ES2238151B1 - PROCEDURE AND DEVICE FOR ENCRYPTION OF IMAGES THROUGH A SYSTRIC GRAPHIC CRYPTOSYSTEM. - Google Patents

Abstract

Procedure and encryption device of images using a symmetric graphic cryptosystem.

A procedure and device is presented for Encrypt scanned images, with any number of colors,   based on a pseudorandom bit generator, cryptographically safe, and in a two-dimensional cellular automaton. The cryptosystem It is safe against all known attacks. This procedure and device is applicable in all those processes in which it is required to protect images, either for transmission or storage, such as in the computer sectors, military, industrial, artistic, cartography and medical.

Description

Procedure and encryption device of images using a symmetric graphic cryptosystem.

Sectors of the technique in which it has application

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Cryptography

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Image processing

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Technologies of the communications

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Informatic security

State of the art

Today there are several methods and algorithms that allow to carry out, in a safe way, the exchange of Information in computer networks. Among such methods stand out symmetric or secret cryptographic systems, which characterized by the fact that both the encryption process and the decryption of the information are similar and both are carried carried out by means of certain algorithms that depend on a key which is only known by the issuer and the receiver of the information. More precisely (see Figure 1), the process that follow for both encryption and data decryption is to carry out an initial transformation, without value cryptographic, of the original data so that they are usable by the algorithm to be used in the iterative module. TO then we proceed to iterate the algorithm of encryption / decryption, which is powered by the user's key that encrypt or decrypt the data. The result of this process returns to undergo a final transformation (which is the inverse of the initial transformation) of so that its result is the encrypted data (if the originals were clear) or deciphered (if the starting ones were already encrypted) The most used secret key cryptosystems in the currently they are DES ([FIPS77]), IDEA ([LMM91]), RC5 ([Riv95]) and Rijndael ([Rij02]). The strength of these cryptosystems symmetrical against possible attacks to break your confidentiality  It is based on keeping the key used secret and intratability computational problem solving the mathematical problem in which base.

In specialized literature there are different proposals for the treatment of images from a point of view cryptographic. The first one is known as cryptography visual ([NS95]) and makes use of the t visual thresholds of n. In this cryptographic procedure, a director elaborates secret n shadows of the image, which photocopy to transparencies, and It also provides, in a secret way, a shadow to each of The n participants. To recover the original image you must superimpose at least t transparencies of the existing n, being impossible to get any information about the initial image with Less than t transparencies. However, this procedure It presents some problems, among which the loss of contrast of the recovered image with respect to the original. Until a short time ago, visual cryptography was only able to manipulate black and white images ([Sti01]) and shades of gray ([BDN00], [LT03]). However, recently a proposal for the visual treatment of color images ([H03]). This fact highlights the importance of protocols Cryptographic for image manipulation. However, the problem persists - either for blank images and black, in shades of gray and colors-, that the image that recover, after carrying out the cryptography protocol visual, loses a lot of resolution in relation to the image original.

Another proposal uses dynamic systems continuous ([Fri97] and [Fri98]), which leads to difficulties in time to implement the protocols on which it is based. These problems are practical, due to the difference between chaotic arithmetic of the proposed dynamic systems, which is continues by its own definition, and the discrete arithmetic that Used in computers. This fact makes the practical implementations lose the chaotic essence of systems on which they are based.

There are also proposals for treatment cryptographic images in which they are used, so iterated, different compression methods thereof ([BA92], [CHCO1], [CL94], [K93] and [Sch9l]). However, in all these proposals presents, again, the problem that the images recovered do not match the originals for a loss of definition in the pixels that compose it. This fact contradicts the very essence of the concept of cryptography, whereby decryption must match what was encrypted. It is true that with image treatment, you can "appreciate" what it was the original image, especially if the first one was widely known, but this loss of resolution prevents encryption of images that require a great definition, such as maps, designs, etc.

It should be noted another proposal that does not have the drawbacks noted above ([HMH02] and [HMV02]). However, this protocol has two drawbacks. He first of all is that you can't use anything practically  more than for images with up to 256 colors or 256 shades of gray, due to the large number of calculations and memory they require. The second drawback of this proposal is that it is not sure, that is, it is possible to carry out an attack on the text of course chosen to obtain the key used to encrypt a image. To succeed with this attack, if you have the encryption machine, just encrypt homogeneous images so iterated and analyze how the cryptosystem evolves, so that The original key can be retrieved.

Finally, in [HMO2] a new one is presented proposal for encryption of scanned images, which uses cellular automata, and which in this case can be defined by Any number of colors. This proposal also presents the advantage of recovering the original image, without loss of contrast, but it is not safe because it can be broken by attacking the text Of course chosen.

In addition to the previous protocols, there are some applications of cryptography with images that make interesting a cryptosystem like the one presented here, so that can be used for these purposes. Such applications allow authentication and visual identification ([NP97]), the identification of documents and digital photo signatures ([BME99] and [OR98]), the schemes to develop methods for intellectual protection of images defined by shades of gray ([0002]), and the schemes for sharing secrets ([TL02] and [T0002]).

Thus, the problem of designing a secure and efficient cryptosystem that allows to encrypt images using any number of colors and whose cryptogram resulting again be an image with the same dimensions as the  original. This problem is the one that is solved in the present invention. That is, in this application the invention of a cryptosystem that allows you to encrypt and describe in a way safe and efficient a digitized image defined by any number of colors, that is, with up to 2 24 = 16,777,216 colors.

References

[BME99] B. Bellamy , JS Mason and M. Ellis , Photograph signatures for the protection of identification documents, Proc. of Crypto &Coding'99 , LNCS 1746 ( 1999 ), 119-128.

[BBS86] L. Blum , M. Blum and M. Shub , A simple unpredictable pseudo-random mumber generator, SIAM J. Comput . 15 ( 1986 ), 364-383.

[BA92] N. Bourbakis and C. Alexopoulos , Picture data encryption using SCAN patterns, Pattern Recogn . 25 ( 1992 ), 567-581.

[BDN00] C. Blundo , A. De Santis and M. Naor , Visual cryptography for gray level images, Inform. Proc. Lett. 75 ( 2000 ), 255-259.

[CC02] CC Chang and JC Chuang , An image intellectual property protection scheme for gray-level images using visual secret sharing strategy, Pattern Recogn. Lett . 23 ( 2002 ), 931-941.

[CHCO1] Ch. Chang , M. Hwang and T. Chen , A new encryption algorithm for images cryptosystems, J. Syst. Software 58 ( 2001 ), 83-91.

[CL94] HK Chang and JL Liou , An image encryption scheme based on quadtree compression scheme, Proc. of Int. Comput. Symp ., 230-237, Taiwan, 1994 .

[FIPS77] Federal Information Standard Publication, Data Encryption Standard , FIPS 46, US Department of Commerce / National Bureau of Standards, National Technical Information Service, Springfield, VI, 1977 .

[Fri97] J. Fridrich , Secure image ciphering based on chaos , Final Technical Report, Rome Laboratories, NY, February 1997 .

[Fri98] J. Fridrich , Symmetric ciphers based on two-dimensional chaotic maps, Internat. J. Bifur. Chaos 8 ( 1998 ), 1259-1284.

[HMO2] L. Hernández Encinas and A. Martín del Rey , Method and apparatus for the encryption of digitized images , Spanish Patent and Trademark Office, Invention Patent Application Number 200201500.

[HMH02] L. Hernández Encinas , A. Martín del Rey and A. Hernández Encinas , Encryption of images with 2-dimensional cellular automata , Proc. of The 6th Multiconference on Systemics, Cybernetics and Informatics, Vol. I: Information Systems Development I, 471-476, Orlando, 2002 .

[HMV02] L. Hernández Encinas , A. Martín del Rey and I. Visus Ruiz , Encryption of images in shades of gray using cellular automata, Proceedings of the VII Spanish Meeting of Cryptology and Information Security, Volume I , 379-389 , Oviedo, 2002 .

[HMMP98] L. Hernández Encinas , F. Montoya Vitini , J. Muñoz Masqué and A. Peinado Domínguez , Maximal periods of orbits of the BBS generator, Proc. 1998 Int. Cont .. on Inform. Secur. & Cryptol ., 71-80, Seoul, 1998 .

[H03] YC Hou , Visual cryptography for color images, Pattern Recogn 36 ( 2003 ), 1619-1629.

[K93] CJ Kuo , Novel image encryption technique ans its application in progressive transmission, J. Electron. Imaging 2 ( 1993 ), 345-351.

[LMM91] X. Lai , JL Massey and S. Murphy , Markov ciphers and differential cryptanalysis, Proc. of Eurocrypt'91 , LNCS 547 ( 1991 ), 17-38.

[LT03] CC Lin and WH Tsai , Visual cryptography for gray-level images by dithering techniques, Pattern Recogn. Lett . 24 ( 2003 ), 349-358.

[LIP] FreeLIP, available at ftp://sable.ox.ac.uk/pub/math/.

[MOV97] A. Menezes , P. van Oorschot and S. Vanstone , Handbook of applied cryptography , CRC Press, Boca Raton, FL, 1997 .

[NP97] M. Naor and B. Pinkas , Visual authentication and identification, Proc. of Crypto'97 , LNCS 1294 ( 1997 ), 322-336.

[NS95] M. Naor and A. Shamir , Visual cryptography, Proc. of Eurocrypt'94 , LNCS 950 ( 1995 ), 1-12.

[OR98] L. O'Gorman and I. Rabinovich , Secure identification documents via pattern recognition and public-key cryptography , IEEE Trans. Anal Pattern Mach. Intell 20 , 10 ( 1998 ), 1097-1102.

[PW85] NH Packard and S. Wolfram , Two-dimensional cellular automata, J. Statist. Phys . 38 ( 1985 ), 901-946.

[Rij02] Rijndael, available at http://csrc.nist.gov/encryption/aes/rijndael/

[Riv95] RL Rivest , The RC5 encryption algorithm, Proc. of The Fast Software Encryption , LNCS 1008 ( 1995 ), 86-96.

[RSA78] RL Rivest , A. Shamir and L. Adleman , A method for obtaining digital signatures and public-key cryptosystem , Commun. ACM 21 ( 1978 ), 120-126.

[Sch9l] C. Schwartz , A new graphical method for encryption of computer data, Cryptologia 15 ( 1991 ), 43-46.

[Sti01] DR Stinson , Cryptography. Theory and Practice, 2nd. edition , CRC Press, Boca Raton, FL, 2001 .

[TL032] CC: Thien and JC Lin , Secret image sharing, Computer & Graphics 26 ( 2002 ), 765-770.

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Explanation of the invention. Brief Description of the Invention

From the general scheme of symmetric key cryptosystems mentioned in the section on the State of the Art (see Figure 1), the general scheme of the symmetric graphic cryptosystem that is proposed In this invention. This scheme follows the same general structure from the previous one, but it presents some particular modifications, which make it unique for the treatment of images defined by any number of colors (see Figure 2).

Starting from the data of an image digitized, stored in a file, we proceed to a first data transformation, through the Initial Transformation, whose task is to adapt the data that defines the image to that can be manipulated by the Iterative Module. One time known the fundamental data of the image, the values corresponding to the number of rows and columns are sent to Pseudorandom bit generator that, along with the key supplied by the user, proceeds to generate a sequence of pseudorandom bits of sufficient length to be used in the Iterative Module.

The Iterative Module receives the following data:

one.

Number of rows in the image (known from the image),

2.

Number of columns in the image (known from the image),

3.

Value of each of the pixels (known from the image),

Four.

Pseudorandom Bit Sequence (secret and derived from the key),

and proceeds to encryption or described of the pixels of the image. These processes are based on mathematical operations that modify the pixels of the starting image, giving rise to the encrypted image, if the original it was the clear image to be encrypted; or to the image in clear, if the What is used in the algorithm is the encrypted image. The processes Encryption and decryption are similar, although not exactly same, and use the same key of Username.

Once the image pixels have been modified by the Iterative Module, are transformed by the Final Transformation, which returns them so they can be stored in a file and can be treated as an image.

Detailed description of the invention

From the general scheme of the process of Encryption / decryption of images described herein invention (see Figure 2), a Detailed description of how to carry out both processes.

To do this, first of all the mathematical tools used in the cryptosystem proposed symmetric graph, the following will be commented on protocol that is followed to obtain the secret key to be used both when encrypting and decrypting an image and finally we will describe the encryption process, to Then submit the decryption.

1. Mathematical tools

In the present graphical cryptosystem key symmetric for encryption and decryption of images defined by pixels and with any number of colors, two are used Basic math tools: a bit generator pseudorandom, cryptographically secure, and a cellular automaton two-dimensional reversible. The first one allows to obtain a sequence of pseudorandom bits, derived from the secret key of the user, and the second uses the secret bit sequence generated by the first to carry out both the process of Encrypted as described.

A pseudorandom bit generator (GBPA) is a deterministic algorithm that provides as output a very large bit sequence g >> l that appears to be random, by providing a really random bit sequence of much smaller length l as input. The input to the algorithm is known as seed , while the output it provides is called a pseudorandom bit sequence ([MOV97]). Therefore, it is very desirable that the bit generator used has good pseudorandom properties in order to avoid possible attacks by statistical analysis of the sequences it generates. Thus, it is necessary that the generator be cryptographically safe (GBPACS) that is, that its safety be based, for example, on the difficulty of solving a mathematical problem. In this sense, security means that there is no polynomial time algorithm that can distinguish a pseudorandom generator sequence from a really random sequence of the same length, with a probability significantly greater than 1/2. Among the most used GBPACS are the RSA generator ([RSA78]) and the BBS generator ([BBS86]), for which their safety is based on the alleged intratability of solving the problem of the entire factorization.

The other tool to be used will be a reversible two-dimensional automaton ([PW85]). A cellular automaton (AC) is defined as the quatern A = (L, S, V, f), where L is the cellular space formed by a 2-dimensional matrix, of size r \ s, of identical objects called cells , < i, j>, with 0 i i \ leq r - 1, 0 le j \ leq s - 1. S is the set of states , that is, the finite set of all possible values that cells can take. The index set V \ subset Z_ {2} is a finite set ordered so that for each cell, <i, j>, its neighborhood , V_ {<ij>} is the following set:

V_ {<ij>} = \ {<i + \ alpha, j + \ beta>, \ forall (\ alpha, \ beta) \ in V \} \ subset L.

In addition, the local transition function f : S ^ n → S is the function that determines the evolution of AC over time. Since the ACs that will be used are finite, so that they are well defined, periodic boundary conditions will be considered, that is, the cellular space will be understood as a bull in two dimensions:

a_ {ij} {} ^ {(t)} = a_ {kl} {} ^ {(t)} \ Leftrightarrow i \ equiv k \ (mod (r - 1)) \ y \ j \ equiv l \ (mod (s-1)),

where a_ {ij} ^ {(t)} \ in S represents the state of the cell <i, j> at time t, since mod b is the operation that consists in taking the rest of the entire division of a by b . An AC is said to be reversible (ACR) if there is another AC, called its inverse , that determines its inverse evolution.

2. Data reading and secret code

The cryptographic treatment of an image It begins with the Initial Transformation which, after reading from the image file, I, provides the following data: number of colors, c, with 2 ≤ c ≤ 2 24; number of rows: r; number of columns: s; and the binary expression of each One of the r \ times s pixels of the image:

P_ {ij} = (p_ {ij} {} ^ {1}, p_ {ij} {} 2}, ..., p_ {ij} {} ^ {24}), 1 \ leq i \ leq r, 1 \ leq j \ leq s.

with p_ {ij} ^ {n} \ in Z_ {2}. Also, if the pixel P_ {ij} occupies the position m counting from from the top left of the image, you have to m = (i - 1) s + j, with 1 \ leq m \ leq r \ times s.

The key to the crypto cryptosystem developed in this invention is the key of the GBPACS used, which will allow get a secret pseudo random bit sequence. So, The security of the cryptosystem is guaranteed by the security of the  GBPA Note that to break the proposed cryptosystem you must Determine the generator key. As generators to be used recommend the BBS generator or the RSA, although it can be used Any other that is cryptographically secure. If used as key K, the pseudorandom bit sequence will be denoted by B = (B_ {l}, B_ {2}, ..., B_ {r \ times s}), this sequence being of length r \ times s \ times 24, where B_ {m} = (b_ {m1}, b_ {m2}, ..., bm_ {24}), and b_ {mn} \ in Z_ {2}

3. Encryption process

The protocol for encrypting an image, which is the Iterative Module (see Figure 2), uses an ACR A = (L, S, V, f), defined as follows:

(i)

He cell space, L, is a rectangular matrix of the same size as the image, so that L can be considered as a set of r \ times s pixels.

(ii)

He set of states is S = Z_ {2} \ times ^ {... (24 ...} \ times Z_ {2}, with | S | = 2 24; so each color can be identify with an element of S. If x_ {m} \ in S, it is x_ {m} = (u_ {m} ^ {l}, ..., u_ {m} ^ {24}) where u_ {m} ^ {n} \ in Z_ {2}, 1 \ leq n \ leq 24.

(iii)

He index set, V, is publicly selected so that | V | = 24.

(iv)

To determine the encrypted pixel of P_ {ij}, Q_ {ij}, 1 \ leq i \ leq r, 1 \ leq j \ leq s, the 24 pixels of the neighborhood of P_ {ij} are taken into account, V_ {<ij>}: P_ {ij1}, P_ {ij2}, ..., P_ {ij24}, and the transition function f: S 24 \ rightarrow S as follow:

one

that is, q_ {ij} ^ {n} = b_ {mn} \ varoplus p_ {ijn} ^ {n}; where m is the position of the pixel P_ {ij}, B_ {m} is the m -th component of the bit sequence B, \ pi_ {n}: S \ rightarrow Z_ {2} (n)} is the projection on the nth component and \ varoplus is the XOR operation.

The encrypted image, C, results from a single application of the transition function to each of the pixels of the image in clear I. In this way, the encrypted image will be also defined by r \ times s pixels, but now it will contain d colors, 2 ≤ d ≤ 2 24.

As you can see from the construction of the cryptosystem, its expansion factor (the ratio between sizes of the encrypted image and the clear image) is 1. By On the other hand, it is not necessary to iterate the ACR more than once, since The security of the cryptosystem is not increased by that fact.

Once the encryption process is finished, the Final Transformation receives from the Iterative Module the number of image colors, d; the number of rows, r; the one with columns, s; and the binary values of each of the pixels, Q_ {ij}, of the encrypted image C. From this data, we proceed to the transformation of the data that allows it to be stored in a file of image.

4. Decryption process

The process described is similar to that of encryption and only differs in the Iterative Module, that is, the Initial and Final Transformations are the same. The receiver of the Encrypted image uses the inverse AC of A = (L, S, V, f), that is, A <-1> = (L, S, W, g). In this case, L and S are the same for A <-1> than for A. The set of indexes of A <-1>, is the same set of indexes as that of A, but taken in order Inverse, that is, W = -V.

To describe a pixel Q_ {kl}, with 1 ≤ k \ leq r, 1 \ leq l \ leq s, 24 pixels are taken into account from the neighborhood of Q_ {kl}, W <{k, l>}: Q_ {ij1}, Q_ {ij2}, ..., Q_ {ij24}, and the transition function g: S 24 is applied \ S as follows:

2

with b 'tn? gkln = p_ {kl} n; t the position of Q_ {kl}, \ pi_ {n}: S \ righ Z_ {2} {{n}} is the projection on the nth component and the symbol \ varoplus represents the XOR operation.

Thus, to recover the t -th pixel, P {kl}, it is to be applied ga transition function corresponding encrypted pixel, Q {kl}. The clear image, I, is recovered by applying once the transition function to each pixel of C. According to this process, the recovered image is exactly the same as the original (pixel by pixel), that is, there is no loss of resolution.

In summary, an object of the present invention is it constitutes an encryption and description procedure by a symmetric graphic cryptosystem based on:

a) A pseudorandom bit generator cryptographically secure,

b) A two-dimensional cellular automaton reversible,

that encrypts and describes scanned images, defined by any number of colors.

A particular object of the present invention is it constitutes an encryption and description procedure through a symmetric graphic cryptosystem in which the generator of cryptographically secure pseudo-random bits, from the secret key shared by two users and that is used as generator seed, generate a sequence of bits pseudorandom A specific embodiment of said procedure is  the one in which encryption procedure is based on a reversible two-dimensional cellular automaton defined by a quatern (L, S, V, f), where L is a generic image of the same size as the one to be used in the encryption process; S is the set consisting of the 2 24 = 16,777,216 possible colors that they can define the image; V is the neighborhood of each pixel and f is the transition rule that determines the evolution of cellular automaton, as previously mentioned.

Another specific embodiment of said procedure is the one in which description procedure by means of a symmetric graphic cryptosystem according to claims 1 and 2, characterized by a reversible two-dimensional cellular automaton defined by a quatern (L, S, W, g), where L is an image generic of the same size as the one to be used in the decryption process; S is the set formed by the 2 24 = 16,777,216 possible colors that can define the image; W is the neighborhood of each pixel and g is the transition rule that determines the evolution of the cellular automaton, as it has been commented above.

Another object of the present invention is It is a device to encrypt and describe images by means of a symmetric graphic cryptosystem constituted by a electronic system that implements in hardware or software a algorithm for the execution of the procedure above mentioned.

Another object of the present invention is constitutes a usable data storage device to encrypt and describe images using a cryptosystem symmetric graph, characterized in that it implements an algorithm for the execution of the aforementioned procedure.

Finally, another object of the present invention it is the use of the mentioned procedure and device previously in all those processes in which it is required Protect images, either for transmission or storage. Note that a user can use a secret key both to encrypt an image and transmit it to a recipient with which you share your key, as to store it in a way secure on his own hard drive, with a key that only he knows. Thus, among the main applications of this invention The following stand out:

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Secure storage of any image through its encrypted image in the format of the original image

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Transmission of all types of images that have been previously encrypted, so that the information they contain is not accessible, except for those are authorized

These applications are very useful in fields related to the following activities:

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Computing

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Military

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Industrial

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Artistic

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Mapping

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Medical

Description of the figures

Figure one

General scheme of a symmetric key cryptosystem

In this figure the general scheme is presented for encryption and decryption of data using a cryptosystem of symmetric or secret key. First, the data, which are subjected to an Initial Transformation, without character  cryptographic, so that they can be manipulated by the Module Iterative, which is where the process of encryption / decryption, using a user key that only he known. After this process, the resulting data is sent  to the Final Transformation, which rearranges the data in the form Inverse to how it was done with the Initial Transformation. How result the encrypted data is obtained, if the originals they were clear; or those described, if the starting ones were already encrypted

Figure 2

General scheme of the proposed encryption / decryption process

The general scheme of the protocol presented in this invention it is shown in this figure. It can be seen that, in general, its structure responds to the scheme of symmetric key cryptosystems (see Figure 1). However, there are Some differences to highlight. Among others, that the key to user is used by a pseudorandom bit generator, cryptographically secure, to extend the original key to a much longer key and that is used for encryption / decryption from image. On the other hand, the data that are supplied by each module for the proposed protocol.

Figure 3

Generation of the bit sequence from the key secret

This figure shows the procedure that is continue to generate the pseudorandom bit sequence from the user's secret key and that will be supplied to the Module Iterative for carrying out the encryption / decryption of the image. This procedure is the same for both the protocol Encryption as description. In particular in the figure it presents the protocol to follow in the particular case in which consider the BBS generator, but any other GBPACS will follow a Very similar procedure.

Figure 4

Proposed protocol for image encryption

Figure 4 develops the process that leads to implemented in the Iterative Module for the encryption of an image. Saying process needs to know the number of rows, columns, the value in bits of each pixel and the pseudorandom bit sequence generated at  from the key. From this data, and knowledge public of the BBS module and the neighborhood, the process of encrypting each of the pixels in the image.

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Figure 5

Proposed protocol for decryption of an image

This figure presents the protocol that is proposes for decryption of an image. This process is very similar to encryption. Only the order in which they are considered varies the neighbors of each pixel and in the way of choosing the bits of the pseudorandom sequence.

Figure 6

Example of clear image

Figure 6 presents an example image in Of course to be encrypted. The image corresponds to a "Self-portrait" of Tamara de Lempicka and contains 602 rows, 800 columns, that is, 481600 pixels; and c = 85803 colors.

Figure 7

Example Encrypted Image

Figure 7 includes the result of Encrypt the image shown in Figure 6 using the key that It is included in the section dedicated to the detailed Exhibition of a embodiment of the invention. Due to the properties of cryptosystem that is presented, the encrypted image has the same size than the original, that is, 602 rows and 800 columns; or what which is the same, 481600 pixels. The number of colors is, as it would fit wait, much older: 474799.

Detailed statement of an example of realization of the invention Description

The following describes a possible implementation of how to carry out the encryption process and of decryption of any image, following the marked guidelines in the section on the detailed description of the invention.

The image shown in the Figure 6, defined by r = 602 rows, s = 800 columns, that is, for a total of 481600 pixels; and by c = 85803 colors.

Keys

The choice of the keys depends on the generator pseudo random bit chosen. In this case, we have considered the GBPACS known as BBS, since it has been characterized in [HMMP98] and are known, therefore, for what parameters of the same obtain maximum orbit lengths.

To obtain the keys of this generator you they must consider two large prime numbers, p and q, each of they congruent with 3 module 4 and checking the conditions noted in [HMMP98]. Next, the value of the BBS module: n = p \ times q, which is made public, while keep the values of p and q secret. The publication of value of n does not reduce the security of the cryptosystem since the it is based on the difficulty of calculating the values of p and q, it is  say, of factoring n. The next step is to determine the value of the secret key that will be shared by the two users that They will exchange the encrypted image. This key is the seed of BBS generator, K, which must also verify certain conditions (see [HMMP98]). From the previous values, iterate the function x2 (mod n) to obtain the sequence of numbers that will give rise to the bits. More precisely, the process to follow to generate the bit sequence is as follows (see Figure 3): it is considered x_ {0} = K and the expression is iterated given by

x_ {i} = (x_ {i-1}) 2 (mod \ n), i> 0,

so that from the values integers x_ {i} get the bits of the sequence. In the Original generator proposal ([BBS86]) was only considered the least significant bit (the parity bit) of x_ {i}; without However, it has been shown ([VV85]) that if the flowers are taken log_ {2} (log_ {2} n) \ rfloor less significant bits of x_ {i}, the BBS generator is still safe, assuming the number factoring problem is an intractable problem computationally Considering this new version of BBS, its efficiency is increased notably.

In the example at hand, it will be considered a key that could well be used in practice since its Length is 1024 bits (recommended value for implementations practices), and that is given by the following values:

p = 21356 60840 00904 44908 14294 61912 33044 48726 67056 27770 91639 84681 78856 45992 32341 56958 35057 42091 15098 30798 10115 93632 49071 27705 00854 09456 56744 86832 77097 70615 03863,

q = 19102 22295 03150 73922 29063 28699 65980 67095 94325 63598 98052 32092 35809 52388 60543 17244 68454 91521 66614 46956 28835 97718 10065 68101 69525 42919 27519 18819 59100 55918 43279,

n = p \ times q = 40795 86951 21099 38917 54804 02638 77833 57710 21051 85001 83480 19522 46842 87856 97634 85052 14129 09959 66022 75789 15738 85235 98425 52977 83390 32214 40675 81164 15742 55828 31687 5401 581601601601601601601601601601601601601601601601601601601601601601601601601601601601601601601601601601601601601601601701601601601601601601601601601601601601601701 6701706 6706 6707706 6701 6701706 72558 40139 07770 04502 97538 17997 97372 88123 63690 00159 61886 13363 80260 01716 07863 16076 66545 94908 6777.

Once the BBS module is released, n, the two users who are going to use the cryptosystem proposed in this invention, they agree on the secret key that they are going to use, K, which in this case will be the seed of the BBS generator. Note that as the generator's public key, it doesn't have to be modified (except when the safety regulations so advise), the secret key must be different for each image, or at least, for each pair of users. That seed could be The next:

K = 24036 88089 14855 42194 08780 82014 68160 80201 24435 74791 86003 70808 69817 02168 06034 74249 97038 26708 94839 69522 81767 89191 94832 26050 76074 09495 06651 79114 81213 15981 23484 51879 02828 49820 38094 47857 03683 77627 64872 17160 52538 54161 84144 97589 01730 51799 78262 51461 25123 11304 71889 41449 99949 34474 26583 39113 30749 85764 42420 85026 68074 3088.

From the previous data, it must be generated a sequence of at least

602 \ times 800 \ \ times \ 24 = 11558400 \ bits,

to ensure that they can Encrypt all pixels of the original image. It must have note that it is not necessary to iterate 11558400 times the BBS algorithm according to the modification indicated above. In this case, given that \ lfloor log_ {2} (log_ {2} n) \ rfloor = 10, the number of iterations will be 10 times Minor.

Encryption

According to the encryption protocol mentioned previously, a neighborhood must be chosen publicly for the ACR. In this example, the square of size 5 will be considered \ times 5 around cell <i, j>, except for one's own cell, so you will have:

V = \ {(- 2, -2), ..., (-2, 2), ..., (0, -1), (0, 1), ..., (2, -2), ... (2, 2)\},

and the neighborhood, V_ {<ij>}, can be represented as follow:

3

The previous set can be represented by two variables h and w, so that V_ {<ij>} = {(i + h, j + w)}, being:

h = \ lfloor (n-1) / 5 \ rfloor - 2, w = (n-1) (mod \ 5) -2, 1 \ leq n \ leq 12,

h = \ lfloor n / 5 \ rfloor -2, w = n (mod \ 5) -2, 13 \ leq n \ leq 24,

where \ lfloor a \ rfloor is the greater integer that is less than to.

According to this neighborhood election, for determine the encrypted pixel of P_ {ij}, Q_ {ij}, 1 \ leq i \ leq r, 1 \ leq j \ leq s, the 24 pixels of the neighborhood of P_ {ij}, V_ {<ij>}: P_ {i-2, j-2}, ..., P_ {i-2, j + 2}, ..., P_ {i, j-1}, P_ {i, j + 1}, ..., P_ {i + 2, j + 2}, and the function of transition f: S 24 \ righ S as follows:

4

that is, q_ {ij} ^ {n} = b_ {mn} \ varoplus p_ {i + h, j + w} ^ {n}; where m = (i - 1) s + j is the pixel position P_ {ij}, B_ {m} the m -th component of the bit sequence B, \ pi_ {n}: S \ rightarrow Z_ {2} ^ {(n)} is the projection on the nth component and the XOR operation.

Decoded

Once you have publicly chosen the neighborhood V above, for the reverse ACR you have to:

W = \ {(2, 2), ..., (2, -2), ..., (0, 1), (0, -1), ..., (-2, 2), ..., (-2, -2) \}.

Also in this case, the neighborhood of the cell <k, l>, W <k, l>}, can be encoded by them two variables h and w: W <<k, l>} = {(k – h, 1 – w)}. So, the  transition function g: S 24 \ righ S, to be used for Describe a pixel is as follows:

5

with b 'tn? q_ {kh, lw} n = p_ {kl} n; t = (k - h - 1) s + 1– w the position of Q_ {kh, lw}, and therefore you have to b 't, n} b = (k-1-h) s + lw, n}, \ pi_ {n}: S \ rightarrow Z_ {2} ^ {(n)} is the projection on the nth component and the symbol \ rightarrow represents the XOR operation.

Operation and implementation

The proposed scheme for encryption and Described images have been implemented in a practical way through several programs using the C ++ language in a 1000 MHz Pentium III computer with two microprocessors and 512 Mbytes of RAM. In particular and since the keys do not can be determined or manipulated with standard libraries of C ++ due to its size, for the generation of the keys and pseudo random bit streams the library has been used FreeLIP (Large Integer Package) developed by A.K. Lenstra and in the news maintained by P. Leyland (see [LIP]). For other part, the encryption / decryption protocol has been implemented in C ++ Visual Studio .Net 6.0.

With these implementations, which are not completely purified, the computing time needed to generate the private key of the BBS generator (cousins p and q), the 1024-bit public key (n) and secret key (K) has been 45 seconds; while for bit sequence generation 12 million bit pseudorandom the necessary time has been 75 seconds In relation to encryption processes and decryption, the time required to read the original image that is shown in Figure 6, store it in memory and encrypt it, using the sequence generated above, it has been 9 seconds. The same previous process (reading, storage and execution) carried out for the encrypted image (see Figure 7) It has required 10 seconds.

As you can see, the longest time of computing takes the process of generating the keys, what which was predictable. Note also that the procedure of encryption / decryption is very fast, since for the size of the images used (602 x 800 pixels) only about 10 are required seconds of execution On the other hand, the times presented previously they could be improved if programs are debugged used or if they are implemented in hardware.

Claims (6)

1. Encryption and description procedure using a symmetric graphic cryptosystem characterized in that it uses

to)

A cryptographically pseudo random bit generator sure,

b)

A reversible two-dimensional cellular automaton,

that encrypts and describes scanned images, defined by any number of colors. 2. Method of encryption and description by means of a symmetric graphic cryptosystem according to claim 1, characterized in that the cryptographically secure pseudo-random bit generator, from the secret key shared by two users and which is used as the generator seed, generates a sequence of pseudorandom bits. 3. Encryption method by means of a symmetric graphic cryptosystem according to claims 1 and 2, characterized by a reversible two-dimensional cellular automaton defined by a quatern (L, S, V, f), where L is a generic image of the same size as the one it will be used in the encryption process; S is the set formed by the 2 24 = 16,777,216 possible colors that can define the image; You see the neighborhood of each pixel and f is the transition rule that determines the evolution of the cellular automaton. 4. Description procedure by means of a symmetric graphic cryptosystem according to claims 1 and 2, characterized by a reversible two-dimensional cellular automaton defined by a quatern (L, S, W, g), where L is a generic image of the same size as the one it will be used in the decryption process; S is the set formed by the 2 24 = 16,777,216 possible colors that can define the image; W is the neighborhood of each pixel and g is the transition rule that determines the evolution of the cellular automaton. 5. Device for encrypting, storing data and describing images characterized in that it is constituted by an electronic system that implements in hardware or software an algorithm for the execution of a procedure according to claims 1 to 4. 6. Use of the procedure according to claims 1 to 4 and of the device according to claim 5 for the protection of storage and transmission of images.