CN112910626A

CN112910626A - Data encryption and decryption method based on power operation

Info

Publication number: CN112910626A
Application number: CN201911217496.7A
Authority: CN
Inventors: 涂岩恺; 曹亚光
Original assignee: Xiamen Yaxon Networks Co Ltd
Current assignee: Xiamen Yaxon Networks Co Ltd
Priority date: 2019-12-03
Filing date: 2019-12-03
Publication date: 2021-06-04

Abstract

The invention discloses a data encryption method based on power operation, which comprises the following processes: generating a key C consisting of at least 10 digits; processing the secret key C to become a specific real number which is used as a base number a of the power operation; converting information H (plaintext) to be encrypted into 16-system representation, establishing a unique sequential relation K of characters A to F of 0-9, and recording the sequential value of each plaintext hexadecimal character in the K as i; and sequentially encrypting each plaintext character according to a corresponding rule to obtain a corresponding ciphertext, and sequentially splicing the ciphertexts to form a final encrypted numeric string. The invention also discloses a data decryption method based on the power operation, which is used for decrypting the data encrypted by the data encryption method.

Description

Data encryption and decryption method based on power operation

Technical Field

The invention belongs to the field of encryption, and particularly relates to a data encryption and decryption method based on power operation.

Background

The traditional encryption algorithm such as AES and ECC algorithm needs to be subjected to processes such as grouping operation, multi-round encryption and even nonlinear curve calculation, the operation is time-consuming, and the problem is more prominent particularly on some embedded systems with limited resources. Therefore, for an embedded system with limited resources, an encryption algorithm with certain security, easier implementation and lower consumption of computing resources is urgently needed.

Disclosure of Invention

The present invention is directed to a method for encrypting and decrypting data based on power operation, so as to solve the above problems. Therefore, the invention adopts the following specific technical scheme:

according to an aspect of the present invention, there is provided a data encryption method based on power operation, the data encryption method including the steps of:

the method comprises the following steps: generating a key consisting of at least 10 digits C ═ C₁C₂C₃...C_NWherein N is more than or equal to 10;

step two: processing the secret key C to become a specific real number which is used as a base number a of the power operation;

step three: converting the information H (plaintext) to be encrypted into 16-system representation, converting the information to be encrypted into a character string consisting of characters within the range of 0-9 and A-F, establishing a unique sequential relation K of the characters from 0 to 9 and A-F, and recording the sequential value of each hexadecimal character of the plaintext in the K as i;

step four: for a series of hexadecimal plaintext characters to be encrypted, m represents the sequence of one character in the plaintext, the mth character (starting from m being 1) is to be encrypted, the sequence of the character in K is taken as i, the base number is calculated by taking a as the power, i is the power, and a conversion value is calculated:

step five: expressing T by a scientific counting method, taking the first 20 effective numbers and recording as TE;

step six: calculation of C1+ C2+ … … + C_NThe first two digits of the arithmetic sum are modulo 10Fibonacci sequence d initial values B1, B2; if the arithmetic sum has only one bit, then B1 is 0 and B2 is the arithmetic sum; calculating the subsequent sequence value Bj ═ B_j-1+B_j-2)mod 10；

Step seven: subtracting the numbers with the Bj smaller than 5 by using 9 to ensure that the value of the Bj is larger than 5;

step eight: taking a random number r between 1 and 10, taking the r-th bit of TE, B_m*2-1Long digit strings are marked as secret text segments;

step nine: get B_m*2Long random numbers are recorded as random number segments, and the encrypted text segments and the random segments are spliced to form encrypted data;

step ten: and returning to the step four, wherein m is m +1, continuously processing all plaintext characters into encrypted data, and sequentially splicing into a final encrypted numeric string.

According to another aspect of the present invention, there is provided a data decryption method based on power operations for decrypting data encrypted via the data encryption method according to claim 1, comprising the steps of:

step 1: the decryptor holds the secret key C ═ C₁C₂C₃...C_N(N ≧ 10) and the order relationship K of hexadecimal characters;

step 2: processing the secret key C to become a specific real number which is used as a base number a of the power operation;

and step 3: for all characters in 0-9, A-F, corresponding to the sequence i in the sequence relation K, calculating all conversion values by taking a as the base number of the power calculation and i as the power:

and 4, step 4: all Ti is expressed by a scientific counting method, the first 20 effective numbers are taken and are marked as TEi;

and 5: taking the arithmetic sum of C1+ C2+ … … CN, taking the first two digits of the arithmetic sum as the initial values B1 and B2 of the 10Fibonacci sequence, if the arithmetic sum has only one digit, then B1 is 0, B2 is the arithmetic sum, calculating the subsequent sequence value B_j＝(B_j-1+B_j-2)mod 10；

Step 6: to B_jNumbers less than 5, subtracted by 9, ensure B_jThe value is more than 5;

and 7: decrypting the mth character, and taking the sum of S-1 + B1+ B2+. + B_2m-2If 2m-2 is 0 and S is 1, take B of the encrypted digit string from S bit_2m-1Long characters as single encrypted text segment followed by B_2mThe numeric string is a random number;

and 8: searching whether the ciphertext segment belongs to a subfield of Ti in all Ti, if so, corresponding to the ith character in the sequence K, and solving a single ciphertext;

and step 9: and (5) returning to the step 7 to circulate until S exceeds the length of the ciphertext digit string, namely, all ciphertexts are decoded, and finishing decryption to obtain the decrypted plaintext.

By adopting the technical scheme, the invention has the beneficial effects that: the encryption and decryption method has certain safety and can be applied to occasions of quick encryption and decryption.

Drawings

To further illustrate the various embodiments, the invention provides the accompanying drawings. The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the embodiments. Those skilled in the art will appreciate still other possible embodiments and advantages of the present invention with reference to these figures. Elements in the figures are not drawn to scale and like reference numerals are generally used to indicate like elements.

FIG. 1 is a flow chart of a data encryption method of the present invention;

fig. 2 is a flow chart of the data decryption method of the present invention.

Detailed Description

The invention will now be further described with reference to the accompanying drawings and detailed description.

As shown in fig. 1, the process steps of the data encryption method of the present invention are as follows:

step 100: the encryption method is a simplified encryption method, so that the key is required to be a number of 0-9. Generating a key consisting of at least 10 digits C ═ C₁C₂C₃...C_N(N ≧ 10), N is greater than 10 to ensure that the subsequent different power operation results have large random and non-repeating floating point values.

Step 102: and processing the key C to be a specific real number serving as a base number a of the power operation. Processing judges C1, and if C1 is 0, let C1 be 1 when the base number is transformed. Then, C is taken as the decimal part of a, and the integer part of a is set as 1. The purpose of this step is to avoid a being too close to the integer 1, since any power operation result with a base 1 is 1, so as to avoid reducing the randomness of the subsequent power operation result data.

Step 104: and converting the information H (plaintext) to be encrypted into a 16-system representation, converting the information to be encrypted into a character string consisting of characters within the range of 0-9 and A-F, and establishing a unique sequential relation K of the characters from 0-9 and A-F. The sequential value in K for each plaintext hexadecimal character is noted as i, and separate encryption of each plaintext character is performed, beginning with step 106.

Step 106: for a string of hexadecimal plaintext characters to be encrypted, m represents the sequence of one character in the plaintext, n represents the length of the plaintext character, and the mth character (starting from m ═ 1) to be encrypted takes the sequence of the character in K and is marked as i. Taking a as the base number of the power calculation, taking i as the power, calculating a transformation value:

step 108: t is expressed by scientific counting method, and the first 20 significant digits are taken and recorded as TE.

Step 110: calculation of C1+ C2+ … … + C_NThe first two digits of the arithmetic sum are modulo 10 initial values B1, B2 of the Fibonacci sequence (if the arithmetic sum has only one bit, then B1 is 0 and B2 is the arithmetic sum value). Calculating the subsequent sequence value Bj ═ B_j-1+B_j-2)mod 10

Step 112: and subtracting 9 from the number of Bj smaller than 5 to ensure that the value of Bj is larger than 5. Therefore, the length of the subsequent digit fetching string is ensured to be larger than 5, and the uniqueness and the non-repeatability of the subsequent digit fetching string can be ensured.

Step 114: taking a random number r between 1 and 10, taking the r-th bit of TE, B_m*2-1And long digit strings are marked as ciphertext segments.

Step 116: get B_m*2And long random numbers are recorded as random number segments, and the spliced encrypted text segments and the random segments are combined into encrypted data.

Step 118: and judging whether m is equal to n or not, if not, returning to the step 106, if m is equal to m +1, continuously processing all plaintext characters into encrypted data, and if so, sequentially splicing the encrypted data of all plaintext characters into a final encrypted digital string.

The data encryption method is described below as an example:

randomly generating a key consisting of at least 10 digits, assuming that C ═ C₁C₂C₃...C_N＝0123456789。

The base number of the power operation is generated, and the key C is processed, so that C1 is 0, and C1 is 1 when the base number is converted. C is set as a fractional part and an integer part is set to 1. Therefore, the base of the power operation is "a" 1.1123456789.

Suppose that hexadecimal representation of encrypted information to be encrypted is 0xA6, and the order relation K of hexadecimal characters is { a, B, C, D, E, F,0,1,2,3,4,5,6,7,8,9 }. For a character a to be encrypted, since the order in the order relation K is 1, a base number calculated in a power of a and 1 in a power of a, a conversion value is calculated:

the T1 is expressed by scientific counting method, the first 20 significant digits are taken and recorded as TE₁＝25002719357763596673。

Taking the arithmetic sum of C1+ C2+ … … CN 1+1+2+3+4+5+6+7+8+9 as 46, taking the first two digits of the arithmetic sum as the initial value of the modulo 10Fibonacci sequence, B1 as 4, and B2 as 6. Calculating the subsequent sequence value B₃＝(B₂+B₁)mod 10＝0；B4＝(B₃+B₂)mod 10＝6；B5＝(B₄+B₃)mod 10＝6；B6＝(B₅+ B4) mod 10 ═ 2, and so on.

To B_jNumbers less than 5, subtracted by 9, ensure B_jThe value is greater than 5. The new Fibonacci sequence value is B1-5, B2-6, B3-9, B4-6, B5-6, B6-7, … ….

Taking an arbitrary random number r between 1 and 10, assuming r is 9, and TE₁From bit 9, B₁The 5 long digit string is used as the ciphertext segment of the processing result, which is 35776.

Random generation of B₂The combination of the cipher and random number segments into a final encryption result of 35776987487 is a random number segment of 6 bits length, say 987487.

The next character 6 continues to be encrypted, with the order i in the order relation K being 13, and the second encrypted character m being 1.

Calculating a transformation value:

expressed by scientific counting method, the first 20 significant digits are taken and recorded as TE₁₃＝89714886258396854164。

Taking an arbitrary random number r between 1 and 10, assuming that r is 3, taking the 3 rd bit of TE, B_2*m-1B3 is a 9-long string of numbers that results in a transformed ciphertext fragment, i.e., 714886258.

Random generation of B_2*mB4 is a random number segment of 6 bits length, assumed to be 159876, which is combined into a final encryption result of 714886258159876.

The encryption results are concatenated sequentially so that the final ciphertext encrypted for plaintext 0xA6 is 35776987487714886258159876.

As shown in fig. 2, the process steps of the data decryption method of the present invention are as follows:

step 200: the decryptor holds the secret key C ═ C₁C₂C₃...C_N(N ≧ 10), and a sequential relationship K of hexadecimal characters, and the ciphertext length is L.

Step 202: and processing the key C to be a specific real number serving as a base number a of the power operation. Processing judges C1, and if C1 is 0, let C1 be 1 when the base number is transformed. Then, C is taken as the decimal part of a, and the integer part of a is set as 1. The purpose of this step is to avoid a being too close to the integer 1, so as to avoid reducing the randomness of the result data of the subsequent power operation.

Step 204: all characters in 0-9, A-F correspond to the sequence i in the sequence relation K. Taking a as the base number of the power calculation and i as the power, calculating all conversion values:

step 206: all Ti are expressed in scientific notation, taking the first 20 significant digits and recording as TEi.

Step 208: c1+ C2+ … … CN arithmetic sum, modulo 10Fibonacci sequence initial values B1, B2 with the first two digits of the arithmetic sum (if the arithmetic sum has only one bit, B1 is 0, B2 is the arithmetic sum). Calculating the subsequent sequence value B_j＝(B_j-1+B_j-2)mod 10。

Step 210: to B_jNumbers less than 5, subtracted by 9, ensure B_jThe value is greater than 5. Therefore, the length of the subsequent digit string is ensured to be more than 5, and uniqueness and non-repeatability are ensured.

Step 212: decrypting the mth character, and taking the sum of S-1 + B1+ B2+. + B_2m-2(if 2m-2 is 0, S is 1) taking the encrypted digit string starting from the S bit, B_2m-1Long characters as single encrypted text segment, followed by B_2mThe numeric string is a random number.

Step 214: in all Ti, the ciphertext field is searched whether it belongs to the subfield of Ti, and if so, the ciphertext field corresponds to the ith character in the sequence K, so that a single ciphertext is solved.

Step 216: and judging whether S is larger than L, if not, if m is m +1, returning to the step 212, and if so, indicating that all the ciphertext is decoded, completing decryption and obtaining decrypted plaintext.

The data decryption method is described below as an example:

for ciphertext 35776987487714886258159876, its length L is 26. According to the fact that the decryption party holds the secret key C as C ═ C₁C₂C₃...C_N＝0123456789 and the endianness K is K ═ a, B, C, D, E, F,0,1,2,3,4,5,6,7,8,9, and all the characters are calculated

To obtain

T1＝2.500271935776359667311159723011E-2，

T2＝2.781166683835771992705810099639E-2，

T3＝3.093618743065363453331950183258E-2，

T4＝3.441173441012806377571776593657E-2，

T5＝3.827774407456039213654327568551E-2，

T6＝4.257808321937733161017345149162E-2，

T7＝4.73615468849189755651888180462E-2，

T8＝5.26824120234593780465524670163E-2，

T9＝5.860105336832444459976415972771E-2，

T10＝6.518462849324398608379010303221E-2，

T11＝7.250783983516176576371565444246E-2，

T12＝8.065378232701547842976306662736E-2，

T13＝8.971488625839685416476310431376E-2，

T14＝9.979396606253272957152770772555E-2，

T15＝0.11100538692995152892871109416014，

T16＝0.12347636248615412019030013173553。

All Ti are expressed by scientific notation, taking the first 20 significant figures, and obtaining:

TE1＝25002719357763596673，

TE2＝27811666838357719927，

TE3＝30936187430653634533，

TE4＝34411734410128063775，

TE5＝38277744074560392136，

TE6＝42578083219377331610，

TE7＝47361546884918975565，

TE8＝52682412023459378046，

TE9＝58601053368324444599，

TE10＝65184628493243986083，

TE11＝72507839835161765763，

TE12＝80653782327015478429，

TE13＝89714886258396854164，

TE14＝99793966062532729571，

TE15＝11100538692995152892，

TE16＝12347636248615412019。

from the key C, B1-5, B2-6, B3-9, B4-6, B5-6, B6-7, … … are calculated as described in the encryption step.

Starting with the m-1 character, S-B, decryption according to the ciphertext 35776987487714886258159876_2m-2Then, from the encrypted string, a string having a total length of B1 ═ 5, i.e., the ciphertext fragment 35776 of the first character, starting from bit 1 is extracted. 35776 is searched in TE 1-TE 16, and it is found that there is a character string 35776 in TE1, which indicates that the first character corresponds to TE1, i.e. corresponds to the first bit in the sequence K, the reverse search sequence K is { A, B, C, D, E, F,0,1,2,3,4,5,6,7,8,9}, the sequence number 1 is A, i.e. the first character is decrypted as A.

Similarly, when the m-th character is decrypted, S-1 + B1+ B2-1 +5+ 6-12, then from the encrypted character string, a character string with a total length of B3-9 starting from the 12 th bit is extracted, that is, the encrypted text segment corresponding to the 2 nd character is 714886258. 714886258 is searched in TE 1-TE 16, and it is found that a character string 714886258 exists in TE13, the 2 nd character corresponds to TE13, namely, the 13 th bit in the sequence K is found, the reverse check sequence K is { A, B, C, D, E, F,0,1,2,3,4,5,6,7,8,9}, the 13 th character is 6, namely, the 2 nd encrypted character is decrypted to 6.

The m-th character is decrypted, S-1 + B1+ B2+ B3+ B4-1 +5+6+9+ 6-27, S is found to exceed the ciphertext length L-26, which indicates that the ciphertext is completely decrypted, and the decryption is finished, namely, the plaintext is 0xA 6.

While the invention has been particularly shown and described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims

1. A data encryption method based on power operation, the data encryption method comprising the steps of:

step six: calculation of C1+ C2+ … … + C_NThe first two digits of the arithmetic sum are modulo 10Fibonacci sequence initial values B1, B2; if the arithmetic sum has only one bit, then B1 is 0 and B2 is the arithmetic sum; calculating the subsequent sequence value Bj ═ B_j-1+B_j-2)mod 10；

2. The data encryption method based on power operation as claimed in claim 1, wherein the specific process of step two is: judging C1, if C1 is 0, making C1 be 1; then, C is taken as the decimal part of a, and the integer part of a is set as 1.

3. A data decryption method based on power operations, for decrypting data encrypted by the data encryption method according to claim 1, comprising the steps of:

4. The method for decrypting data based on power-of-law operation as claimed in claim 3, wherein the step 2 comprises the following specific processes: judging C1, if C1 is 0, making C1 be 1; then, C is taken as the decimal part of a, and the integer part of a is set as 1.