):
42 69 6b 72 61 6d 6a 69 74 20 53 61 72 6b 61 72
LRC code generated from P (Say, L): 0 1 0 1 0 0 0 1
P is encrypted with the following key:
2B 28 AB 09 7E AE F7 CF 15 D2 15 4F 16 A6 88 3C

A one-bit error is injected in the 8th bit position of the
intermediate cipher generated after 7th round and the
encryption process continues through 3 more rounds of
AES encryption. As a consequence, an erroneous
cipher text is generated at the output as follows:
8A 88 3E 2D DC 16 77 90 4D B3 05 3E CA 04 4D 0C
P’ generated from the above erroneous cipher:
B2 C9 A7 34 CF 60 C6 24 75 F5 4B CD 9F 97 3C 62
LRC code generated from P’(Say, L’): 1 1 1 1 0 1 0 1

L and L’ are finally compared and it is observed that
they are not same. This indicates that some error has
occurred and the cipher text generated and hence it is
useless to transmit.
The proposed approach has minimized the overhead of
comparison from 128 pairs of bits to 8 pairs of bits.
Although an additional module of LRC generator that
has been introduced in our approach causes an extra
overhead of the new approach, yet the proposed
technique is superior.

A probabilistic approach to tackle Error
The proposed scheme suggests that the plain text will
be encrypted odd number of times, say n, with the same
key to produce n number of cipher texts. It is assumed
that the probability of occurrence of a single bit error
amidst the rounds must not reach 0.5 so that out of n
cipher texts at most (n – 1)/2 number of cipher texts
may be erroneous whereas the least number of error
free cipher texts is (n + 1)/2. Majority Rule is then
applied over the n number of ciphers and as a result the
error free cipher text is achieved.

Propagation Effect of AES contd..
Proposed Algorithm: SBM 1.2
2. Encrypt P n number of times with AES Encryptor to
find ciphers {Ci, i = 1 to n}, n being odd
3. Majority rule is applied over Ci to find the error-
free cipher text C which is directly transmitted
through the channel.

Block diagram: SBM 1.2

Experimental results:
Input Message P (128 bits):
42 69 6b 72 61 6d 6a 69 74 20 53 61 72 6b 61 72
Key K (128 bits):
2B 28 AB 09 7E AE F7 CF 15 D2 15 4F 16 A6 88 3C
Error-free Cipher:
FC 41 16 48 BE C0 16 A7 FC 5C 3F 43 F4 13 F4 A0

The Plain text P has been encrypted by the key 5
numbers of time and as per the assumption at most 2
numbers of ciphers texts may be erroneous. The
erroneous cipher texts are as follows:
Erroneous cipher text 1:
D2 06 F1 26 BE 27 E9 EE FA CF AF 6B 55 25 D6 0D
Erroneous cipher text 2:
24 E2 C9 55 1C 30 E0 58 5D D7 3C 64 EA 2F CA F7

As per the assumption, the rest of the cipher texts (3
numbers) are error free.
The Majority Rule is then applied over the 5 cipher
texts and finally the error-free output cipher is
generated as follows:
FC 41 16 48 BE C0 16 A7 FC 5C 3F 43 F4 13 F4 A0

Although in the experiment the plain text has been
encrypted 5 times, It can be realized that with the
increase in the number (n) of cipher texts, the scheme
guarantees reliable communication on its part, even
with the occurrence of error with higher probability
(0.5 * (1 – 1/n)); that means that if n increases the
tolerance also increases.

A Hybrid Architecture to overcome the Error
The algorithm SBM 1.3 proposes a hybrid architecture
to ward off the Error Propagation Effect of AES. The
proposed scheme is the combination of the algorithms
SBM 1.1 and SBM 1.2, that makes use of both the
Longitudinal Redundancy Check code and the Majority
Rule in parallel. The algorithm checks for the effect of
error propagation in 2 different paths and finally the
error-free cipher text is obtained ensuring a reliable
communication.

Proposed algorithm: SBM 1.3
2. Generate an LRC code (8 bits), say L1, out of P
3. Encrypt P with AES Encryptor to find the cipher
text, say C’
4. Decrypt C with AES Decryptor to find P’
5. Generate an LRC code (8 bits), say L2, out of P’
6. L1 and L2 are now compared. If L1 and L2 are found
to be same, C’ is fed to the comparator.

7. Encrypt P n number of times with AES Encryptor to
find ciphers {Ci, i = 1 to n}, n being odd
8. Majority rule is applied over Ci to find the cipher
text C” which is also fed to the comparator.
9. If C’ and C” are found to be same, say C, it is
considered to be error-free and is transmitted
through the channel.

Propagation Effect in Selective AES
Input Key Words for the message of N words. Message
is divided into K parts each of k blocks. Each block is
of M words.
Find the occurrence of any keyword in the blocks,
starting with the first block in the first part. If it occurs,
encrypt that block using the algorithm SBM 1.3 and all
the blocks thereafter in the part.
Repeat (1-2) for all parts, j=1 to K. When j=K, the
proposed scheme of encryption is complete.

Propagation Effect in Selective AES

Overall conclusion
In this thesis we have studied the effect in detail. The
relative mathematical analysis has been cited in the
thesis. Error propagation effect in case of selective AES
and its comparison with normal AES has also been
studied. In this thesis four algorithms, viz. SBM 1.1,
SBM 1.2, SBM 1.3 and SBM 1.4, have been proposed
for preventing Error Propagation Effect of AES. The
corresponding experimental results have also been
provided so as to prove the algorithms to be efficient to
overcome the error propagation effect of the Rijndael
used as Advanced Encryption Standard.

Future scope
It is assumed that the probability of occurrence of a
single bit error amidst the rounds is maximum 50%.
Further research works may be extended to achieve
certainty in preventing the Error Propagation Effect of
AES algorithm under all circumstances.
When the number of rounds is increased in AES, the
complexity of AES encryption and decryption also
increases. So, the length of the key may increased to
512 bits in order to increase the number of rounds.
Future research may include the above mentioned
considerations.

Error Propagation Effect of AES and Techniques to ward off the problem

Error Propagation Effect of AES and Techniques to ward off the problem

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