HIDE: Hybrid Symmetric Key Algorithm for Integrity Check, Dynamic

Key Generation and Encryption

Jayagopal Narayanaswamy, Raghav V. Sampangi and Srinivas Sampalli

Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada

Keywords:

Dynamic Key Generation, Chained Key Generation, Encryption, Integrity Check.

Abstract:

This paper proposes a hybrid encryption technique that generates a key dynamically, along with integrity check

parameters. Our approach generates the key stream using a chained approach, beginning with an initial pre-

shared key. Subsequent keys are derived using logical operations on intermediate cipher texts and intermediate

keys generated in each stage. This is an improvement over chaining techniques, which use a cipher text to

derive successive keys. We validate our algorithm by proof-of-concept implementation and security analysis.

1 INTRODUCTION

Block ciphers split a message into blocks of identical

sizes, which are encrypted with key blocks. A key for

a block cipher remains the same or is derived from an

initial key using functions such as the Feistel function

(Knudsen, 1994). In contrast, stream ciphers encrypt

a stream of bits from a message with a key bit-by-bit

using the logical exclusive-OR (XOR) operation. The

key stream is generated by a PRNG through a ﬁxed

size input called the seed.

In stream ciphers, the encryption operation is sim-

ple but vulnerable to attacks such as distinguishing

and key recovery attacks (Hell et al., 2009). Stream

ciphers generate a continuous stream of key bits us-

ing a Linear Feedback Shift Register (LFSR) that re-

quire an n-bit seed value. A drawback with a LFSR is

that an n-bit pattern may repeat in the key stream be-

fore completing all 2

possible patterns (Zeng et al.,

1991). To avoid this issue a Non-Linear Feedback

Shift Register (NLFSR) has been proposed, but there

are no generic designs for a NLFSR (Dubrova et al.,

2008) (Bardis et al., 2004). In addition, in both block

and stream ciphers, the key is derived from an ini-

tial key or a seed, therefore, knowledge of the initial

key reveals information about the original message.

To overcome this issue, we use multiple keys that are

generated dynamically.

Recently, an algorithm called Hummingbird was

proposed as a hybrid of the stream and block ci-

pher approaches that was designed for resource-

constrained devices, such as, Radio Frequency Iden-

tiﬁcation (RFID) systems (Engels et al., 2010). Hum-

mingbird follows the traditional encryption process of

block ciphers such as substitution and looping; while

a key is derived through the stream cipher principle.

The key generation and encryption process in Hum-

mingbird is computationally expensive. However, we

compare our algorithm with Hummingbird as an ex-

ample. We don’t inherit any property of the Humming

algorithm in our approach.

After the encryption process, any encrypted mes-

sage is hashed to offer integrity. Hashing is a one-way

mathematical function, which converts the variably

sized messages into a ﬁxed size output called a Mes-

sage Digest (MD). The receiver veriﬁes the integrity

of received message by hashing it and then compares

it with the received MD.

In this paper, we propose a hybrid encryption al-

gorithm that requires a simple (Exclusive-OR) XOR

operation. We use the stream cipher approach to de-

rive a key, while the block cipher approach is adopted

in the encryption process. In our approach, a key

stream is generated from a previous key block and

an intermediate cipher text block, which is encrypted

with a message block-by-block using the XOR op-

eration. In addition to encryption, a ﬁxed-size ﬁ-

nal key in each round is used as the MD that pro-

vides the integrity to the message. Since we use only

the XOR operation throughout the encryption process

and provide the integrity check parameter without us-

ing any external hashing algorithm, we expect that

our approach will reduce the computational complex-

ity as well as increase performance. We have imple-

mented the algorithm and we show that our algorithm

can withstand such potential attacks as differential,

124

Narayanaswamy J., V. Sampangi R. and Sampalli S..

HIDE: Hybrid Symmetric Key Algorithm for Integrity Check, Dynamic Key Generation and Encryption.

DOI: 10.5220/0005273901240131

In Proceedings of the 1st International Conference on Information Systems Security and Privacy (ICISSP-2015), pages 124-131

ISBN: 978-989-758-081-9

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

known cipher text, known plain text, distinguishing

and key recovery attacks. We also conducted stan-

dard security analysis tests (such as, entropy analysis,

periodicity check, frequency test, poker test, run test,

serial test etc.) and have included the results in the

security analysis section.

2 BACKGROUND AND

LITERATURE REVIEW

In stream ciphers, an LFSR plays an important role

in the generation of a key stream. One possible im-

plementation of a Pseudo Random Number Genera-

tor (PRNG) is using an LFSR. An LFSR can be con-

structed by the consecutive assembly of shift regis-

ters. An n-bit LFSR produces a continuous bit stream

from an n-bit seed. One of the drawbacks of an LFSR

is that it will form a cycle on or before reaching 2

patterns for a given n-bit seed (i.e. the same sequence

of bits will be generated on or before reaching 2

pat-

terns) (Zeng et al., 1991).

To overcome this drawback, an NLFSR was in-

troduced (Dubrova et al., 2008) (Bardis et al., 2004).

NLFSRs avoid the linearity problem and extend the

cyclic period. A common way of constructing an

NLFSR is to use more than one LFSR connected

through logic gates. Logic gates are used to choose

the current LFSR output from a list of connected LF-

SRs. Thus, linearity can be broken easily and the

cyclic period will be extended. Even though NLFSR

acts as an alternative to LFSR, there is no NLFSR

that guarantees a long cyclic period. Furthermore,

a general technique for constructing NLFSRs has

been an open problem (Lv et al., 2012) (Rachwalik

et al., 2012) (Hu and Gong, 2011) (Mandal and Gong,

2012).

Block ciphers offer better security over stream ci-

phers, however the latter are computationally more

efﬁcient. Hybrid approaches that combine the ben-

eﬁts of both have been the focus of recent research.

Trivium (De Canni

ere, 2006) is the stream cipher that

uses the block cipher principle for the key genera-

tion process. The Hummingbird algorithm encrypts

the message block-by-block and uses internal regis-

ters to update the key stream. It has a small block size

of 64-bits, which is further divided into four smaller

blocks of 16-bits each that are equivalent to the num-

ber of bits in the internal state register. Initially, the

internal state register is loaded with random bits. Fur-

thermore, the LFSR and the cipher text are used to re-

generate the internal state register bits. It uses a 256-

bit key that is split into four 64-bit keys to encrypt

the message. Two more secret keys, namely, K5 and

K6, are introduced and these are derived from the ini-

tial four keys. The Hummingbird algorithm has four

rounds of substitution and permutation and uses four

keys on each round to encrypt the message. In the

ﬁfth round, the output is encrypted with key K5 fol-

lowed by a ﬁnal substitution and then encryption with

key K6. This approach is more suitable for resource-

constrained devices such as RFID systems. It is re-

sistant to differential as well as linear attacks (Engels

et al., 2010). However, we use this algorithm as an

example of a hybrid approach and our algorithm does

not inherit any properties used in Hummingbird.

Kutuboddin and Krupa (Jinabade and Rasane,

2013) have extended the research on the Humming-

bird algorithm to increase its computational efﬁ-

ciency. They propose an approach, which replaces the

traditional Hummingbird modulo operation by intro-

ducing Field Programmable Gate Array (FPGA). As

the proposed approach uses XOR operation, compu-

tational efﬁciency is better compared to the original

version.

Integrity is an important component of network

security that prevents an anonymous entity from data

manipulation. The Integrity of the message can be

achieved through hashing algorithms, such as, MD5,

SHA1, SHA2, SHA3, etc. Traditional hashing is a

mathematical one-way function, which encrypts the

message but decryption is not possible. It converts

any variable size message to a ﬁxed size output called

the Message Digest (MD). A collision between two

MD is possible after hashing 2

messages. How-

ever, as the encryption (or decryption) and hashing

are disjoint operations, the use of hashing will lead to

computational overhead on the system (Kumar et al.,

2011) (Hu and Wang, 2009) (Li et al., 2012).

In recent years, a hybrid approach called Authen-

ticated Encryption (AE) has provided integrity as well

as authenticity for short messages (Jeddi et al., 2013).

However, it requires a Message Authentication Code

(MAC), which is derived from the hashing technique.

This creates further computational overhead. For ex-

ample, Signcryption was proposed for the asymmet-

ric key algorithm (Zheng, 1997)(Wang et al., 2013),

which replaced a traditional encrypt and sign practice

by integrating message signatures (similar to MD) as

a part of an encryption process. Zheng et al.’s (Zheng,

1997) work on the signcryption scheme is based on

the theory that a combined computational cost of a

signature (using hashing) and encryption will be less

than their individual costs. In signcryption, part of

the key is generated using a hashing algorithm to pro-

vide the integrity, and the same key is used to en-

crypt (using an asymmetric key algorithm) the mes-

sage to offer conﬁdentiality, integrity and authentica-

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tion (Zheng, 1997).

Our literature review concludes that existing algo-

rithms are weak in generating a key or the encryp-

tion process leads to computational overhead. To ﬁll

a gap between computational overhead and to support

a strong dynamic key generation process to encrypt

the message, we propose a new approach that uses

a simple XOR operation for better computation, and

Intermediate Cipher Text (ICT) to generate the key

dynamically.

3 PROPOSED APPROACH

3.1 Overview

Table 1 contains a list of notations that are used in the

proposed approach.

In block ciphers, common modes of encryption

such as Cipher Block Chaining (CBC), Propagating

Cipher Block Chaining (PCBC) and Cipher Feedback

(CFB) use the cipher text as part of the encryption.

This may lead to some information about the original

message being revealed to an attacker. To avoid this

issue, our approach uses an Intermediate Cipher Text

(ICT) to generate a dynamic key. Since the dynamic

key is used on each block of the message encryption,

the cipher text bits are completely random.

Table 1: Notations.

Keys to encrypt in Round One

Keys to encrypt in Round Two

n Last block

l Current block

Prediction bit

M Message to be encrypted

, m

...m

Message blocks

XOR Logical bit-by-bit XOR operation

δ() Derivation function

ρ() Prediction function

γ() Inversion function

Message block x

Round One key block x

Round Two key block x

ICT

Intermediate Cipher Text block x

Cipher Text block x

α,β

Chunk β of component α (α can be

, ICT

, K

, CT

)

KG1 Key generation for Round One

KG2 Key generation for Round Two

Figure 1: Overview of the encryption process.

A hybrid encryption algorithm is proposed, which

includes both stream cipher and block cipher features.

This approach consist of two parts: a key generation

part (based on stream ciphers) and two rounds of en-

cryption (or decryption) using a basic XOR opera-

tion (employing message blocks as in block ciphers).

The message is encrypted block-by-block with differ-

ent (block) keys on each message block. The size of

one block in the message is 128-bits in sixteen 8-bit

chunks.

Figure 1 illustrates the overall encryption process.

This approach requires two initial keys that encrypt

the ﬁrst block in each round. Except for the initial key,

every successive key (to encrypt each block) is de-

rived from the bits in the current key block and an ICT

block. In general, blocks of message are encrypted

using blocks of keys generated using the stream ci-

pher scheme. Key generation and encryption follows

a chained approach, with the current (block) keys and

ICTs used to generate (block) keys for the encryption

of the subsequent message blocks. The encryption

and key generation processes are described later in

this section.

3.2 Assumptions

It is assume that the initial key used to encrypt the ﬁrst

block of the message in each round is generated by the

sender and securely transmitted to the receiver. The

key used to encrypt the message is randomly chosen

from a set of strong keys.

3.3 Design

3.3.1 Key Generation

Since it is assumed that the key is known only to the

sender and the receiver, we generate successive keys

from the previous keys with the help of an intermedi-

ate cipher text (ICT). The term “intermediate cipher

text” represents an encrypted message after Round

1, whereas the actual cipher text is generated after

Round 2 (as will be discussed in detail in the encryp-

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Figure 2: Key Generation Process Overview.

tion section). The key generation process in this ap-

proach is different for both rounds. Each round uses a

different initial key (K

& K

) to encrypt the ﬁrst

block in the message. To encrypt each successive

block in the message, we introduce a combination of

prediction and derivation techniques to generate suc-

cessive keys (K

a1...n

for Round 1 and K

b1...n

for Round

2) from a previous key block and an ICT block.

In prediction, three bits in every chunk per block

are used to choose the i

bit within the respective

chunk. The value of i

is based on the three binary

bits chosen in the chunk. The value of i

is a decimal

representation of the 3-bit binary. In a chunk, 3-bits

are selected in a clockwise direction starting from the

most signiﬁcant bit (MSB) in the chunk to the least

signiﬁcant bit (LSB) to choose one out of eight pos-

sible values for i

, which is repeated 8 times starting

from the MSB to the LSB. The value of i represents

the position of the binary bit in the chunk. Each value

of i

predicts a new bit that is used to generate chunks

per block in every successive key. As shown in Fig-

ure 2, three bits are rotated in a clockwise direction to

yield one out of eight possible values for i

In derivation, the successive key is generated by

XORing the (i

− 1)

position of the binary bit with

the (i

+ 1)

position of the binary bit to form a new

bit. The same process is repeated in every chunk per

block to generate a whole key for encrypting the suc-

cessive block in the message. The whole process of

key generation offers a randomness in the key stream

without forming a cycle.

The process for applying prediction and

derivation in combination to generate a key is as

follows. In Round 1, the key is derived from key

series based on the ICT block’s prediction. In

contrast, Round 2’s successive keys are derived from

the ICT block based on the key block’s prediction.

To generate a key, the prediction and derivation

combination is applied alternatively on an ICT block

and a key block over two rounds.

3.3.2 Encryption (or Decryption)

Initially, in Round 1, four out of eight bits (say

0, 2, 3, 5) in every chunk in a key K

are inverted.

The ﬁrst chunk in the initial key K

is XORed with

the ﬁrst chunk in the ﬁrst block of the message, which

produces the ﬁrst chunk in ICT

(which represents the

ICT ﬁrst block). Again, four out of eight bits (say

2, 4, 5, 7) in every chunk in ICT

are inverted (this pro-

cess is common throughout the ICT blocks), which is

followed by successive key generation operations (al-

ready discussed in detail earlier). The output of the

key generation operation will be the ﬁrst chunk in the

key K

to encrypt the ﬁrst chunk of the next mes-

sage block. The ﬁrst chunk of key K

is XORed with

the second chunk of key K

that will be used to en-

crypt the second chunk in the ﬁrst block of the mes-

sage. In conclusion, every ﬁrst chunk in each block

of the message is directly XORed with the ﬁrst chunk

of the respective key, whereas the successive chunks

in each block in the message are encrypted with the

XORed output of the successive chunk in the present

key and the currently derived chunk for the next key.

For example, the 4

chunk in message C

will be

encrypted with the XORed output of the 4

chunk in

the current key C

and the 3

chunk in the next

key C

Round 2 follows the same procedure as Round 1,

except that the message and initial key K

will be re-

placed by the ICT and key K

respectively. In addi-

tion, the inversion operation is applied on bits 1, 4, 6, 7

and 0, 1, 3, 6 for the key and the ICT respectively. The

output of Round 2 is the ﬁnal cipher text. Every block

in a message is XORed with the key block to gener-

ate a cipher text. Figure 3 illustrates the encryption

process.

A decryption process is symmetric with encryp-

tion in reverse manner.

3.3.3 Integrity Check

The ﬁnal keys (say K

a(n+1)

and K

b(n+1)

) in each round

of encryption will act as the integrity check param-

eter. In this approach, the 128-bit key K

a(n+1)

will

be concatenated with the 128-bit key K

b(n+1)

to form

a 256-bit message digest, which is used for integrity

check.

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Figure 3: Encryption Process.

3.4 Example

3.4.1 Encryption and Key Generation

In this section the two rounds of the encryption pro-

cess will be explained with a generic example. Each

round used different initial key (K

and K

). Further,

the message (M) is segmented into different blocks.

The ﬁrst block of the plain text message is encrypted

with a key combination of K

(the present key) and

(the currently derived key) at Round 1 that gener-

ates the ﬁrst ICT block.

Let the message blocks be:

M = M

, M

, ..., M

(1)

Round − 1 : Encrypting the ﬁrst block of the mes-

sage: The message block will be encrypted chunk

by chunk. Before the XOR operation, bit positions

0, 2, 3, 5 will be inverted in the ﬁrst chunk of an initial

key. Then, the ﬁrst chunk in the ﬁrst block of the mes-

sage will be XORed with the initial key’s ﬁrst chunk

(which is after the inversion).

= γ(C

) (2)

ICT

= E

) (3)

Once again, bits 2, 4, 5 and 7 in the ICT will be in-

verted before the key generation process and the out-

put will be used to generate a key to encrypt the next

chunk as well as the block.

ICT

= γ(C

ICT

) (4)

Each bit of the key, C

, is generated from the

previous key, C

, whereas, n bits in C

ICT

chooses

a bit in C

to produce the new key, C

. In

general, a current key, K

, is generated from the

prediction of a previous ICT block, ICT

l−1

, and the

derivation of the previous key, K

a(l−1)

, in Round 1.

Every ﬁrst chunk in the message block is directly

XORed with the inversion of the ﬁrst chunk in the key,

whereas the 2

to 15

chunk in the message will be

encrypted with an inversion of the XORed value of

the next chunk key with next block’s chunk’s key.

Key Generation: for initial chunks only

= ρ(C

ICT

l−1

[δ(C

a(l−1)

)]) (5)

For the 2

to 15

chunks

= [C

]XOR[C

a(l+1)l

] (6)

...

,15

= [C

,15

]XOR[C

a(l+1)l

,14

] (7)

The generic equation for encryption in Round 1 is as

follows:

ICT

= E

), ICT

= E

), ..., ICT

= E

)

(8)

Figure 4 is an example diagram for the encryp-

tion and integrity check processes. For this exam-

ple, it is assume that the message contains only two

blocks and that each one has only two chunks (the

typical block size used in this example is 16-bits,

which is composed of two 8-bit chunks). The initial

key, K

(10011010 11011011), is encrypted with the

message (00101101 00110011 10111011 01000011)

which produces, in Round 1, the ICT (00000011

11010010 10000001 01001111). Then, in Round 1,

the ICT block is used to predict a derivation bit in a

key block, whereas in Round 2 a key block predicts

the derivation bit in the ICT block. Further, in Round

2, the cipher text (11110011 01000111 00111000

10111101) will be obtained by encrypting the ICT

with the key block K

(10111011 00101100). Fi-

nally, the concatenation of the last derived keys, K

and K

, will act as the message digest (01000111

11100010 10111001 11001111).

Round − 2 : In this Round, the encryption process

is the same as in Round 1. But in the key generation

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Figure 4: An example of the Encryption and Integrity Check

Process.

process, the prediction and derivation functions are

interchanged between an ICT block and a key. An ini-

tial key (K

) encrypts the ﬁrst block of the ICT block.

To encrypt subsequent blocks, a current key (K

) is

generated from the prediction of a previous Key block

b(l−1)

) and the derivation of a previous ICT block

(ICT

l−1

). In Round 2, the bits chosen to invert are dif-

ferent form Round 1. For a key bits 1, 4, 6 and 7 are

inverted before encryption, whereas bits 0, 1, 3 and 6

are inverted for the ICT chunks (after the encryption,

but before the key generation process).

Encrypting ﬁrst block of the message:

= γ(C

) (9)

= E

ICT

) (10)

ICT

= γ(C

ICT

) (11)

Key Generation: for initial chunks only

= ρ(C

b(l−1)

[δ(C

ICT

l−1

)]) (12)

For the 2

to 15

chunks

= [C

]XOR[C

b(l+1)l

] (13)

...

,15

= [C

,15

]XOR[C

b(l+1)l

,14

] (14)

The generic equation for encryption in Round 2 is as

follows:

= E

(ICT

), CT

= E

(ICT

), ..., CT

= E

(ICT

)

(15)

3.4.2 Message Digest

The ﬁnal keys generated from each round will be con-

catenated to yield the 256-bit Message Digest.

MD = K

a(n+1)

||K

b(n+1)

(16)

4 ANALYSIS AND DISCUSSION

This proposal has successive key derivation function,

which uses both a key as well as a message to choose

the next key dynamically. Every message block is en-

crypted with a different key chosen from the 2

128

pos-

sible combination keys for a given 128-bits in the key

space. As successive keys are generated based on a

message and a key in any one process of either pre-

diction or derivation, the generated key is completely

dynamic. Thus, it guarantees that there would be no

regular cycle in a key bit stream. The algorithm is a

very simple, which uses XOR operations to generate

keys as well as encrypt a message. It can withstand

a variety of attacks (chosen-plain text attack, chosen-

cipher attack, differential attack, linear attack and dis-

tinguishing attack) (Hell et al., 2009) (Zulkiﬂi, 2008)

(Northwood, online).

4.1 Cryptanalysis

A short description of possible attacks and their anal-

yses are explained in this section. Chosen-plain text

and chosen-cipher text attacks are targeted on sym-

metric key encryption schemes. Both attacks work

on the principle of choosing a piece of information

for retrieving an original message for a given cipher

text or to reach a cipher text for a given plain text.

In this approach, since the key is changed for every

block encrypted, chosen-plain text and chosen-cipher

text attacks are hard to launch. A differential attack

compares an input value with an output value to ob-

tain a possible key. Since this proposal relies on both

a key and an ICT, and the key is chosen from a strong

key, a differential attack is difﬁcult to implement. In

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Figure 5: Sample 1.

linear cryptanalysis, an equation is formed from plain

text and cipher text, which is equated to possible key

bits to reveal some information about the message. To

avoid this issue, the key generation process i switched

between prediction and derivation techniques. A dis-

tinguishing attack focuses on stream ciphers that com-

pare a given sequence of values to check the random-

ness. A dynamically generated key ensures that there

will be no relation between the current and previous

keys, so launching a distinguishing attack is difﬁcult.

4.2 Security

In addition to the attacks mentioned above, tests were

done using a cryptanalysis tool called Cryptool (url,

2014). As mentioned earlier, though the key genera-

tion part is in the nature of a stream cipher, the actual

encryption process adopts a block cipher approach.

The security analysis of the proposed approach was

compared with existing block cipher algorithms such

as AES, DES, IDEA, MARS, Twoﬁsh etc. (the imple-

mentation of which is available as a built in option in

Cryptool). Graphs are presented below with ﬁve dif-

ferent scenarios, which are based on the cryptanaly-

sis tests (entropy test, periodicity test, frequency test,

poker test, run test and serial test) (Wu et al., 2011)

(Biebighauser, 2000) (Soto, online). The results from

this analysis show that our algorithm passes the above

mentioned tests and that the security level is no lower

than the pool of example algorithms used. Figures 5,

6, 7 display the sample graphs that were taken from

the security analysis with different sample inputs.

The proposed algorithm provides non-linearity in

the key cycle, which is achieved by using an interme-

diate cipher text block. However, using cipher text

to encrypt a message is vulnerable, so two rounds of

encryption were designed with an ICT as the second

round key generator instead of the cipher text. Ap-

plying key generation from a key for the ﬁrst round

and an ICT for the second round ensures a dynamic

property in successive keys.

Figure 6: Sample 2.

Figure 7: Sample 3.

4.3 Performance

The performance of our approach has yet to be

tested, but it is expected to be computationally efﬁ-

cient, which is our contention based on the following

claims. Initially, the computation is required only for

the encryption part, but the integrity check does not

require any additional computation. As the key gen-

eration process is a bitwise operation, it is the only

difﬁculty in this approach. The number of operations

required per bit is only fourteen, which includes en-

cryption (or decryption), an integrity check and key

generation. We identiﬁed from our research that an

increase in performance would require an increase in

the hardware component, which may not be appropri-

ate depending on the requirements of the application.

However, we are currently working on the key gener-

ation part.

5 CONCLUSION AND FUTURE

WORK

In this paper, a hybrid encryption algorithm is pro-

posed with increased security. In our approach,

blocks of message are encrypted using the blocks of

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keys generated by a stream cipher scheme. Key gen-

eration and encryption follows a chained approach in

which current (block) keys and ICTs are used to gen-

erate (block) keys for the encryption of subsequent

message blocks. This approach is feasible for en-

crypting a message using a hybrid stream cipher and

block cipher approach. The novelty of our approach

is its dynamic key generation from an intermediate ci-

pher text with an the integration of an integrity check.

We are currently extending our research to optimize

the computational efﬁciency of our approach.

REFERENCES

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