CN106027227A - Fermat number number-theoretic transform and SAFER (Secure And Fast Encryption Routine) cipher algorithm combined block encryption method - Google Patents

Abstract

The invention provides a Fermat number number-theoretic transform and SAFER (Secure And Fast Encryption Routine) cipher algorithm combined block encryption method. The method comprises seven rounds of encryption; two groups of subkeys are used by each round of the encryption, and the length of the subkeys is equal to the length of a block cipher; fifteen groups of the subkeys are generated by a key extending algorithm selected by a user, and the plaintext length of block encryption is 16 bytes, namely 128 bits; results generated after the seven rounds of the encryption needs to be carried out with a "mixed exclusive or/modular addition" operation with the fifteenth group of the subkeys; each round of the encryption is divided into a confusion layer and a diffusion layer; at the confusion layer, the "mixed exclusive or/modular addition" operation is carried out firstly, then a nonlinear transform is carried out, and at last the "mixed exclusive or/modular addition" operation is carried out again and the results are output to the diffusion layer; and the fast number-theoretic transform whose the length is 16 is adopted by the diffusion layer. According to the Fermat number number-theoretic transform and SAFER cipher algorithm combined block encryption method provided by the invention, on the premise of guaranteeing the encryption security and the high efficiency, the computation complexity is further reduced

Description

The block encryption that a kind of Fermat number number theoretic transform combines with SAFER cryptographic algorithm Method

Technical field

The present invention relates to a kind of block encryption algorithm, it is possible to realize the encryption method of data or image simply, safely.

Background technology

Block cipher, as an important branch of symmetric cryptography, plays highly important work at information security field With, the common development promoting block cipher theoretical of research to the design and analysis of block cipher.Its design derives from Shannon The classic paper Communication Theory of Secret System that 1949 deliver, the research of modern block cipher Start from 20 century 70 mid-terms, the history of existing more than two decades.Research in early days is entered substantially about data encryption standards (DES) OK, being proposed need to be to the password of similar DES, such as, LOKI, FEAL etc..Block cipher is theoretical and application develop rapidly benefit The end of the nineties, the AES of the U.S. plans and the NESSIE plan in Europe at the beginning of 21 century.

SAFER (Secure And Fast Encryption Routine) series of packets cryptographic algorithm includes SAFER K- 64, SAFER K-128, SAFER SK-64, SAFER SK-128, SAFERSK-40, SAFER+ and SAFER++.SAFER series Password has more following characteristics: (1) they be all the algorithm of byte-oriented, Encrypt and Decrypt and key schedule use all Being the byte computing to byte, this makes it advantageous in the application of the aspects such as Smart card；(2) round function encrypted uses " replacement-linear transformation " structure, in iteration each takes turns, the reversible letter first wheel input action one controlled by respective loops Number S, is then applied to a reversible linear transformation LP；(3) in key schedule, employ " key deviation ", i.e. To each sub-key plus a constant, it is to avoid produce weak key.

SAFER++ is state-of-the-art algorithm in SAFER series of cryptographic algorithm, has above all of advantage, and Diffusibility optimum in SAFER series of cryptographic algorithm and minimum complexity, but in the realistic case, it may be desirable to simpler AES be encrypted application.

Summary of the invention

Cryptographic security, high efficiency and computation complexity cannot be taken into account not in order to overcome existing block cipher Foot, the present invention provides a kind of under ensureing cryptographic security and high efficiency premise, reduces the Fermat number of computation complexity further The grouping encryption method that number theoretic transform combines with SAFER cryptographic algorithm.

The technical solution adopted for the present invention to solve the technical problems is:

The grouping encryption method that a kind of Fermat number number theoretic transform combines with SAFER cryptographic algorithm, described block encryption side Method includes that 7 take turns encryption, and each wheel uses two groups of sub-keys, and the length of sub-key is equal with the length of block cipher；15 groups of sons are close Key is produced by customer option key expansion algorithm, and the length of the plaintext of block encryption is 16 bytes that is 128；Encryption is taken turns the 7th The result of rear generation needs to do " mixing XOR/mould to add " computing with the 15th group of sub-key；

Often wheel encryption is divided into and obscures layer and diffusion layer, first passes around " mixing XOR/mould adds " computing obscuring layer, then enters Line nonlinearity converts, and finally again passes by " hybrid guided mode adds/XOR " computing and outputs results to diffusion layer, and diffusion layer uses length It it is the quick Fermat number transform of 16.

Further, the result produced after taking turns encryption the 7th needs " to add " with the 15th group of sub-key phase, " adding " operation now Refer to the 1st, 4,5,8,9,12,13,16 bytes add by bit mould 2, i.e. XOR between byte, the 2nd, 3,6,7,10,11,14, 15 byte moulds 256 add；Owing to transform length is the multiple of 4, the structure of therefore this conversion uses the butterfly structure of radix-4FFT, Output through Fermat number transform is the output result taking turns encryption.

Preferably, when the figure place inputting data is 8, the check figure of described quick Fermat number transform is 2, and modulus is 257.

Further, described diffusion layer solves Fermat number by the extra method increasing memory space storage record symbol Conversion overflow problem；

When 256 this value occurs, need the location records symbol of a byte, the 3bits in the middle of location records symbol For recording the encryption round number i that numerical value occurs, span 1～7, it is 001 with binary representation₂To 111₂；Rear 4bits remembers The byte location j that record numerical value occurs, span 0～15, with 0001₂To 1111₂Represent the 1st～15 bytes, and with binary system 0000₂Represent the 16th byte；Record is replaced 256 after numerical value position, and the numerical value of replacement is preset by encryption end, Span is from 0 to 255.

Further, in described diffusion layer, if repeatedly there are 256 numerical value in an AES, then need multiple continuously Location records symbol, now with the extreme higher position 1 of location records symbol represent this record symbol be in this AES Later record symbol, forms record symbol block with it for interval.If this time the most there are not 256 these numbers in AES Value, then represent with zero record symbol；Zero record symbol has 16 bits and constitutes, and former 4 bits are as zero record symbol Mark, value of statistical indicant is 1000₂After, 12bits represents the encryption number of times not occurring 256 numerical value continuously, and span is from 1 To 4095；When 256 numerical value do not have occurrence number to reach 4096 continuously, then zero record symbol of another 16bits is needed to remember Record；Quickly Fermat number transform is as diffusion layer, needs location records symbol and the support of zero record symbol, during transmission ciphertext, needs Record symbol section it is connected on ciphertext end, then to need during decoding to carry out according to record symbol section.

The a length of 128bits of described block cipher.

The technology of the present invention is contemplated that: often wheel encryption is divided into and obscures layer and diffusion layer, and total of three step composition one is taken turns and added Close, represent wheel number to be encrypted with i.The most often take turns data x to be inputted and sub-key K_2i-1Do once " mixing XOR/mould adds " Computing.Then, obtained result uses formula through a nonlinear transformation, the 1st, 4,5,8,9,12,13,16 byte datas (1), the 2nd, 3,6,7,10,11,14,15 byte datas use formula (2).Finally, by result and the sub-key of nonlinear transformation K_2iPhase " adds ", and adding here refers to that the 1st, 4,5,8,9,12,13,16 byte moulds 256 are added, and the 2nd, 3,6,7,10,11,14,15 Byte adds by bit mould 2, and this computing is referred to as " hybrid guided mode adds/XOR " computing, and acquired results is the output obscuring layer.

Diffusion layer takes the Fermat number Fast transforms of a length of 16.The figure place of input data is 8, can select Fermat number Conversion modulus M=257, check figure a=2.Owing to transform length is the multiple of 4, therefore the structure of this conversion can use radix- The butterfly structure of 4FFT is accelerated to calculate speed.Output through Fermat number transform is the output result taking turns encryption.

The result obtained due to Fermat number direct transform is between 0 to 256, and the bit wide of AES only has 8bit.When just When the number that conversion obtains is equal to 256, spilling can be produced more than bit wide.Record symbol is stored below by the extra memory space that increases Number method solve this problem.When 256 this value occurs, need the location records symbol of a byte.Location records 3bits in the middle of symbol, for recording the encryption round number i that numerical value occurs, span 1～7, is 001 with binary representation₂ To 111₂.The byte location j that rear 4bits record numerical value occurs, span 0～15, we are with 0001₂To 1111₂Represent the 1st ～15 bytes, and with Binary Zero 000₂Represent the 16th byte.Record is replaced 256 after numerical value position, the numerical value of replacement Being preset by encryption end, span is from 0 to 255.

If 256 numerical value repeatedly occurs in an AES, then need multiple continuous print location records symbol, now with position The extreme higher position 1 putting record symbol represents that this record symbol is last record symbol in this AES, between with it being Every forming record symbol block.If this time 256 these numerical value does not the most occur in AES, then represent with zero record symbol, As Fig. 4 shows the structure of zero record symbol.Zero record symbol has 16 bits and constitutes, and former 4 bits are as zero record symbol Mark, value of statistical indicant is 1000₂After, 12bits represents the encryption number of times not occurring 256 numerical value continuously, and span is permissible From 1 to 4095.When 256 numerical value do not have occurrence number to reach 4096 continuously, then need zero record symbol of another 16bits Carry out record.Thus, Fermat number transform, as diffusion layer, needs location records symbol and the support of zero record symbol.Transmission ciphertext Time, need record symbol section to be connected on ciphertext end, then need during decoding to carry out according to record symbol section.

Deciphering is the inverse process of encryption.The first step of deciphering is such as the final step of encryption.Difference is what it was carried out Computing is " hybrid guided mode adds/XOR " computing.Taking turns decrypting process subsequently into seven, often wheel deciphering first passes through the inverse of Fermat number transform Conversion.

Beneficial effects of the present invention is mainly manifested in: on the premise of ensureing that cipher round results is good, it is proposed that a kind of ratio The new block encryption algorithm that the computation complexity of SAFER++ is lower.By the computation complexity of this AES is analyzed, And randomizing data ability and anti-attack ability are tested, it was demonstrated that it is low good with safety that this algorithm has computation complexity The feature such as good.

Accompanying drawing explanation

Fig. 1 is the population structure of Safer-Fermat AES, K₁,K₂,…,K₁₅Son needed for representing often wheel encryption is close Key.

The one of Fig. 2 Safer-Fermat algorithm takes turns encryption signal, represents and add by bit mould 2 in figure ,+represent mould 256 Adding, ex represents that exponent arithmetic, lg represent logarithm operation.16-FNT represents the Fermat number transform of a length of 16.

Fig. 3 Fermat number transform of the present invention desired position record symbol structure.

Zero record symbol structure needed for Fig. 4 Fermat number transform of the present invention.

Fig. 5 is that the one of Safer-Fermat algorithm takes turns deciphering signal, and symbol "-" represents that mould 256 subtracts.

Fig. 6 be algorithm once encryption with deciphering design sketch, wherein (a) for input data, (b) be the 7th take turns encryption defeated Go out；(c) be the 7th take turns deciphering output.

Fig. 7 is the success rate test figure of AES.

Fig. 8 is the Randomness test figure of AES.

Fig. 9 is the bright ciphertext independence test figure of AES.

Figure 10 is the diffusibility test figure of AES.

Detailed description of the invention

The invention will be further described below in conjunction with the accompanying drawings.

Reference Fig. 1～Figure 10, the grouping encryption method that a kind of Fermat number number theoretic transform combines with SAFER AES, Altogether needing 7 to take turns encryption, each wheel uses two groups of sub-keys, and the length of sub-key is equal with the length of block cipher.Sub-key (K₁,K₂,…,K₁₅) produced by customer option key expansion algorithm, the present invention use the sub-key identical with SAFER++ generate Method (see the nonlinear Cryptanalysis of Wu Wenling, Ma Hengtai, Tang Liu English .5 wheel SAFER++. electronic letters, vol, 2003,7:961- 965.).The length of the plaintext of block encryption is 16 bytes that is 128.The result produced after taking turns encryption the 7th needs and sub-key K₁₅Phase " adds ", " adding " now operation refers to the 1st, 4,5,8,9,12,13,16 bytes add by bit mould 2, i.e. XOR fortune between byte Calculating, the 2nd, 3,6,7,10,11,14,15 byte moulds 256 add.

The length of the plaintext of block encryption is 16 bytes that is 128.The result produced after taking turns encryption the 7th needs close with son Key K₁₅Phase " adds ", " adding " now operation refer to sub-key and the 1st, 4,5,8,9,12,13,16 byte datas add by bit mould 2, I.e. XOR between byte；Sub-key and the 2nd, 3,6,7,10,11,14,15 byte data moulds 256 add.Above-mentioned and K₁₅Operation Computing is called " mixing XOR/mould adds " computing.

In the present invention, the often wheel AES of new algorithm is as in figure 2 it is shown, represent in figure and add by bit mould 2 ,+represent mould 256 add, and ex represents that exponent arithmetic, lg represent logarithm operation.Exponent arithmetic function and logarithm operation function are unique in encryption round Nonlinear transformation.If directly doing non-linear function transformation in a program to need to consume substantial amounts of resource.Table look-up so using The mode of method obtains function return value.The exponential transform obscured in byte and logarithmic transformation can be previously stored, from And reach the purpose of simplified operation.

We represent encryption round number with i below, and the often wheel encryption of Fig. 2 includes three steps, and wherein obscuring layer is the first two Step.In each of the steps, it will be assumed that the data of input are x.

Obscure layer: input data x and sub-key K_2i-1Do the most aforementioned " mixing XOR/mould adds " computing, then obtained Result through nonlinear transformation (step one).Wherein the 1st, 4,5,8,9,12,13,16 byte datas are by following non-linear change Exchange the letters number is tried to achieve:

x→45^xMod257 (during x=128, arranges 45¹²⁸Mod 257=0) (1)

2nd, 3,6,7,10,11,14,15 byte datas are tried to achieve by following non-linear transform function:

x→log₄₅Xmod257 (during x=0, arranges log₄₅0mod 257=128) (2)

Finally, by the result of nonlinear transformation and sub-key K_2iPhase " adds " (step 2), adding here refer to sub-key with 1st, 4,5,8,9,12,13,16 byte data moulds 256 are added；Sub-key and the 2nd, 3,6,7,10,11,14,15 byte datas by Bit mould 2 adds, and this computing is referred to as " hybrid guided mode adds/XOR " computing, and acquired results is the output obscuring layer (chaotic layer).

Diffusion layer: take the Fermat number Fast transforms (16-FNT) (step 3) of a length of 16

$X_k=\underset{n=0}{\overset{15}{\Σ}}{x}_n{2}^{nk}\left(\mathrm{mod}257\right),k=0,1,...,15---\left(3\right)$

X in formula_nNth data, X is inputted for Fermat number transform module_kKth data are exported for Fermat number transform module.Defeated The bit wide entering data is 8, can select Fermat number transform modulus M=257, check figure a=2.Due to transform length be 4 times Number, therefore the structure of this conversion can use the butterfly structure of base 4 (radix-4) FFT to accelerate to calculate speed.Through Fermat number The output of conversion is the i-th output result taking turns encryption.

The result obtained due to Fermat number direct transform is between 0 to 256, and the bit wide of AES only has 8bit.When just When the number that conversion obtains is equal to 256, spilling can be produced more than bit wide.Store up below by extra 8 bit storage space that increase Deposit record symbol to solve this problem.When 256 this value occurs, need the location records symbol of a byte, such as Fig. 3 exhibition Show the structure of location records symbol.Record symbol value S_pFormula is as follows:

S_p=h × 2⁷+i×2⁴+j (4)

In formula, h is end mark flag bit numerical value.3bits in the middle of location records symbol overflows appearance for recording numerical value Encryption round number i, span 1～7, it is 001 with binary representation₂To 111₂.Rear 4bits record numerical value overflows the word occurred Joint position j, span 0～15, we are with 0001₂To 1111₂Represent the 1st～15 bytes, and with Binary Zero 000₂Represent the 16 bytes.Record is replaced 256 after numerical value position, and the numerical value of replacement is preset by encryption end, and span is from 0 To 255.

Such as the 7th takes turns existence 256 these values in the second byte, then the numerical value of location records symbol is 01110010₂.As Really repeatedly there are 256 numerical value in an AES, then need multiple continuous print location records symbol, now with rearmost position record The extreme higher position 1 of symbol represents that this record symbol is last record symbol in this AES, is formed with it for interval Record symbol block.If this time 256 these numerical value does not the most occur in AES, then represent with zero record symbol, such as Fig. 4 exhibition Show the structure of zero record symbol.Zero record symbol has 16 bits and constitutes, and former 4 bits are as the mark of zero record symbol Will, value of statistical indicant is 1000₂After, 12bits represents the encryption number of times not occurring 256 numerical value continuously.According to bit wide, take Value scope can be from 1 to 4095.When 256 numerical value do not have occurrence number to reach 4096 continuously, then need another 16bits's Zero record symbol carrys out record.Thus, Fermat number transform as diffusion layer, need location records symbol and zero record symbol Hold.During transmission ciphertext, the application is connected on ciphertext end record symbol section, then needs to carry out according to record symbol section during decoding.

Deciphering is the inverse process of encryption.The first step of deciphering is such as the final step of encryption.Difference is what it was carried out Computing is " hybrid guided mode adds/XOR " computing.Taking turns decrypting process subsequently into seven, often wheel deciphering first passes through the inverse of Fermat number transform Conversion.

Taking turns deciphering structure as Fig. 5 illustrates one, deciphering is the inverse process of encryption, and the first step of deciphering is as last in encryption One step, difference is that its computing carried out is " hybrid guided mode adds/XOR " computing.Symbol "-" in figure represents that mould 256 subtracts.So Decrypting process is taken turns in rear entrance seven, and often wheel deciphering needs the inverse transformation of Fermat number transform, and transformation for mula is as follows

$x_n=241\×\underset{k=0}{\overset{N-1}{\Σ}}{X}_k{2}^{-nk}\left(\mathrm{mod}257\right),n=0,1,...,N-1---\left(5\right)$

According to the cryptographic structure of SAFER++, one transformation matrix needs 3 displacements and 16 sub-additions, and one takes turns encryption needs Wanting 8 transformation matrixs, the most whole ciphering process needs 168 displacements and 896 sub-additions.Quick due to a length of 2 power sides Fermat number transform can improve speed to use base 2 type FFT form, and can use radix-4FFT during a length of 4 power side It is accelerated calculating.The addition number of times of the Radix-4FFT of a length of N is Nlog2N, and multiplication number of times m_r4For

$m_{r4}=\frac{3}{8}N{\log }_{2}N---\left(6\right)$

For Fermat number transform, multiplication can use displacement to replace, so at the Radix-4FFT of a length of 16 In form Fermat number transform, required addition number of times has 64 times, shift count 24 times.Seven take turns encryption needs 448 sub-additions and 168 times altogether Displacement, complexity is lower than conventional cryptography structure.

Safer-Fermat AES is carried out simulating, verifying, 16 data 1 of a width of 8bit of input bit, 2,3,4,5, 6,7,8,9,10,11,12,13,14,15,16.After seven take turns encryption, encrypted data is 154,184,235,159,55, 113,166,34,183,124,231,100,62,174,201,191.Encrypting and decrypting exports as shown in Figure 6.In the drawings through seven The deciphering output data of wheel are 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, represent successful decryption.

100 groups of data of stochastic generation, test encryption and decryption success rate, represent correct encryption and decryption with 1, represent with 0 and add Decryption error.Test result as it is shown in fig. 7, all success.Fig. 8 is that the frequency balance of Safer-Fermat AES is surveyed Trying, shared by Hamming weight, the average proportions of length of the plaintext is 50.16%, and close to 50%, cipher round results is good.Fig. 9 is invention The bright ciphertext test independence test of algorithm, vertical coordinate, for taking ratio (occupy proportion), illustrates often to organize bright close in figure Literary composition Hamming distance accounts for the average proportions 50.13% of one group of length of the plaintext, and close to 50%, the bright ciphertext independence of algorithm is good. Figure 10 gives its diffusibility test result, vertical coordinate for change ratio (change proportion), figure illustrates each group close The average proportions 50.224% of literary composition and the Hamming distance of previous group ciphertext with one group of length of the plaintext, close to 50%, algorithm bright Literary composition diffusibility is good.

Fig. 1 is the population structure of Safer-Fermat AES.Each wheel uses two groups of sub-keys, the length of sub-key Equal with the length of block cipher.Sub-key (K₁,K₂,…,K₁₅) produced by customer option key expansion algorithm.Block encryption Length of the plaintext is 16 bytes that is 128." mixing XOR/mould add " computing i.e. with sub-key K₁₅Phase " adds ", " adding " behaviour now Refer to the 1st, 4,5,8,9,12,13,16 bytes add by bit mould 2, i.e. XOR between byte, the 2nd, 3,6,7,10,11, 14,15 byte moulds 256 add.

In Fig. 2, represent and add by bit mould 2 ,+representing that mould 256 adds, ex represents that exponent arithmetic, lg represent logarithm operation.Refer to Number operation function is unique nonlinear transformation in encryption round with logarithm operation function.If directly doing functional transformation in a program Need to consume substantial amounts of resource.So using the mode of look-up table to obtain function return value.The index obscured in byte and Logarithm operation can carry out calculated in advance storage, thus reaches the purpose of simplified operation.

Fig. 3 is Fermat number transform desired position of the present invention record symbol structure.Whole record symbol has 8bit bit wide. 3bits in the middle of location records symbol is for recording the encryption round number i that numerical value occurs, span 1～7, with binary representation It is 001₂To 111₂.The byte location j that rear 4bits record numerical value occurs, span 0～15, we are with 0001₂To 1111₂ Represent the 1st～15 bytes, and with Binary Zero 000₂Represent the 16th byte.Record is replaced 256 after numerical value position, replaces The numerical value changed is preset by encryption end, and span is from 0 to 255.

Fig. 4 is zero record symbol structure needed for algorithm.4 bits were as the mark of zero record symbol in the past, and value of statistical indicant is 1000₂After, 12bits represents the encryption number of times not occurring 256 numerical value continuously, and span can be from 1 to 4095.When 256 When numerical value does not has occurrence number to reach 4096 continuously, then zero record symbol of another 16bits is needed to carry out record.

One of Safer-Fermat algorithm shown in Fig. 5 takes turns deciphering.Symbol "-" represents that mould 256 subtracts.

Fig. 6 carries out simulating, verifying to Safer-Fermat AES, 16 data 1 of a width of 8bit of input bit, and 2,3, 4,5,6,7,8,9,10,11,12,13,14,15,16.After seven take turns encryption, encrypted data is 154,184,235, 159,55,113,166,34,183,124,231,100,62,174,201,191, deciphering reverts to 1 later, and 2,3,4,5,6,7, 8,9,10,11,12,13,14,15,16。

Fig. 7 is the test of algorithm success rate, and encryption and decryption success rate is tested, represented with 1 by 100 groups of data of stochastic generation Correct encryption and decryption, represents encryption and decryption mistake with 0.Through testing us it appeared that the success rate of algorithm reaches 100%, demonstrate The correctness of algorithm

Fig. 8 is algorithmic theory of randomness test." 0 ", " 1 " balance by frequency test test ciphertext.Stochastic inputs is in plain text 10000 groups, then statistics generates the ratio of length of the plaintext shared by the Hamming weight often organizing ciphertext.Through test, Hamming weight with The average proportions of length of the plaintext is 50.16%.Close to 50%.New AES " 0 ", " 1 " balance are good.Its randomness i.e. Meet the requirement of general AES.

Fig. 9 is AES bright ciphertext independence test result.Input first group 16 0 in plain text, then constantly to first Individual byte adds 1, the most at most can obtain 256 groups in plain text.When first character joint is equal to 255, start constantly second word Joint adds 1.Thus obtained plaintext group has certain statistical property, and statistics is often organized bright ciphertext Hamming distance and accounted for one group of length of the plaintext Ratio.Through the emulation testing average proportions of 10000 times 50.13%, it was demonstrated that the bright ciphertext independence of this algorithm is good.

Figure 10 is diffusibility test.I.e. test the effect of new algorithm diffusion layer Fermat number transform.From data conversion effective Property consider, block encryption algorithm should be sensitive to change in plain text, i.e. in plain text snowslide phenomenon.In testing according to block cipher Avalanche criterion, change the arbitrary bit of clear packets, changing of the only about half of bit of ciphertext block should be caused.Input is initial In plain text 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16.Certain in the initial 128bit in plain text of the most random change One bit, generates another group in plain text.Change previous group any bit in plain text the most every time.By each group of ciphertext of statistics with The Hamming distance of previous group ciphertext and the ratio of one group of length of the plaintext, test diffusibility in plain text.Test through 10000 times, Ratio is 50.224%.Prove that the plaintext diffusibility of this algorithm is good.

Claims (6)

1. the grouping encryption method that a Fermat number number theoretic transform combines with SAFER cryptographic algorithm, it is characterised in that: described point Group encryption method includes that 7 take turns encryption, and each wheel uses two groups of sub-keys, and the length of sub-key is equal with the length of block cipher； 15 groups of sub-keys are produced by customer option key expansion algorithm, and the length of the plaintext of block encryption is 16 bytes that is 128；? 7 take turns encryption after produce result need do " mixing XOR/mould to add " computing with the 15th group of sub-key；Often wheel encryption is divided into and obscures layer With diffusion layer, first pass around " mixing XOR/mould adds " computing obscuring layer, then carry out nonlinear transformation, finally again pass by " hybrid guided mode adds/XOR " computing also outputs results to diffusion layer, and diffusion layer uses the quick Fermat number transform of a length of 16.

2. the grouping encryption method that Fermat number as claimed in claim 1 number theoretic transform combines with SAFER cryptographic algorithm, it is special Levy and be: the result produced after taking turns encryption the 7th needs " to add " with the 15th group of sub-key phase, " adding " now operate and refer to the 1st, 4,5,8,9,12,13,16 bytes add by bit mould 2, i.e. XOR between byte, the 2nd, 3,6,7,10,11,14,15 byte moulds 256 add；Owing to transform length is the multiple of 4, the structure of therefore this conversion uses the butterfly structure of radix-4FFT, through Fermat The output of transformation of variables is the output result taking turns encryption.

3. the grouping encryption method that Fermat number as claimed in claim 2 number theoretic transform combines with SAFER cryptographic algorithm, it is special Levy and be: when the figure place inputting data is 8, the check figure of described quick Fermat number transform is 2, and modulus is 257.

4. the block encryption side that the Fermat number number theoretic transform as described in one of claims 1 to 3 combines with SAFER cryptographic algorithm Method, it is characterised in that: described diffusion layer solves Fermat number by the extra method increasing memory space storage record symbol and becomes Change overflow problem；

When there is 256 this value, needing the location records symbol of a byte, the 3bits in the middle of location records symbol is used for The encryption round number i that record numerical value occurs, span 1～7, it is 001 with binary representation₂To 111₂；Rear 4bits records number The byte location j that value occurs, span 0～15, with 0001₂To 1111₂Represent the 1st～15 bytes, and with Binary Zero 000₂ Represent the 16th byte；Record is replaced 256 after numerical value position, and the numerical value of replacement is preset by encryption end, value Scope is from 0 to 255.

5. the grouping encryption method that Fermat number as claimed in claim 4 number theoretic transform combines with SAFER cryptographic algorithm, it is special Levy and be: in described diffusion layer, if 256 numerical value repeatedly occurs in an AES, then need multiple continuous print location records With the extreme higher position 1 of location records symbol, symbol, now represents that this record symbol is last record in this AES Symbol, forms record symbol block with it for interval.If this time the most there are not 256 these numerical value in AES, then with zero note Record symbol represents；Zero record symbol has 16 bits and constitutes, and former 4 bits are as the mark of zero record symbol, mark Value is 1000₂After, 12bits represents the encryption number of times not occurring 256 numerical value continuously, and span is from 1 to 4095；When 256 When numerical value does not has occurrence number to reach 4096 continuously, then zero record symbol of another 16bits is needed to carry out record；Quickly Fermat Transformation of variables, as diffusion layer, needs location records symbol and the support of zero record symbol, during transmission ciphertext, needs record symbol Section is connected on ciphertext end, then needs to carry out according to record symbol section during decoding.

6. the block encryption side that the Fermat number number theoretic transform as described in one of claims 1 to 3 combines with SAFER cryptographic algorithm Method, it is characterised in that: a length of 128bits of described block cipher.