Pseudo-random bit generator based on multim-modal maps

1. A method for generating binary sequences through a pseudo-random bit generator based on chaos, comprising the following steps:

providing a generator block and a validation block;

defining a k-modal map on the generator block; the k-modal map is defined by:

ƒ β =β( d r+1 −x )( x−d r ), x∈ℑ r ,

generating a set of k independent sequences represented as {x 1 , x 2 , x 3 , x 4 , . . . xk}, wherein each independent sequence is produced using a dynamic system by a logic unit processing;

combining the k independent sequences to obtain a single sequence (Z);

using the single sequence (Z) as a generator block output;

wherein the set of k independent sequences defines maximal numbers of modals in a family and an interval ℑ=[a, b] is divided between k subintervals ℑ 0 =[d 1 , d 2 ), . . . , ℑ k−1 =[d k−1 , d k ], then a system ƒ β is a piecewise function by k; the parameterized family is defined by the following piecewise function

wherein: d r =r/k,(r=0,1,2, . . . , k−1), k is the number of modals, β=β(k,γ) is the bifurcation parameter, γ=1/k is the carrying on capacity; to obtain the maximum value of β with k modals there is a direct relationship, β max =4k/γ;

entering the generator block output as input on the validation block, the validation block including an encryption algorithm by a stream-cipher;

validating a combined sequence by evaluating the output of the generator to be sure that the sequence is cryptographically secure.

2. A pseudo-random bit generator based on chaos comprising a processor and a memory and a logic unit processing, wherein logic unit processing includes a block 1 and a block 2 ;

wherein the block 1 :

defines a k-modal map;

chooses k initial conditions and k different parameters of bifurcation;

generates real numbers of chaotic sequence, wherein each independent chaotic sequence is produced using a dynamic system by the logic unit processing;

provides a partition of the phase space where the k-modal map evolves;

generates binary sequences by using the phase space partition;

selects pseudo-random bit sequences that pass the National Institute of Standards and Technology (NIST) suite of statistical test; combines the chaotic independent sequences to obtain a single sequence (Z);

uses the single sequence (Z) as an output for the block 1 :

and

wherein the block 2 :

takes the output of the block 1 as an input of the block 2 ;

provides a grayscale image of size N*M;

chooses an initiation vector IV (size N*1) (stochastic vector);

generates an augmented image of size N*(M+1) given by the stochastic vector and the image;

mixes the pseudo-random bit sequence generated in the block 1 with the sequence of bits given by the augmented image.

3. The method for generating binary sequences through a pseudo-random bit generator based on chaos according to claim 1 , wherein the stream-cipher by multi-modal dynamical systems comprises a pseudo-random generator block based on k multi-modal maps 110 , in the inputs of the pseudo-random generator block has a k number 102 which denotes the number of modals and k initial conditions denoted by the vector [x 0 ] 104 , and output the pseudo-random sequence Z 106 .

4. The method of claim 1 , wherein the validation step comprises using a suite of independent statistical tests; and comparing said evaluation with a method of encryption; where in some encrypted, the result is always the same every time an image is encrypted with the same key, C 1 =C 2 ; if the histograms from images C 1 and C 2 are subtracted, the result is zero, indicating that is the same image; if images C 1 ≠C 2 , under the condition that were encrypted with the same key x 1 ; and in the reverse (decryption) always produces as output of the original image, no matter what embodiment obtained in the encryption process; the encryption process is probabilistic while the decryption process is deterministic.