Patent Publication Number: US-2002012431-A1

Title: Encryption system using light interference theory

Description:
BACKGROUND OF THE INVENTION  
       [0001] The present invention relates generally to encryption systems, and more particularly, to an encryption system that is implemented using the concepts of light interference theory.  
       [0002] The Data Encryption Standard (DES) and Rivest Shamir Aldeman (RSA) cryptographic systems are two of the best known and most widely used cryptographic systems. The effective size of the cryptograph key of the DES system is 56 bit. As a result, the DES system is relatively insecure, because the bit size of the cryptograph key is not large. Software implementations of DES encryption are also slow due to the complexity of the system. The RSA algorithm is based on the computationally difficult problem of factoring large prime numbers, since its processes rely on complicated mathematics which execute slowly in software. Thus, software implementations of the RSA algorithm are also relatively slow. The present invention overcomes the problems of both the DES and RSA cryptographic systems by enabling a relatively fast, more secure encryption without requiring excessive computation.  
       SUMMARY OF THE INVENTION  
       [0003] The invention is an encryption system using the mathematics of light interference theory to increase security and speed encryption. It segments and converts a 128 bit cryptograph key into two digital optical signals with amplitudes, wavelengths, initial phases, and a resulting aberration (optical path length difference) determined at point P where the two digital optical signals meet. The invention efficiently increases length of the cryptograph key.  
       [0004] Using a digital light interference signal generator to generate the aberration value changes dynamically, the luminance of light at the interference fringe at point P will change as the aberration changes. Using the luminance of light at the interference fringe as a random number, then the ciphertext will be generated by XOR operations between the plaintext and the random numbers determined by the luminance at point P. Since the calculations of the digital light interference signal generator are relatively simple, the encrypting and decrypting processes are sped up as a result.  
       [0005] The cryptographic system of the present invention can be used in secure computer systems and secure communication systems as well as other systems requiring secure, fast encryption and decryption. It can be used in relatively low cost, high performance products whether enabled in software on hardware or in embedded hardware. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0006] These and other features, objects and advantages of the present invention will become apparent from the following description and drawings wherein like reference numerals represent like elements in several views, and in which:  
     [0007]FIG. 1 is a functional block diagram of the encryption and decryption system in accordance with the principles of the present invention.  
     [0008]FIG. 2 is a diagram showing a cryptograph key segment and the conversion process in accordance with the principles of the present invention.  
     [0009]FIG. 3 is a diagram showing an encryption process in accordance with the principles of the present invention.  
     [0010]FIG. 4 is a diagram showing a decryption process in accordance with the principles of the present invention.  
     [0011]FIG. 5 is a list showing a sample plaintext.  
     [0012]FIG. 6 is a list showing the resulting ciphertext from encryption using cryptograph key “key1”.  
     [0013]FIG. 7 is a list showing the same sample plaintext as used in FIG. 5.  
     [0014]FIG. 8 is a list showing the resulting ciphertext from encryption using cryptograph key “key2”. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT  
     [0015] Set forth below is a description of what are currently believed to be the preferred embodiments or best examples of the invention claimed. Future and present alternatives and modifications to the preferred embodiments are contemplated. Any alternates or modifications in which insubstantial changes in function, in purpose, in structure or in result are intended to be covered by the claims of this patent.  
     [0016] Two digital optical signals which have the same amplitude A, wavelength λ, and initial phase Φ 0 . If the aberration is ΔS at point P where the two digital optical signals meet, then the difference of the light waves at the optical path is ΔS/λ. Since the initial phase Φ 0  of the two digital optical signals is the same, then the difference of phases at point P where the two digital optical signals meet is ΔΦ=2π*ΔS/λ.  
     [0017] For example, the displacement of the two digital optical signals at point P where they meet (y1 and y2) can be expressed as follows:  
       y 1 =A  sin (ω t+π*ΔS/λ+Φ   0 )  
       y 2 =A  sin (ω t−π*ΔS/λ+Φ   0 ) 
     [0018] where, ω is angular speed, and t is time. The light interference (Y) of the two digital optical signals at point P, when the displacements of the two digital optical signals are combined, is expressed as the following, where Y=y1+y2:  
       A  sin (ω t+π*ΔS/λ+Φ   0 )+ A  sin (ω t−π*ΔS/λ+Φ   0 ) =2 A  sin ((2 ωt+ 2Φ 0 )/2) cos ((2 π*ΔS /λ)/2) =2 A  cos (π*Δ S /λ) sin ((ω t+Φ   0 ). 
     [0019] To simplify computation, for instance, let variable t=0, then the mathematical equation will be  
       Y= 2A cos (π*Δ S /λ) sin (Φ 0 ). 
     [0020] Because the luminance of the light interference fringe at point P has a positive correlation with wave propagation energy, the equation can be further simplified to the following:  
       Y=A * cos (π*Δ S /λ) sin (Φ 0 ) 
     [0021] If we set aberration ΔS equal to variable x, the function of luminance and aberration is the following:  
       f ( x )= A * cos (π/λ* x )* sin (Φ 0 ). 
     [0022] This function is used as the light interference signal generating function.  
     [0023] To generate the initial state of a light interference signal the following difference equations are used:  
       x   1   =A * cos (π/λ* x   0 )* sin (Φ 0 )+ y   0    
     
       y 
       1 
       =−x 
       0 
     
     [0024] To generate the sequential random numbers to be used in creating the ciphertext, the following two equations are used:  
       x   n+1   =A * cos (π/λ* x   n )* sin (Φ 0 )+ y   n    
     
       y 
       n+1 
       =−x 
       n 
     
     [0025] Here, n=1,2,3, . . . , and y n  is a feed-back signal based on the previous element of the random number stream.  
     [0026] Thus, a light interference signal generator used to generate a stream of random numbers used in creating the ciphertext or deciphering the ciphertext can be determined by the two equations above.  
     [0027] When inputs A, λ, Φ 0  and x 0 , y 0  for initial values of x n  and y n  are input into a light interference signal generator, the aberration x n  will change dynamically, and the luminance of light interference fringe x n+1  will be output as stream of random numbers (x 1 , x 2 , x 3 , . . . ) by the light interference signal generator, based on the initial state values input into the light interference signal generator.  
     [0028] The cryptograph key used is ordinarily a 128 bit key. If the key is smaller, the key buffer will be filled by a repeat of the cryptograph key until the key buffer is filled at 128 bit. The cryptograph key is 128 bit, if it is segmented by 32 bit, it will generate four sub keys (K1, K2, K3, K4), which are used with different equations to change the sub keys to amplitude A, wavelength λ, initial phase Φ 0 , and aberration x 0  of digital optical signal. Here, the A, λ, Φ 0  and x 0  are floating point data.  
     [0029] For instance, the range of values used in the light interference signal generator could be the following ranges:  
     0.90000000000 &lt;=A&lt; 1.00000000000  
     0.50000000000&lt;=λ&lt;0.60000000000  
     8.00000000000&lt;=Φ 0 &lt;9.00000000000  
     0.80000000000 &lt;=x   0 &lt;0.90000000000 
     [0030] The equations in the key converter can be linear equations, or any other relatively quickly calculated equation. One example of a key conversion process can be expressed as the following code:  
     [0031] begin  
     [0032] tmp=(double) K1/π;  
     [0033] A=0.9+(tmp−(int) tmp)*0.1;  
     [0034] tmp=(double) K2/π;  
     [0035] λ=0.5+(tmp−(int) tmp)*0.1;  
     [0036] tmp=(double) K3/π;  
     [0037] Φ 0 =8.0+(tmp−(int) tmp);  
     [0038] tmp=(double) K4/π;  
     [0039] x 0 =0.8+(tmp−(int) tmp)*0.1;  
     [0040] end  
     [0041] This uses the four different 32 bit sub keys from the 128 bit key. The sub keys are then used to set the initial states of the light interference generator.  
     [0042] In addition, initial value y 0  of feedback signal y n  can be 0.0, or any other convenient value.  
     [0043] An example of the process follows. The plaintext consists of a stream of data (m 1 , m 2 , m 3 , . . . ) and a random stream of data (x 1 , x 2 , x 3 , . . . ) is generated by the light interference signal generator. The ciphertext stream of data (c 1 , c 2 , c 3 , . . . ) is generated by an XOR (exclusive OR) operation between the plaintext stream of data and the random stream of data generated by the light interference signal generator, on an element by element basis. In other words, an element of the ciphertext is generated by an XOR operation between the associated elements of the plaintext and the random stream of data generated by the light interference signal generator, as follows:  
     [0044] For encrypted element c i  of the ciphertext, c i =m i  XOR x i  (for i=1,2,3, . . . ).  
     [0045] To decipher the ciphertext, the ciphertext stream of data (c 1 , c 2 , c 3 , . . . ) is used, and the random stream data (x 1 , x 2 , x 3 , . . . ) is again generated again by a light interference signal generator. Because the same initial states are used in the light interference signal generator, the random stream of data will be the same. The plaintext stream of data (m 1 , m 2 , m 3 , . . . ) is recovered by an XOR (exclusive OR) operation between the ciphertext stream data and the random stream of data generated by the light interference signal generator using the same initial conditions for the two optical signals. The decrypted plaintext, then, is determined as follows:  
     [0046] For decrypted element (plaintext element) m i  of the plaintext, m i =c i  XOR x i  (for i=1,2,3, . . . ).  
     [0047]FIG. 1 is a functional block diagram of the encryption and decryption system. In the process of encryption, the system segments and converts the cryptograph key  10  into the initial values of a light interference signal, then inputs those values into a digital light interference signal generator  12 . The generator outputs the luminance of the light interference fringe as a random number stream into the encryptor  14 , which then encrypts the stream data from the plaintext input device  16 , and finally encrypted data is output into the communication circuit  20 .  
     [0048] The decryption process is similar to the encryption process, with the only difference being difference is that the encrypted stream data input into decryptor  22 , then decrypted with random number from digital light interference signal generator  24 , the decrypted data will be output into the plaintext output device  26 .  
     [0049]FIG. 2 is a diagram showing a cryptograph key segment  50  and the conversion process. The maximum length of the cryptograph key is 128 bit, if the key is segmented by 32 bit, four sub keys (K 1 , K 2 , K 3 , K 4 ) are generated, key converter  11  then uses different equations to change the sub keys to amplitude A, wavelength λ, initial phase Φ 0 , and aberration x 0  of digital optical signal. The four sub keys are then input into the digital light interference signal generator  13 .  
     [0050]FIG. 3 is a diagram showing the encryption process. A stream of data from the plaintext input device  30  is input into the encryptor  32 . Aberration x 0 , amplitudes A, wavelengths λ,initial phases Φ 0  from the cryptograph key converter are set as initial values. These values are input into light interference signal generating function f(x n )  48 , the result calculated by f(x n ) plus feedback signal y 0  by the adder  35 , and the new result input into the encryptor as x n+1 . In the encryptor, data m n+1  from plaintext stream data are computed with x n+1  by XOR operations, then encrypted data will be outputted into the communication circuit  38  as ciphertext element c n+1 . Meanwhile, x n+1  is also transferred into buffer  1  as the next x n  in f(x n ). x n  is changed to −x n  in an inverter  36 , and transferred to buffer  2 , then transferred into buffer  3  as feedback signal y n+1 . y n+1  will be used as y n  in next computation process, completing the feedback loop.  
     [0051]FIG. 4 is a diagram showing the decryption process. The decryption process is similar to the encryption process, the only difference being that data element c n+1  in encrypted stream data from the communication circuit  40  is input into the decryptor  42  instead of the plaintext. The ciphertext is then combined with data x n+1  in the random number stream data from the digital light interference signal generator by a series of XOR operations, and the decrypted data elements are output into the plantext output device  44 .  
     [0052] To verify the properties of the system, a software program was successfully developed using the invention. Sample data were encrypted and decrypted. FIG. 5 and FIG. 7 show plaintext data. FIG. 6 shows encrypted data generated using the invention and a first cryptograph key, key1. FIG. 8 also shows encrypted data, generated using the invention and a second cryptograph key, key2.  
     [0053] While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those of ordinary skill in the art that changes and other modifications can be made without departing from the invention in its broader aspects. Various features of the present invention are set forth in the following claims.