Encryption Algorithm of RSH (Round Sheep Hash)

INTRODUCTION

Now the common method is encrypting data by hash function. Hash function can changes the input message string of arbitrary length into the fixed-length output string. Output string is called hash value (Mironov, 2005) of input message. It generally is used to generate message digest and Key encryption. The existing hash function divides into password and the no password. Now the study is the following two:

Modification Detection Codes (MDCs): MDCs is discussed more than other no-password encryption. The common MDCs are: One-way Hash Functions (OWHFs) (Benson et al., 1994; Katz and Koo, 2008; Barak, 2008) and Collision Resistant Hash Functions (CRHFs) (Simon, 1998).

Message Authentication Codes (MACs) (Black, 2000): MACs is discussed more than other password encryption. For the last decades, with the rapid development of network, Many signature algorithm appeared. There are the following:

RSA: RSA algorithm is currently the best known and most widely used digital signature (Rabah, 2006).

The Digital Signature Algorithm (DSA): DSA can only be used for signature and can not be used for encryption (Hwang et al., 2001).

Elliptic Curve Cryptogram (ECC): Based on Elliptic Curve Digital Signature system (Toorani and Beheshti Shirazi, 2009). ECC were more research, including the algorithm optimization (Rabah, 2005a), secure application (Rabah, 2005b; Khalique et al., 2010), Protocol (Nikooghadam et al., 2008) and process optimization (Hwang and Yangz, 2002; Shen et al., 2006). Based on Elliptic Curve Digital Signature with the key short, fast and safe operation, etc., so In cryptography, it occupies a very important position, applications continue to expand. Another problem is that people are concerned about the security of digital signature verification (Rabah, 2005c) and application problems. In addition wavel algorithm (Chen et al., 2003) and digital signature agent (Khan et al., 2008) is relatively popular research.

When the learn and speak platform based on the campus network is developed, we need encrypt and validate the data as related to single sign-on and message digest. In the process of development, the above two Hash function can’t meet the requirements of system development.

According to the research of hash function, a secure hash function should meet the following conditions at least (Rivest, 2005):

Hash function is mainly used for integrity check and improving the validity of digital signatures. The process of hash function is generally shown in Fig. 1(Meneze et al., 1997).

Fig. 1:	General model for an iterated hash function

In this iterative process the arbitrary finite-length input message X is divided into many blocks of fixed length. The preprocessing which is typically known as padding involves appending extra bits as necessary to attain an overall bit-length which is a multiple of the block length. The length of the original message before padding is also included in the last block of the padded input for security reasons. The iterative processing starts with a predefined initial value; using hash function f turn to the message digest; at the final, an optional output transformation g is often used to harden the message digest further.

Based on the existing methods and after the project team to find the information again, the based on a high diophantine equation one-way hash encryption algorithm is proposed. It will be named RSH (Round Sheep Hash) hash algorithm. Repeated practice by more than one year, RSH function be realized and has been verified in our developed system. It is used to meet the system's single sign-on password encryption and meet the request of the digital signature and verifying the file transfer process integrity when users use system.

ENCRYPTION PROCESS OF RSH HASH ALGORITHM

A designed algorithm should have the function of encrypting arbitrary length string. This algorithm can be used for integrity check of data or digital signature. Furthermore, the speed of encryption algorithm is faster. This study presents a one-way hash encryption algorithm based on high diophantine equation.

Fig. 2:	The source string is transformed into the string

The length of encrypted password is 128 bits. In the process of encrypted algorithm, we will select 6 iterations as an optional mid-point. The following paper will introduce the encryption algorithm in details.

Step 1: Generate a 128 bits decimal digit from the source string. At first, the source string is transformed into ASCII decimal digit. If the encrypted source string is a12, the converted string is 974950. Figure 2 shows the general procedure.

When the lengths of number string is less than 128 bits, copy and connect the source string to the string end until the string length is greater than or equal to 128 bits, that is:

The above is the case that the length of the number string is less than 128 bits. But if the length of number string is greater than or equal to 128 bits, the number string is divided into the group of 16 bits. If the last group is less than 16 bits, 0 is filled until to 16 bits.

Then retain 16 bits after each two group is added (the highest 16 bits or the lowest 16 bits, or make by turns). By this time the group numbers are reduced by half, Fig. 3 shows the general procedure.

Fig. 3:	Each two group of 16-bit folded into a group of 16-bit

Fig. 4:	Fill position 0 of the source string with the fixed series

Fig. 5:	The 8 groups data of 16 bits cross multiply and retain the highest(lowest) 16 bits

Fig. 6:	Calculate and intercept the higher powers

If the total length is greater than or equal to 256, repeat these operations until the string length is less than 256.

A string that length is between 128 and 256 is left by extending or folding the string. If the string length is still greater than 128, the string is refolded. Add the front 128 bits to the back data that greater than 128 bits. The result reserve 128 bits.

Step 2: Filled the position 0 in the 128 bits with the fixed series, get a non-zero number string of 128 bits by filling. Such as: Source string is 92371904561020598…, fill position 0 of the source string with the sequence of numeric string (such as: 987654321987654321…), get a new string is 92371994561827598…. Fig. 4 shows the general procedure.

Step 3: Divided the string of 128 bits into 8 groups data of 16 bits (a₁,a₂,a₃,a₄,a₅,a₆,a₇,a₈). The adjacent two groups data is multiplied and retain the highest 16 bits (or retain the lowest 16 bits). The result after multiplying may overflow. Take the absolute value if the result is negative. The method of multiplication is shown in Fig. 5.

Setp 4: There is still a group of 16 bits (is separately a₁, a₂, a₃, a₄, a₅, a₆, a₇, a₈ ). Calculate the higher powers. Abnegate the highest array component in the results after calculating (bit size is between 1 and 16). Retain 8 array components that are from 2 to 9, namely 16*8=128 bits.

If the power of the first iteration is the fixed 8 prime numbers (97, 103, 89, 101, 87, 107, 91, 113) start from the second iteration, the selected power is take the second, the fourth, the sixth, the eighth, the tenth from the group number a₁, a₂, a₃, a₄, a₅, a₆, a₇, a₈. Figure 6 shows the general procedure. This method cannot determine the power of algorithm operation. So it can increase the security of the algorithm.

Setp 5: Repeat iteration until finish six iterations.

The final cipher-text is a number string of 128 bits after computing. Namely 16128 address spaces. Conflict rate is very low.

THE PERFORMANCE TEST OF RSH ALGORITHM

Security: We can see the step 4 is the key step from the above encryption process. The calculate need 20 msec by an Inter dual-core 1.6 GHz CPU. Because there have 6 iterations, the time of violence declassification is:

(1)

We can see the declassification is unrealistic from formula (1). If we known that the text is the mixed 5 bits string of lowercase letters and numbers, the time of violence declassification is:

(2)

It may reduce the computing time if we use fast exponentiation and strassen matrix multiplication. Now the step 4 needs to change into this algorithm, the numbers of iteration*20 ms ec/fast algorithm time (or add power). Then the time of declassification is still invariability. So the strength of this algorithm is still relatively high.

Complexity: The encryption time is about 100 msec that include the time of read encrypted string by test. Speed and encryption strength is a contradiction certainly. Algorithm selects 6 iterations as an optional mid-point after repeated test.

The complexity of algorithm: Set the source number string length len=2ⁿ (Source number string length is about 2 times for the source string length, because it is 0~255 that a byte is converted to decimal digit).There remains the string of 2 ^(n¯1) lengths after an iteration. Therefore the total addition number is approximately:

(3)

Namely it is the same magnitude to the log of the source string length. The speed is very fast. At the same time it also guarantees that the final result is related to each bit of the source string (even).