International Journal of Network Security, Vol.21, No.2, PP.250-258, Mar. 2019 (DOI: 10.6633/IJNS.201903_21(2).09) 250 Construction and Analysis of Key Generation Algorithms Based on Modied Fibonacci and Scrambling Factors for Privacy Preservation Amiruddin Amiruddin1;2, Anak Agung Putri Ratna1, and Riri Fitri Sari1 (Corresponding author: Amiruddin Amiruddin) Department of Electrical Engineering, Universitas Indonesia1 Jl. Margonda Raya, Pondok Cina, Beji, Kota Depok, Jawa Barat 16424, Indonesia Sekolah Tinggi Sandi Negara, Bogor, Jawa Barat, Indonesia2 (Email: [email protected]) (Received Sept. 24, 2017; revised and accepted Apr. 12, 2018) Abstract protect from interception and to ensure the data conden- tiality, many wireless systems use cryptographic systems Cryptographic key is the most important factor for sup- with secret keys that are only available to the legitimate porting encryption of condential data before it is trans- senders and recipients. mitted in a communication network. A good crypto- Various methods or approaches have been proposed to graphic key has properties of random sequence and long generate long and random encryption keys [36]. Each period. For these purposes, a randomness capable and method or approach has advantages and disadvantages lightweight computing algorithm is required. The ran- and cannot be applied to all dierent kinds of applica- domness capability and computation time of such an algo- tions. Therefore, a key generation function should be rithm can be measured by using randomness test and al- tailored and adjusted to the characteristics of the appli- gorithmic complexity analysis, respectively. In this paper, cations that will use it. One important consideration in two models of key generation algorithm using the mod- designing a key generation algorithm is its algorithmic ied Fibonacci and scrambling factor were constructed. complexity [24]. For applications in low-capacity devices Such modication and scrambling factor are intended to for IoT, low complexity algorithms are required. Unfor- support the randomness capability and low algorithmic tunately, the existing key generation algorithms lack the complexity. The proposed key generation algorithms have measurement of their complexity. been simulated and analyzed. The key generation algo- Fibonacci sequence [10] which is a very famous series rithm Model 2 (called hereinafter "Scrambled Fibonacci- function in the eld of mathematics can be used to gener- based") is better than Model 1 in term of randomness, ate encryption keys. It is a sequence of numbers where a despite both having similar linear algorithmic complex- number is found by adding up the two preceding numbers. ity, denoted by . O(n) Beginning with 0 and 1, the sequence goes as 0, 1, 1, 2, Keywords: Cryptography; Key Generation; Randomness; 3, 5, 8, 13, 21, 34, and so forth. Written as a rule, the Scrambled Fibonacci; Scrambling Factor expression is xi = xi−1 + xi−2. Its lightweight operation and ability to save computing time are of the reasons for 1 Introduction using it in the key generation function. Several crypto- graphic methods used Fibonacci sequence or its behavior Wireless communication system and its services have be- for encryption application [9, 12]. Applying Fibonacci is come an important component of modern life and society. suitable for common areas that do not involve data pri- An example of such a wireless network is the Internet vacy. However, for condential data-based applications, of Things (IoT) that grows rapidly, nowadays, to sup- it is necessary to make improvement on the Fibonacci port human beings need on information. However, due to function. Moreover, the operation used in Fibonacci pro- the nature of the Radio Frequency (RF) spectrum used duces a regular pattern (ascending or descending) that as shared transmission medium, wireless communications can be used as an entrance point to analyze the resulted are essentially vulnerable and prone to interception [5]. key sequence. Therefore, it is necessary to modify the The next generation of wireless communication systems Fibonacci operation so that the resulted pattern becomes should support applications with very low communication random and hardens the eorts to analyze it. latency, availability, high reliability and security [27]. To In this paper, a key generation algorithm based on the International Journal of Network Security, Vol.21, No.2, PP.250-258, Mar. 2019 (DOI: 10.6633/IJNS.201903_21(2).09) 251 modied Fibonacci and scrambling factor is constructed a two phase approach to achieve secret key. In the rst and analysed. The key generation function will be ap- step, the sender estimates his state and sends this along plied to the Internet of Things network with constrained with other information which is obtained from his obser- devices that have limited storage, low computing power vation to the recipient. In the second step, the recipient and energy. The contribution of this work is a construc- uses this information including the estimated state of the tion and analysis of key generation algorithm based on sender to generate the secret key. However, the protocol Fibonacci and scrambling factor which satises the re- has not been reported whether it has been implemented quirement for random and long period of key sequences. or not. The remaining of the paper is organized as follows. Sec- Al-Moliki et al. [2] enhanced the condentiality of Vis- tion 2 gives a brief overview of the previous related works ible Light Communication (VLC) networks by suggest- regarding cryptographic key generation methods. Section ing a new key generation protocol for optical Orthog- 3 describes the key generation denition and its perfor- onal Frequency Division Multiplexing (OFDM) schemes mance measurement. The proposed method is described in an indoor environment. The keys are extracted from in Section 4. Section 5 discusses the simulation and the the bipolar OFDM samples produced from optical OFDM result and Section 6 closes the paper with the conclusion. schemes. This approach which emphasizes the source of key generation diers from our proposed approach which emphasizes the process of the key generation. 2 Related Works Karimian et al. [14] proposed a novel approach of key generation that extracts keys from real-valued ECG fea- As technology grows, research on cryptographic key man- tures. However, this approach is only suitable for ECG- agement [17,20,22,25,32] continues to be done in various based applications although it can also be modied for aspects including key generation [14, 18, 28, 29, 34, 35, 37], other eld applications. agreement [3, 6, 7, 13, 15, 33] or exchange [4], distribu- In this research, we proposed new key generation algo- tion [8], assignment [19], authentication [16], and update. rithm based on modied Fibonacci and scrambling factor However, we focus on eorts for key generation to be used to support long periodicity and randomness of the gener- on symmetric cryptosystems. Verma et al. [31] proposed a ated key sequence. The research position of our proposed method for generating cryptographic key using biometrics key generation algorithm among other algorithms is sum- with the help of ngerprint pattern. The algorithm gen- marized in Table 1. erates key by extracting minutiae points and core point and the nal key is obtained from the ngerprint image. Turakulovich et al. Turakulovich et al. [30] discussed com- 3 Key Generation and Perfor- parative factors of the key generation techniques include mance Measurement randomness, key space, key space of biometric, entropy, measured entropy of biometric, convenience and cost, se- 3.1 Key Generation cure saving, update. However, they mostly discussed the factor for biometric-based key generation technique which In the eld of cryptography, key is the most urgent pa- is dierent from our proposed method. rameter for data encryption or decryption. By denition, Hossain et al. [11] proposed a One Time Key (OTK) a key is a sequence of a random string of bits created ex- generation technique based on User ID (UID) and pass- plicitly for scrambling and unscrambling data. Instances word. The key generation method involves a server-side of cryptographic processes demanding the usage of keys process to check for possible collisions between a new UID include, inter alia, the transformation of plain text data and a given UID to the previous client. This process takes into cipher text data (encryption) and vice versa (decryp- a long time so it is not applicable for devices with limited tion), the computation and verication of a digital signa- storage and energy. Torre et al. [29] studied the practical ture, the computation and verication of an authentica- performance of an enhanced channel-based key generation tion code from data, the computation of a shared secret system with a very short roundtrip delay, allowing recip- that is used to obtain keying material, and the derivation rocal channel assessment with increased accuracy. The re- of additional keying material from a key-derivation key. ciprocal channel measurements performed by body-worn There are two types of key, i.e. symmetric and asym- sensor nodes is used to extract encryption keys. Although metric key. Symmetric key is a key used in a symmetric- the performance is slightly increased due to the shorter key cryptographic algorithm which requires that the key round-trip delay, further apparent non-reciprocity in the must be kept secret. Asymmetric key is a key used with channel measurements can probably be attributed to in- a public-key algorithm. In asymmetric key cryptography, accuracy of the received signal strength indication in the there are two corresponding keys, i.e. private and pub- transceiver chip. lic keys. A private key is a cryptographic key used with Tavangaran et al. [27] studied the secret key generation a public-key algorithm that must be kept secret and is protocol for a compound Discrete Memoryless Multiple uniquely associated with an entity that is authorized to Sources (DMMS) with one-way communication in pres- use it.