WO1979000418A1 - Procede et dispositif de chiffrage et dechiffrage - Google Patents

Procede et dispositif de chiffrage et dechiffrage Download PDF

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Publication number
WO1979000418A1
WO1979000418A1 PCT/SE1978/000100 SE7800100W WO7900418A1 WO 1979000418 A1 WO1979000418 A1 WO 1979000418A1 SE 7800100 W SE7800100 W SE 7800100W WO 7900418 A1 WO7900418 A1 WO 7900418A1
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WO
WIPO (PCT)
Prior art keywords
matrix
key
encryption
plaintext
supplied
Prior art date
Application number
PCT/SE1978/000100
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English (en)
Inventor
H Braendstroem
Original Assignee
H Braendstroem
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by H Braendstroem filed Critical H Braendstroem
Publication of WO1979000418A1 publication Critical patent/WO1979000418A1/fr
Priority to DK347779A priority Critical patent/DK347779A/da

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Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0618—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/12—Details relating to cryptographic hardware or logic circuitry

Definitions

  • the present invention refers to a method of encryption of data using one or more encryption keys and the same keys for decryption.
  • the invention also refers to a device for the realization of said method.
  • the cryptosystem shall be able to work according to the principles for ciphers dependent or independent of the unenciphered text (the plaintext).
  • the cipher independent of the plaintext is distinguished by a usually very long sequence of key symbols, consisting of zeros and ones, being added modulo-2 to the plaintext which is also a sequence of zeros and ones.
  • this kind of ciphers may be mentioned form ciphers in which the complete sequence of key symbols constitutes the key.
  • This kind of encryption for example, has been implemented within defence organizations.
  • the drawback of a form cipher is that keys are comsumed at the same rate as that of the information being transmitted. Also, the keys which may be stored on a disc memory both at the transmitter end and at the receiver end of the information, has to be deposited for safe-keeping. For making the circumstantial handling of keys needed unnecessary when form ciphers are being used, the key sequences are often generated by use of feedback shift registers.
  • the sequences of zeros and ones generated by such a shift register have a character that makes them very similar to randomly generated sequences, and they are often called pseudo-random sequences.
  • Such a sequence is completely determined by the values stored in the shift register at the start.
  • This content in the register is in the following called the key.
  • the key will be very short in comparison with the key sequences generated by the shift regis ter, thus considerably simplifying the handling of the key as comparad to corresponding problems when using a form ciphe
  • one drawback when using a feedback shift regis ter is that the resistivity against breaking the enciphered information is very unfavourable. If a part of the plainte and the corresponding enciphered text are known, the length of which needs only be two times the length of the shift register, the key may be determined by solving a system of linear equations.
  • DES Encryption Standard
  • Fig. 1 of the present specification the plaintext is partitioned into blocks M consisting of 64 bits. These bits are as a first step permuted according to a fixed permutation schedule which is dependent on the 16 key words K 1 , K 2 .. K 16 defined by a KEY consisting of 64 bits, 8 of which are parity check bits.
  • K 1 , K 2 .. K 16 defined by a KEY consisting of 64 bits, 8 of which are parity check bits.
  • the block is partitioned into two blocks, a left block L 0 and a right block R 0 , each one consisting of 32 bits. This is followed by an iteration process in 16 steps, defined by the relations
  • R n L n-1 + f(R n-1 , K n ) where f is a non-linear function mapping R n-1 and the keyword K n into a 32-bits block which is added modulo-2 to L n-1 .
  • the keyword K n consists of 48 bits and depends on KEY and the iteration step n defined by a function KS.
  • K n KS(n, KEY).
  • M' L'R' which is subjected to a permutation defined to be the inverse of the permutation of M as discussed earlier. As a result of this last permutation the enciphered block KB is obtained.
  • Each bit of the enciphered block KB is depending on all the bits in the plaintext block M.
  • the DES system copes with relatively high demands for the resistivity against breaking the clphertext since the only way known today for breaking it is to try different keys in a decryption device, and to look for meaningfull plaintexts in the outputs when the enciphered blocks are applied to the inputs.
  • the number of possible keys KEY is 256, or about 10 17 .
  • the DES system also copes with the demands for high rates of encryption and decryption since it may be realized in hardware using LSI chips, and said chips are already available on the market.
  • Plaintext dependent ciphers are "stiff". They are rather expensive to change if the resistivity against break ing is regarded to be insufficient. 3. Plaintext dependent ciphers require passwords within the plaintext blocks in order that errors in the transmission caused by noise may be detected.
  • the object of the invention is to avoid said drawbacks of plaintext dependent ciphers and to obtain a possibility of adapting the system to existing applications including databanks, data communication and speach communication.
  • encryption is performed by partitioning the characters of a plaintext message into blocks of binary digits, each such block being further partitioned into subblocks, each of which is to be possible to interpret as an element in a Galois-field.
  • Said elements are brought to generate a plaintext matrix which is multiplied from the right in a first matrix multiplier by a first key matrix belonging to a prescribed matrix group over said Galois-field and being generated by means of a first encryption key which is applied to a first matrix generator, the output of which is multiplied from the left in a second matrix multiplier by a second key matrix belonging to the same matrix group and being generated by means of a second encryption key which is applied to a second matrix generator.
  • the output from said last-mentioned generator constitutes the encrypted plaintext block which is thereafter transmitted to a receiver where it is to be decrypted.
  • said plaintext block is multiplied from the left in a third matrix multiplier by a third key matrix being the inverse of the second key matrix and being generated by means of the second encryption key which is applied to a third matrix generator.
  • the output of said generator is then multiplied from the right in a fourth matrix multiplier by a fourth key matrix being the inverse of the first key matrix and being generated by means of the first encryption key which is applied to a fourth matrix generator.
  • the output from said last-mentioned generator constitutes the restored original plaintext matrix, and after decoding the original plaintext block will be received.
  • the system according to the invention is further characterized by great resistivity against breaking, and it renders it possible to use algorithms for encryption and for decryption.
  • the implementation is technically simple and cheap.
  • the demand for resistivity against breaking strongly depends on the actual application, but is especially high in connection with the processing of stored Information, when in extreme cases it is necessary for the cryptosystem to resist breaking during 50 years, independently of the breakers access to technical facilities and to the unknown development of technology.
  • the method of encryption and decryption according to the invention is founded on the use of matrices belonging to matrix groups with elements belonging to Galois-fields. Accordingly, a short review will be given of the properties of such fields. Further information may be drawn from the book "An Introduction to Error-Correction Codes" by Shu Lin, Prentice-Hall, London.
  • a Galois-field (GF(p r )) contains p r elements, where is a prime number and r is an arbitrary positive integer. Two arbitrary elements in GF(p r ) may be added or multiplied and the result of such operations will be -usually other- elements in the field.
  • the set of elements differing from 0 in the Galoisfields has the character of a cyclic group, implying that each such element in the field can be interpreted as a power of generating element, also called a primitive element.
  • Such an element is a root of an irreducible polynom of degree r with the coefficients belonging to the prime field GF(p) in GF(p r ).
  • Such a polynom, the roots of which are primitive elements, is called a primitive polynom.
  • the coefficients z 0 , z 1 , z 2 and z 3 are bilinear expressions in x i and y j , where i and j assume values 0, 1, 2 or 3.
  • the addition and multiplication rules for the elements in GF(p r ) are used when matrices of order n (the number of rows and of columns in equal to n) are multiplied.
  • the "general linear group" GL(n,p r ) of order n over the Galois-field GF(p r ) consists of all the non-singular matrices. This group contains a number of subgroups.
  • One such subgroup of special interest in connection with the present invention is the "special linear group” SL(n,p r ) which consists of all determinants which are equal to 1.
  • the invention utilizes matrices belonging to a certain matrix group.
  • a plaintext is partitioned into blocks consisting of strings of elements in a Galois-field GF(p r ) or a bit string. These blocks will then define a plaintext matrix.
  • a key may also be looked upon as a block consisting of a string of elements defining in the same way a key matrix.
  • Fig. 1 illustrates an already known and above described standardized cipher system from the U.S.A.
  • Fig. 2 shows a block diagram of an encryption and decryption system
  • Figs. 3 and 4 show diagrammatically two shift register circuits for use in connection with the system according to Fig. 2.
  • Fig. 5 shows diagrammatically how two shift register may be connected to cooperate.
  • the block diagram of Fig. 2 shows a plaintext message applied as blocks m consisting of, for example, data bits to a matrix encoder 1.
  • the output of said encoder delivers a matrix M for each block m.
  • the elements in the matrix M belong to a Galois-field as described above.
  • the matrix M is supplied to a first input 2 of an encryption device 3. Before that a first cipher key a consisting of data bits has been supplied to a second input 4 of said device, and a second cipher key b to a third input 5 of the same device.
  • a key can as sume 2 16 or 65536 different values.
  • 2 32 4294967304, or about 4 ⁇ 10 9 different combinations of key values a ahd b.
  • two repeated encryptions are executed with two sets of keys a 1 , b 1 and a 2 , b 2 one will obtain 2 64 or about 1,6 ⁇ 10 19 different combinations of key values. It is practically impossible to break such an encrypted message using search routines to find the correct keys.
  • Each cipher key is supplied to a device 6 and 7, respectively for the generation of key matrices.
  • a device 6 and 7, respectively for the generation of key matrices One embodiment for the realization of such a device will be explained in connection with Fig. 3.
  • a key a consisting of 16 bits passes via a switch 31 into a shift register 32 having 16 positions. After that the switch 31 is switched over to the not shown position, and becomes fed back and will be able, at the outputs of each step, to generate a pseudorandom sequence of maximal length.
  • a feedback is used corresponding to the primitive polynom x 16 + x 12 + x 3 + x + 1, defining the modulo-2 addition of the positions 33, 34 and 35.
  • the outputs from each step in the shift register are grouped together into a tetrade ⁇ 0 , ⁇ 1 , ⁇ 2 , ⁇ 3 each consisting of four bits as indicated by the arrows 36, 37, 38 and 39,
  • the elements ⁇ i may be used to generate addresses to two matrices having elements in a Galois-field, or they mey be considered as elements in the Galois-field GF(16). Said last case is shown here.
  • the four elements ⁇ i in the tetrade are supplied two by two to two matrix encoders 40, 41.
  • the encoder 40 generates the matrix A 1 and the encoder 41 generates the matrix A 2 .
  • These matrices may, for example, be
  • a second key matrix B For the purpose of the invention it is in the same way necessary to generate a second key matrix B. This is performed by means of a separate feedback shift register and a matrix encoder, processing the key b, In Fig. 2 the block is intended for generating the key matrix.
  • the tetrade ⁇ i may also be generated by random using a noise generator.
  • a change-over switch 12, 13 between the matrix encoder and its multiplier either the output of the matrix encoder may be directly connected to the multiplier (generating the matrix A or the matrix B) or the same output may be connected to the multiplier via the inverter 9, 10
  • the plaintext matrix M is supplied to a first input on a first matrix multiplier 14.
  • the first key matrix A is supplied to a second input on said multiplier.
  • said key matrix A is multiplied from the right to give the product M «A which has the form of a matrix and which is supplied to a first input on a second matrix multiplier 15 «
  • the invention does not require the limitation of generation of 2 ⁇ 2 matrices.
  • Square matrices of arbitrary order n may be utilized.
  • Fig. 4 exemplifies the generation of matrices of order 3 belongingto the "special linear group" SL(3,16) over a finite field (Galois-field) containing sixteen elements as shown in Fig. 4.
  • the same shift register 30 is being used as in Fig. 3.
  • the elements ⁇ 1 and ⁇ 2 in the tetrade according to Fig. 3 will appear in both the matrices A 1 and A 2 .
  • the appearence of the submatrices A 1 -1 and A 2 -1 is shown below in the formula of the inverse matrix A -1 .
  • Fig. 5 shows an embodiment using two shift registers 50 and 51 to generate a key matrix A.
  • a key a may be partitioned in an arbitrary way into two subkeys a 1 and a 2 . Each one of them is supplied to one of the shift registers 50, 51, said registers being, if desired, of the type previously described.
  • Outputs on the shift registers are connected to a matrix encoder 52 in such a way that an output thereon will generate a key matrix A.
  • Another modification of the invention may be used to increase the resistivity against breaking. This is obtained by making the cycle-time of the shift register a fraction 1/k of the rate by which the plaintext matrices M are supplied to the cipher device. In that way a key matrix consisting of the product of k consecutive matrices A will be gene rated. Said key matrix may then be utilized as a factor in the matrix multiplication with the plaintext matrix M.
  • the control of the processes in the cipher devices, in the matrix encoders and in the matrix decoders requires synchronization of the transmitter and the receiver by means of clock pulses, if necessary under the control of a microcomputer.
  • Matrices M generated during decryption have certain characteristic properties which may be the basis for checking the correctness of transmitted messages.
  • a plaintext matrix may, for example, have the characteristic feature that its determinant is 1. It is also possible that a certain element in each plaintext matrix has a predefined value. These and other characteristics may easily be checked and identified.
  • Error detection and error correction is also, at least in principle, possible to perform before decryption. Correct reception requires that the matrices even prior to the decryption belong to the actual matrix group, let it be denoted G.
  • This matrix group is a subgroup of the "general linear group" GL(n,p r ). Said group may be partitioned into "cosets" in relation to G, quite analogously to the theory for line ar codes. However, an important difference is that the group GL(n,p r ) will not be commutative, and that further de velopment of the said theory must be performed. A primary objective will be to find subgroups (G) to the group GL(n,p r ) that are suitable both from the encryption and from the encoding point of view.

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Storage Device Security (AREA)
  • Error Detection And Correction (AREA)
  • Detection And Prevention Of Errors In Transmission (AREA)

Abstract

Le chiffre et le chiffrage de l'information d'un message se font en divisant le texte en clair du message en blocs de bits et par une division supplementaire de ces blocs en sous-blocs qui sont consideres comme des elements d'un champ de Galois. Une matrice (M) en clair de ces elements est multipliee par une premiere matrice-cle (A) d'un groupe sur ce champ de Galois, le produit resultant (M-A) etant multiplie par une seconde matrice-cle (B) du meme groupe sur ce champ Galois. Le produit final (B-M-A) alors obtenu constitue le bloc du message chiffre. (K). Le chiffrage se fait en multipliant le produit transmis (B-M-A) par les matrices-cles inverses (A-1, B-1) generees par les memes cles (a, b) que celles utilisees pour le chiffrage et prises dans l'ordre convenable.
PCT/SE1978/000100 1977-12-21 1978-12-20 Procede et dispositif de chiffrage et dechiffrage WO1979000418A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
DK347779A DK347779A (da) 1977-12-21 1979-08-20 Kryptograferingssystem

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
SE7714587A SE7714587L (sv) 1977-12-21 1977-12-21 System for meddelanden
SE7714587 1977-12-21

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WO1979000418A1 true WO1979000418A1 (fr) 1979-07-12

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US (1) US4322577A (fr)
EP (1) EP0011615B1 (fr)
JP (1) JPS55500476A (fr)
SE (1) SE7714587L (fr)
WO (1) WO1979000418A1 (fr)

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Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
AU572446B2 (en) * 1981-01-28 1988-05-12 Trans-Cryption Inc. Personal identification system
EP0395618A2 (fr) * 1989-04-28 1990-10-31 Emile Paul Henry Musyck Système cryptographique par blocs de données binaires
EP0395618A3 (fr) * 1989-04-28 1992-10-21 Emile Paul Henry Musyck Système cryptographique par blocs de données binaires
WO1991018460A1 (fr) * 1990-05-19 1991-11-28 Rolf Trautner Procede de chiffrement de donnees numeriques par blocs
AU648433B2 (en) * 1991-10-02 1994-04-21 American Telephone And Telegraph Company A cryptographic protocol for secure communications
EP0624013A1 (fr) * 1993-05-05 1994-11-09 Zunquan Liu Dispositif et procédé de chiffrage de données
WO1994026045A1 (fr) * 1993-05-05 1994-11-10 Zunquan Liu Repertoire de mappages pour un systeme cryptographique
US5412729A (en) * 1993-05-05 1995-05-02 Liu; Zunquan Device and method for data encryption
US5539827A (en) * 1993-05-05 1996-07-23 Liu; Zunquan Device and method for data encryption
AU693094B2 (en) * 1993-05-05 1998-06-25 Zunquan Liu A repertoire of mappings for a cryptosystem
CN1054245C (zh) * 1993-05-05 2000-07-05 刘尊全 数据加密的装置和方法
FR2748144A1 (fr) * 1996-04-25 1997-10-31 Sagem Procede de transmission securisee entre un emetteur et un recepteur, emetteur et recepteur pour la mise en oeuvre du procede

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JPS55500476A (fr) 1980-07-31
US4322577A (en) 1982-03-30
EP0011615B1 (fr) 1983-06-15
SE7714587L (sv) 1979-06-22
EP0011615A1 (fr) 1980-06-11

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