Patent Publication Number: US-2016234009-A1

Title: Chaotic Baseband Modulation Hopping Based Post-Quantum Physical-Layer Encryption

Description:
RELATED U.S. APPLICATION DATA 
     Provisional application No. 62/113,462, filed on Feb. 8, 2015. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not Applicable. 
     REFERENCE CITED 
     U.S. Patent Documents 
     U.S. Pat. No. 0,208,893 A1 August 2010 Morio Toyoshima et al. 
     U.S. Pat. No. 0,131,454 A1 February 2008 Ingrid Verbauwhede 
     U.S. Pat. No. 0,157,872 A1 July 2005 Takatoshi Ono et al. 
     U.S. Pat. No. 7,218,735 B2 May 2007 Jean-sebastien Coron 
     Other Publications 
     Song Y. Yang, Cryptanalytic Attacks on RSA, Springer, 2007. 
     Daniel J. Bernstein, Post-Quantum Cryptography, Springer, 2009. 
     Peter W. Shor, Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer, Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, Nov. 20-22, 1994, IEEE Computer Society Press, pp. 124-134. 
     Lov K. Grover, A Fast Quantum Mechanical Algorithm for Database Search, Proceedings, STOC 1996, Philadelphia Pa., USA, pp. 212-219. 
     Donny Cheung et al., On the Design and Optimization of a Quantum Polynomial-Time Attack on Elliptic Curve Cryptography, Quantum Information &amp; Computation, 9(7&amp;8):610-621, July 2009. 
     Wenhua Li et al., Chaotic FH Codes for FH-SSMA Communications, Journal of China Institute of Communications, 1996. 
     TECHNICAL FIELD 
     This invention relates generally to secure communication systems, and more specifically, to a post-quantum physical-layer encryption based on chaotic baseband modulation hopping. 
     BACKGROUND OF THE INVENTION 
     Encryption is an important approach to secure communications. Traditional encryption algorithms include asymmetric and symmetric methods. Popular traditional asymmetric encryption algorithms consist of the Rivest-Shamir-Adleman (RSA) cryptosystem and Elliptic Curve Cryptography (ECC), and symmetric encryption algorithms include the Advanced Encryption Standard (AES), ZUC, and stream cipher. 
     Quantum computer can crack RSA and ECC completely with the Shor&#39;s quantum algorithm. The security strength of AES will be reduced half by Grover&#39;s quantum algorithm. In recent years, post-quantum cryptography is a hot research topic. A few non-quantum methods have been proposed in the literature which can survive the quantum computer attack, such as code-based cryptography, Hash-based cryptography, lattice-based cryptography, and multivariate quadratic equations cryptography. All these encryption algorithms are implemented in the digital domain. 
     Another post-quantum cryptography is based on quantum mechanism. Theoretically, any eavesdropping will be detected by the quantum cryptography system following the non-cloning theorem. Classical quantum cryptography, especially quantum key distribution (QKD), has a few limitations: (1) It cannot fight against the man-in-the-middle attack because of lack of mutual authentication; (2) Because of the hardware implementation limit, some backdoors may exist which can be utilized to find the quantum key. 
     Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions and chaotic system parameters. There are two kinds of chaotic dynamic systems: continuous and discrete. Chaos has been used to provide secure communications. For example, discrete chaotic map has been used to design Frequency Hopping (FH) codes, and Direct-Sequence-Spread-Spectrum (DSSS) codes. Chaotic signal can also be used as a non-sine carrier. 
     According to the International Organization for Standardization (OSI) model, encryption can be designed in both the above-physical layer and physical-layer. RSA, ECC, and AES are all processed in the digital domain, which is above the physical layer. QKD is a physical-layer asymmetric encryption approach. Other physical-layer secure communication systems include physical-layer scrambling and spread spectrum communications. 
     This invention proposes a new physical-layer symmetric encryption method which is suitable for all communication systems and can defend the quantum computer attack such as Shor&#39;s algorithm and Grover&#39;s algorithm. It can also be applied to help QKD against the man-in-the-middle attack. 
     SUMMARY 
     This invention is related to secure communication systems, and more specifically, to a post-quantum physical-layer encryption based on chaotic baseband modulation hopping. The basic idea is that the baseband modulation such as constellation, mapping, power level, will vary symbol-by-symbol according to an assigned random sequence. We name this approach as Baseband Modulation Hopping (BMH). Chaotic dynamic systems such as discrete chaotic maps are applied to generate the BMH codes. 
     At the transmitter side, chaotic dynamic systems are first selected and pre-shared with the receiver (not just limited to chaotic systems. Other random sequence generators can also be applied in this invention). The pre-shared key is used as the chaotic dynamic system parameters and initial values. Because chaotic systems are extremely sensitive to its system parameters and initial values, tiny difference will generate two totally different chaotic random sequences. From the raw chaotic sequences, we can generate BMH random codes. One method is quantization-based. Another method is to select certain bits from the raw chaotic sequence. A baseband modulation library (BML) is designed in advance and pre-shared between the transmitter and the receiver. Each constellation/mapping approach is assigned a tag. For example, QAM is assigned “1”, and QPSK is assigned “2”. There are two baseband modulation hopping approaches: (1) The quantized chaotic random sequence and BML are used to generate the BMH code sequence while the user information is used as the modulation information; (2) The user information and BML are used to generate the BMH sequence code while the quantized chaotic sequence is used as the modulation information. Multiple chaotic sequences will be generated in parallel, and are used for constellation/mapping sequence code, scrambling sequence code, and power control sequence code. 
     At the receiver side, the pre-shared key and chaotic sequence generator (the same as in the transmitter side) are used to generate the BMH modulation sequence. Then the BMH demodulation module will recover the encoded user information. In the first approach, the chaotic BMH sequence code is used to determine the constellation/mapping for each symbol. Traditional demodulation techniques can be applied directly to decode the user information. In the second approach, because the user information is used to design the BMH sequence code, we cannot know the baseband modulation for each symbol in advance. The BMH demodulation module will de-code the constellation/mapping for each symbol by the known chaotic sequence. Then the user information is recovered from the de-coded BMH sequence. 
     The BMH physical-layer encryption can be combined with (1) digital-domain based encryption algorithms such as AES, code-based post-quantum cryptography; (2) other physical-layer secure communication techniques such as FH and DSSS; (3) QKD to provide mutual authenticated key distribution. 
     This invention can be applied to all kinds of communication systems including wireless (radio frequency, optical, quantum channel, sonar) and wire (optical fiber, power line, telephone line, wire quantum channel, etc.). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention may be understood, by way of examples, to the following drawings, in which: 
         FIG. 1  is a top view of the chaotic BMH based post-quantum physical-layer encryption/decryption system. 
         FIG. 2  is one example of raw chaotic sequences generated by the logistic chaotic map. 
         FIG. 3  illustrates one example of quantized chaotic sequences generated from  FIG. 2 . 
         FIG. 4  shows the first signal constellation/mapping approach. 
         FIG. 5  shows the second signal constellation/mapping approach. 
         FIG. 6  shows the third signal constellation/mapping approach. 
         FIG. 7  shows the fourth signal constellation/mapping approach. 
         FIG. 8  shows the modulation module of the first chaotic BMH mode. 
         FIG. 9  illustrates the demodulation module of the first chaotic BMH mode. 
         FIG. 10  is the modulation module of the second chaotic BMH mode. 
         FIG. 11  illustrates the demodulation module of the second chaotic BMH mode. 
         FIG. 12  is the BMH with phase scrambling. 
         FIG. 13  is the BMH with random power control. 
         FIG. 14  is the combination of BMH and DS/FH. 
         FIG. 15  shows the multi-round BMH modulation based encryption/decryption. 
         FIG. 16  shows the channels suitable for BMH. 
     
    
    
     DETAILED DESCRIPTION OF THIS INVENTION 
       FIG. 1  shows the block diagram of a top view of the chaotic BMH based post-quantum physical-layer encryption/decryption system. There are three components: transmitter  001 , receiver  002 , and the channel  003 . 
     The basic flowchart of the BMH encryption system is explained as follows. At the transmitter side  001 , the raw user information  004  is first encoded  005  by digital-domain AES encryption, and/or channel encoding. Pre-shared key  010  is used as the chaotic system  008  parameters and initialization values. The chaotic sequence generator  009  generates a quantized chaotic sequence. The BML  011 , chaotic sequence generator output and encoded user information are used as the input to the BMH modulation module  006 . The BMH modulated information is input into the carrier module  007  and transmitted through the channel  003  to the receiver  002 . At the receiver side  002 , the received signal from the channel is first carrier de-modulated  015 , then input into the BMH demodulation module  014 . Pre-shared key  018  is used as the system parameters of the chaotic map  016 . The chaotic sequence generator module  017  generates the chaotic sequences. The BMH demodulation module  014  recovers the encoded user information. The decode module  013  recovers the original user information  012 . 
     There are a number of methods to formulate the chaotic systems. The first example is logistic map defined as 
         x ( n+ 1) =r ( n ) *x ( n )*(1− x ( n ))   (1)
 
     where r(n) is the system parameter of the logistic map and x(1) is the initialization.  FIG. 2  is one example of raw chaotic sequences generated by the logistic chaotic map. The second example is the Hennon map defined as 
         x ( n+ 1)=1− a*x ( n ) *x ( n ) +y ( n )   (2)
 
         y ( n+ 1) =b*x ( n )   (3)
 
     where a and b are the system parameters of the Hennon map and x(1) and y(1) are the initialization. The pre-shared key is used as x(1), y(1), a, b to generate the chaotic sequence. Multiple chaotic maps can be cascaded to formulate a hyper-chaotic system to generate more chaotic sequences at the same time. 
       FIG. 3  illustrates one example of quantized chaotic sequences generated from  FIG. 2 . The raw chaotic sequence in  FIG. 2  has values between (0, 1). The first method to generate the quantized chaotic sequence is through quantization. (0, 1) is divided into 4 intervals: (0, 0.25), (0.25, 0.50], (0.50, 0.75], (0.75, 1.00), which are tagged with 1, 2, 3, 4, respectively. In BML, each constellation/mapping has a special tag. From the BML and quantized chaotic sequence, the BMH random code is generated. The quantization values (0.25, 0.50, 0.75) are also used as the pre-shared key, together with the chaotic system parameters and initialization. This invention does not limit only the quantization method. 
     Various kinds of constellation/mapping can be used to set up the BML such as BPSK, QPSK, QAM, PPM.  FIG. 4  shows the first signal constellation/mapping approach. It is a binary I/Q  403 / 404  constellation. 0 ( 401 ) and 1 ( 402 ) are mapped to (I=1, Q=0) and (I=−1, Q=0), respectively. This constellation/mapping is tagged with “1” in BML. 
       FIG. 5  shows the second signal constellation/mapping approach. It is a binary I/O  503 / 504  constellation. 0 ( 501 ) and 1 ( 502 ) are mapped to (I=−1, Q=0) and (I=1, Q=0), respectively. This constellation/mapping is tagged with “2” in the BML. 
       FIG. 6  shows the third signal constellation/mapping approach. It is a two-bit constellation/mapping. It is tagged as “3” in the BML. I ( 605 )/Q ( 606 ) constellation is defined as  00  ( 601 ), 01 ( 602 ), 10 ( 603 ), 11 ( 604 ). 
       FIG. 7  shows the fourth signal constellation/mapping approach. It is two-bit constellation/mapping. It is tagged as “4” in the BML. I ( 705 )/Q ( 706 ) constellation is defined as 00 ( 701 ), 01 ( 702 ), 10 ( 703 ), 11 ( 704 ). 
       FIG. 8  shows the modulation module of the first chaotic BMH mode. The BMH random sequence module  802  utilizes the quantized chaotic sequence  801  and BML  805  to generate the random symbol-by-symbol constellation/mapping sequence. The baseband modulation module  803  modulates the user&#39;s information  806  by using the random symbol-by-symbol constellation/mapping from the module  802 . The baseband modulated signal is then input into the carrier modulation module  804 . 
       FIG. 9  illustrates the demodulation module of the first chaotic BMH mode. The same BMH modulation sequence as in the transmitter is generated through the baseband random sequence module  902 , by using the quantized chaotic sequence module  901  and BML  905 . The baseband demodulation module  903  and traditional carrier demodulation techniques  906  recover the user&#39;s information  904  symbol-by-symbol. 
       FIG. 10  is the modulation module of the second chaotic BMH mode. The difference between the first and second modes is how to assign the functions of the chaotic sequence and user&#39;s information. Unlike the first approach, in the second approach, the baseband random sequence module  1002  generates the random symbol-by-symbol constellation/mapping sequence by using the user&#39;s information  1001  and BML  1005 . The baseband modulation module  1003  modulates the quantized chaotic sequence  1006 . The final step is the carrier modulation module  1004 . 
       FIG. 11  illustrates the demodulation module of the second chaotic BMH mode. In the second approach, the modulated information (quantized chaotic sequence  1101 ) is computed from the pre-shared key. But the symbol-by-symbol constellation/mapping generated from the user information is not known. The baseband demodulation module  1102  cannot use the traditional communication baseband demodulation techniques. A Viterbi algorithm is designed to decode the symbol-by-symbol constellation/mapping tag defined in the BML  1104  after carrier demodulation  1105 , and then the user information  1106  is recovered from the decoded constellation/mapping sequence. 
       FIG. 12  is the BMH with phase scrambling. It is a combination of the first BMH (constellation/mapping based) approach and stream ciphering. At the transmitter side  1201 , a special chaotic sequence  1208  is generated. A random phase generated from the chaotic sequence  1208  is multiplexed with the BMH modulation output  1205  of the encoded user information  1204  in the scrambling module  1206 . Then the scrambled baseband modulation signal is input into the carrier modulation module  1207 , and transmitted through channel  1203 . At the receiver side  1202 , the received carrier signal from the channel  1203  is first gone through the carrier demodulation module  1212 . Then the de-scrambling module  1211  de-scrambles the random phase added to each symbol. Finally the baseband demodulation module  1210  recovers the user&#39;s information  1209  by using the quantized chaotic sequence  1213 . 
       FIG. 13  is the BMH with random power control. Compared with the added random phase, a random power control is generated is generated in the power control module  1306 . Other modules are the same as in  FIG. 12 . The transmitter  1301  has encoded user information  1304 , BMH modulation  1305 , power control  1306 , quantized chaotic sequence  1308 , and carrier modulation  1307 . The modulated carrier signal is transmitted through channel  1303 . The receiver  1302  has carrier demodulation  1312 , de-power control  1311 , BMH demodulation  1310 , quantized chaotic sequence  1313 , and recovered user information  1309 . 
       FIG. 14  is the combination of BMH and Discrete sequence (DS) and Frequency Hopping (FH). DS and FH are two popular spread spectrum techniques which provide secure communications. BMH can be combined with DS/FH to provide anti-jamming, secure communications. Chaotic BMH modulation  1401  is combined with DS/FH  1402 . The modulated signal is transmitted through channel  1403 . The receiver will demodulate DS/FH  1404  and then chaotic BMH  1405 . 
       FIG. 15  shows the multi-round BMH modulation based encryption/decryption. At the transmitter side, after first-round chaotic BMH modulation  1501 , a common constellation/mapping  1502  is used to demodulate the BMH signal, and then input into the second round BMH encryption  1503 . At the receiver side, the second-round BMH signal is first demodulated  1504 . Then the symbol-by-symbol constellation/mapping sequence is modulated by the public constellation/mapping  1505 . Finally, the first-round BMH demodulation  1506  is applied to recover the user&#39;s information. 
       FIG. 16  shows the channels suitable for BMH. This invention is suitable for various wireless  1602  (radio frequency, optical, quantum, sonar, single carrier and multi-carrier, OFDM, MIMO, etc.) and wire communication channels  1603  (optical fiber, power line, telephone line, single carrier and multi-carrier, etc.).