Ensuring information security through 123-bit recursive substitution of bits through prime-nonprime detection of sub-stream (RSBP)

Transcription

1 Journal of Scientific & Industrial Research 584 Vol. 68, July 2009, pp J SCI IND RES VOL 68 JULY 2009 Ensuring information security through 123-bit recursive substitution of bits through prime-nonprime detection of sub-stream (RSBP) Saurabh Dutta 1 * and Jyotsna Kumar Mandal 2 1 B C Roy Engineering College, Durgapur , India 2 Department of Computer Science & Engineering, Faculty of Engineering, Technology & Management, Kalyani University, Kalyani , India Received 02 July 2007; revised 26 March 2009; accepted 27 March 2009 This paper presents a 123-bit private-key based block-cipher, RSBP, which is capable of encrypting files of up to 11 MB. It is formulated on the basis of base-10 value corresponding to a block of bits, which is to be checked if is prime or not. It results in an alteration of size for file being encrypted. Its executable performance is analyzed on the basis of execution time, graphical layout of frequency distribution of characters, and Chi square values for varying degrees of freedom. RSBP is found to be highly compatible with existing cryptosystems. Keywords: Block-cipher, Cryptography, Cryptosystem, Prime, Private-key Introduction In application-based scientific research on information security, role of a ciphering protocol with proven efficiency is inevitable. This paper presents one such newly developed protocol, recursive substitution of bits through prime-nonprime detection of sub-stream (RSBP), using a 123-bit private-key. Proposed RSBP Scheme followed in RSBP Approach (Fig. 1) to encrypt bit-streams using RSBP 1-3 involves following steps: Step 1 Decompose source stream into a finite number of blocks, each preferably of same size, L. Step 2 Calculate total number of primes and non-primes from 0 to (2 L -1). Accordingly, find minimum how many bits are required to represent each of these two numbers. Step 3 For block under consideration, calculate decimal number corresponding to D. *Author for correspondence saurabh.dutta@bcrec.org Step 4 Find out if D is prime or nonprime. If D is a prime, code value is 1 and if not so, it is 0. Step 5 In series of primes or non-primes (whichever be applicable for D) in the range of 0 to (2 L -1), find position of D. Represent this position in terms of binary values. This is rank of this block. After repeating these steps (3, 4 and 5) for all blocks, steps to be followed are: Step 6 For N number of blocks, in the target stream of bits, put all N code values one by one starting from MSB position. So, in the target stream, first N bits are code values for N blocks. Step 7 For putting all rank values in target stream, start from N th bit from MSB position and then come back bit-by-bit. Immediately after N th bit, put rank value of N th block, followed by rank value of (N-1) th block, and so on. In this way, rank value of first block will be placed at the last. Step 8 Combining all code values as well as rank values, if total number of bits in target stream is not a multiple of 8,

2 DUTTA & MANDAL : INFORMATION SECURITY THROUGH 123-BIT PRIVATE-KEY BASED BLOCK-CIPHER 585 Fig. 1 Encryption of 16-bit stream, S = using RSBP then make it so by inserting at most 7 bits. Insertion of these extra bits is to be started from (N+1) th position. So, a maximum of 7 right shifting operations may have to be performed in (N+1) th position, where that many 0 s are inserted. The scheme to be followed to decrypt encrypted bitstream is simple to derive. Encrypted stream (T= ) generated in Fig.1 is decrypted (Fig. 2). An Outline of Sample Implementation of RSBP Take a plaintext P as LAN (Local Area of Network) 3,4. Corresponding 144-bit stream is as follows: S= Blocks are constituted of a unique dimension (8 bits) by scanning bit-stream in MSB-to-LSB direction. It is observed that in the range of 0 to 255 (2 8-1), there are 54 primes and 202 non-primes. So, rank value corresponding to code value of 1 (prime) should be of 6 bits and same corresponding to code value of 0 (nonprime) should be of 8 bits. Code value and rank value for all blocks are calculated. Accordingly, encrypted bit-stream obtained is as follows:

3 586 J SCI IND RES VOL 68 JULY 2009 Fig. 2 Decryption of T = using RSBP T= Text corresponding to T is cipher text, C, which is Results and Discussion Sample files of varying types have been encrypted using RSBP for 8-bit blocks. Table 1 presents a report 1,3,4-6 of results obtained. Files were encrypted in machine with 810T mother board, 500 MHz CPU, 64 MB RAM, and 20 GB HDD. For fast implementation, blocks have been constituted only of 8 bits. Analysis of Results For files of.com category (Table 1), there is an average storage reduction of 0.36% (Fig. 3) by horizontal black bar for source file size and horizontal white bar for encrypted file size. However, alteration of sizes does

4 DUTTA & MANDAL : INFORMATION SECURITY THROUGH 123-BIT PRIVATE-KEY BASED BLOCK-CIPHER 587 Table 1 Report of results obtained in executing RSBP Source file Source Encrypted Encryption Decryption CS value* DF** Size size size time time alteration tlib.exe unzip.exe rppo.exe prime.exe tcdef.exe % triangle.exe ping.exe netstat.exe clipbrd.exe emstest.com thelp.com win.com keyb.com choice.com diskcopy.com % doskey.com mode.com more.com sys.com snmpapi.dll kpsharp.dll winsock.dll spwhpt.dll % hidci.dll pfpick.dll nddeapi.dll nddenb.dll icccodes.dll kpscale.dll himem.sys ramdrive.sys usbd.sys cmd640x.sys cmd640x2.sys % redbook.sys ifshlp.sys aspi2hlp.sys dblbuff.sys ccport.sys bricks.cpp project.cpp arith.cpp start.cpp chartcom.cpp % bitio.cpp mainc.cpp ttest.cpp do.cpp cal.cpp *CS value, Chi square value; **DF, Degree of freedom

5 588 J SCI IND RES VOL 68 JULY File Sr. No File Size Fig. 3 Relationships between sizes of.com files and corresponding encrypted files Fig. 4 Frequency distribution for UNZIP.EXE and corresponding encrypted file not depend on category of file, as all files are considered as bit-streams. Consequently, even among files of.com category, storage expansion is observed, and among remaining files, storage reduction is observed in a few cases. On the whole, there is a clear tendency of storage expansion, due to an overall storage expansion of 1.585%. Character frequency distribution tests were performed randomly on some pairs of source files and respective encrypted files (Fig. 4). Tendency of having a wide deep black area on plot suggests that, like in source file, there is a steady distribution of all characters in encrypted file. It means encrypted file is heterogeneous and is desirable against possible cryptanalytic attack. Proposal of a 123-bit Key for RSBP Structure of key has been proposed with an assumption on encryption policy. Entire stream of bits of source file is decomposed into a total of 12 segments

6 DUTTA & MANDAL : INFORMATION SECURITY THROUGH 123-BIT PRIVATE-KEY BASED BLOCK-CIPHER 589 and on first 11 segments, encryption policy is applied using RSBP. Final segment is left as such. Each segment is assigned a unique rank value; rank values start with 1 for first segment, starting from beginning of file, and final segment is with rank value of 11. In each segment, blocks are constructed of unique size, but maximum number of blocks in one segment cannot exceed a limiting value. Relationship among rank value of a segment (to:r), unique block size in segment (S), and maximum number of blocks in segment (N) is established. For segment of rank R, there can exist a maximum of N = 2 14-R blocks, each of unique size of S = 2 14-R bits, R starting from 1 and moving till 11. For different values of R, following segments are generated: Segment with R = 1 formed with the first maximum 8192 blocks, each of size 8192 bits; Segment with R = 2 formed with the next maximum 4096 blocks, each of size 4096 bits; Segment with R = 3 formed with the next maximum 2048 blocks, each of size 2048 bits; Segment with R = 4 formed with the next maximum 1024 blocks, each of size 1024 bits; Segment with R = 5 formed with the next maximum 512 blocks, each of size 512 bits; Segment with R = 6 formed with the next maximum 256 blocks, each of size 256 bits; Segment with R = 7 formed with the next maximum 128 blocks, each of size 128 bits; Segment with R = 8 formed with the next maximum 64 blocks, each of size 64 bits; Segment with R = 9 formed with the next maximum 32 blocks, each of size 32 bits; Segment with R = 10 formed with the next maximum 16 blocks, each of size 16 bits; Segment with R = 11 formed with the next maximum 8 blocks, each of size 8 bits. Since total number of segments, maximum number of blocks in a certain segment, and size of blocks for a certain segment are fixed, a static structure of key can be formed. In the structure of secret key, a total of 12 segments should exist, first 11 of which are corresponding to exact numbers of blocks in respective segments of bits, and final segment in key stores original file size. With this proposed format, first 11 segments in the key require respectively 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, and 4 bits, which is 99 bits in total. Final segment requires 24 bits to accommodate source size, since as per the calculation with this key structure, a file (size, MB) can be encrypted, and to store this size in the key, 24 bits are required. Therefore, total size of proposed key is (99+24) bits = 123 bits. In proposed format of key (Fig. 5), each segment is shown through a pillar, and number of bits in a segment equals to pillar height. Left-most pillar stands for first segment from MSB position, and so on. Pillars are made of two colors (11 black pillars and 1 white). Each black pillar stands for storing number of blocks in a segment. For example, left-most black pillar is made of height 14, which indicates that this segment in key is of length 14 bits, and hence it can provide information on exactly how many 8192-bit blocks are in segment with R=1, since it is fixed that maximum 8192 blocks can be present in this segment, and to present 8192 in modulo-2 notation, 14 bits are required. Only white pillar is used in final segment of key to store source file size. Height for this pillar is taken as 24, so that 24 bits are allocated for source file size. Comparative Analysis of RSBP with Existing Ciphers Result of implementing RSBP on files of.cpp category has been compared with the result of implementing existing RSA technique on same set of files 3,5,7-10. Comparison is made in terms of CS values (Table 2). Here, same 10 files of type.cpp have been considered, sizes of which are ranging from 1257 bytes to bytes. CS value between a source file and corresponding encrypted file, encrypted using RSBP, is in range of 2088 to , whereas same between a source file and corresponding encrypted file, encrypted using existing RSA technique, is in the range of 3652 to Degrees of freedom are in the range of 69 to 90. Graphically, using vertical bars (Fig. 6), each vertical white bar stands for CS value obtained implementing RSBP technique, and each vertical black bar stands for CS value obtained implementing RSA technique. There exist three white bars, height of each of which is more than corresponding brown bar. So, for three files, project.cpp, start.cpp, chartcom.cpp, CS values were observed higher for RSBP. Apart from Mathematical complexity in RSBP, main strength of proposed cipher is having a long key-space. A ciphering protocol is computationally secure if cost involved in breaking cipher exceeds the value of encrypted information, and time required to break cipher exceeds usual lifetime of information. In terms of

7 590 J SCI IND RES VOL 68 JULY 2009 Segment size in bits For No. of Blocks in File Segment 1 For No. of Blocks in File Segment 2 For No. of Blocks in File Segment 3 For No. of Blocks in File Segment 4 For No. of Blocks in File Segment 5 For No. of Blocks in File Segment 6 For No. of Blocks in File Segment 7 For No. of Blocks in File Segment 8 For No. of Blocks in File Segment 9 For No. of Blocks in File Segment 10 For No. of Blocks in File Segment 11 For source size Key segment Fig bit key format with 12 segments for RSBP CS Value File Sr. No. Fig. 6 Comparison between CS values for RSBP (white) and RSA (black)

8 DUTTA & MANDAL : INFORMATION SECURITY THROUGH 123-BIT PRIVATE-KEY BASED BLOCK-CIPHER 591 Table 2 Comparison between proposed RSBP and existing RSA on CS values File name File size Chi Chi Degree of Bytes square square Freedom value in value in RSBP RSA bricks.cpp project.cpp arith.cpp start.cpp chartcom.cpp bitio.cpp mainc.cpp ttest.cpp do.cpp cal.cpp invulnerability against possible attacks to key, 123-bit RSBP is highly compatible with existing ciphers like 56- bit DES (Data Encryption Standard), 128-bit AES (Advanced Encryption Standard), 128-bit IDEA (International Data Encryption Standard), or even 168- bit triple DES. Using a high-speed PC, capable of performing 10 6 encryptions in every µs, time required to break key in 128-bit IDEA is years. Obviously, like IDEA or 128-bit AES, 123-bit RSBP also is computationally secure. Conclusions Proposed 123-bit RSBP has been found to enhance security of information transmitted through network. It is an intelligent system, easy-to-implement, fast, and formation of a reasonably long-space has made it highly compatible with existing ciphers in cryptography. References 1 Dutta S & Mandal J K, A space-efficient universal encoder for secured transmission, in Proc Int Conf (MS 2000, Egypt, Cairo), April 2000, Dutta S, Mal S & Mandal J K, A multiplexing triangular encryption technique A move towards enhancing security in E-Commerce, in Proc IT Conf (Computer Association of Nepal, Kathmandu), January 2002, Dutta S, An approach towards development of efficient encryption techniques, Ph D Thesis, The University of North Bengal, West Bengal, India, Mal S, Mandal J K & Dutta S, A microprocessor based generalized recursive pair parity encoder for secured transmission, J Tech, 37 (2003) Kahate A, Cryptography and Network Security (Tata McGraw- Hill, ) Mandal J K & Dutta S, A 256-bit recursive pair parity encoder for encryption, in Advances D-2004, vol 9 n 1 (AMSE, France) 2004, Mandal J K & Dutta S, Ensuring E-security using a private key cryptographic system following recursive positional modulo- 2 substitutions, in Asian Appl Compu Conf, October (Kathmandu, Nepal) Mandal J K, Dutta S & Mal S, Toward implementation of security and storage efficiency for geographical information systems, in Advances B-2004, vol 47 n 3 (AMSE, France) 2004, Schneier Bruce, Applied Cryptography, Protocols, Algorithms, and Source Code in C (John Wiley & Sons Inc., ) Stallings W, Cryptography and Network Security, 3rd edn (Pearson Education).