Multi-party Quantum Covert Communication with Entanglement Private-Keys

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Γώργος Παυλόπουλος
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1 30 0 JOURNL OF PPLIED SIENES Electronics and Information Engineering Vol. 30 No. Jan. 0 DOI: /j.issn TN (0) Multi-party Quantum overt ommunication with Entanglement Private-Keys O Dong SONG Yao-liang. School of Electronic Engineering and Optoelectronic Technology Nanjing University of Science and Technology Nanjing 0094 hina. ollege of communication and Information Engineering Nanjing University of Posts and Telecommunication Nanjing 0003 hina bstract: novel scheme of quantum multi-party covert communication is proposed. Using a pseudo-random sequence the random subset is selected from a set of Greenberger-Horne-Zeilinger (GHZ) shared private-key for encryption. Quantum information is rotated and hidden by disguising it as noise in a quantum error-correcting code. subset of detection is constructed and based on the complement of shared private-keys. ased on the detection scheme of typical error the private-key can be recycled. ompared to other protocols which require more private keys the proposed scheme can significantly reduce key consumption. The ability of eavesdrop detection is optimized. The optimized scheme is robust to the Trojan horse attacking. Keywords: information security covert communication quantum cryptography entanglement private-key [. [ [ (No No.60745) (No ) caodongcn@gmail.com ylsong@mail.njust.edu.cn

2 53. [4 3.. [3. [5 84. [ [5. lice ob ob. 4 bits bits... EPR. H H ϕ = χ γ () χ H γ H. ρ = χ χ ρ = χ χ () Schmidt. ρ = k p k ρ (k) ρ (k) p k = (3). ϕ ρ = Tr ( ϕ ϕ ) = Î ρ = Tr ( ϕ ϕ ) = Î (4) EPR 4 Ψ ± ( 0 ± 0) Φ ± ( 0 0 ± ) k (5) EPR [7. EPR Φ ( 0 0 ) (6) lice ob EPR Φ Φ. η plain = α 0 β (7) ϕ cipher ( =U m ( k η plain ) = U m Φ ηplain ) = [ 0 η plain X η η plain [ 0 (α 0 β ) (β 0 α ) (8) X η.

3 54 30 η plain = U m ( k ϕ cipher ) ( = U m Φ ϕcipher ) = [ 0 (α 0 β ) X ϕ (β 0 α ) [ 0 (α 0 β ) (α 0 β ) (9) i η i plain ϕ i cipher [ Z k η 0 (i) (i) 0(i) η i plain ) (i) X η Zη l. 0(i) (i) η i plain ( k (i) k(i) k(i) k=0 ( l (i) l(i) l(i) l=0 ) () X ϕ.. EPR Figure Encryption and decryption process of EPR-key-based quantum symmetric cipher GHZ GHZ. GHZ control- NOT (NOT) controlled-z. GHZ [8 Ψ = ( 000 ). n n K n i Ψ (ij) = ( 0 (ij) 0(ij) 0(ij) (ij) (ij) (ij) ) (0) j= i lice ob hris. n GHZ Figure Encryption and decryption process of GHZ-key-based quantum symmetric cipher 3 GHZ [9. [ [3. ε HSW Holevo-Schumacher-Westmoreland χ(ε) [ ( = max {p jρ j} S ε ( j p j ρ j )) j p j S(ε(ρ j )) () ε. ρ j {p j ρ j } χ (ε).

4 55.. N NS(ρ) S (ρ) = tr (ρlbρ) ρ von Neumann. NS(ρ). ξ ξ ξ NS(ρ) s i i = NS(ρ). 3. lice ψ H ψ J k c ψ H ψ J. lice ob hris ψ s ψ s NS (ρ) ψ s = NS(ρ) γ= α γ γ ψ s = NS(ρ) κ= β κ κ (3) lice NS (ρ) Ψ GHZ K 0 NS (ρ). K 0 = ( ) k k k (NS(ρ)) =( Ψ Ψ Ψ Ψ Ψ i Ψ i Ψ (NS(ρ)) Ψ (NS(ρ)) ) (4) K 0 3 K 0 K 0 K 0 K 0 GHZ K 0 ; K 0 K 0 GHZ K 0 3. lice K 0 K 0 K 0 ob hris. NS (ρ) (m ) P P 0. ob hris GHZ. ob hris P P GHZ K 0 K 0 P h K 0 h : k h = H Ψ h ( 0 h h 0 h h h h ) (5) P K 0 ob GHZ K P j K 0 j k j = H Ψ j ( 0 j 0j j j j j ) (6) P K 0 hris GHZ K. h j. (6) H H Hadamard ± = ( 0 ± ) /. 3 lice NS (ρ) GHZ ψ s. NS (ρ) ψ s γ γ h [ (h)z = U γ U (h)x γ k h γ k h = ( 0 h 0 h 0 h 0 h h [ ( 0 h 0 h 0 h 0 h h ( h h h h h 0 h ) 0 h ) γ h ( h h h h h [( 0 h 0 h 0 h 0 h h ( h h h h h ) Zγ γ h ) 0 h ) Xγ γ ) Xγ Z γ γ h i = (NS (ρ)). U (h)x γ U (h)z γ (7) lice h γ NOT controlled-z γ. ψ s κ κ j = U (j)z κ [U (j)x κ k j κ k j ( 0 j 0j 0j 0j 0j j ) [( 0 j 0j 0j 0j 0j j ) κ ( j j j j j j ) Z κ κ ( j j j j j j ) [( 0 j 0j 0j 0j 0j j ) X κ κ ( j j j j j j ) X κz κ κ (8)

5 56 30 U (j)x κ U (j)z κ lice j κ NOT controlled-z κ. lice 0 (N kc NS(ρ)) γ κ N k c γ 0 (N kc NS(ρ)) κ 0 (N kc NS(ρ)). 4 P P lice P I h ( NS(ρ) ) s h ξ h lice U h γ 0 (N kc NS(ρ)) U h ( γ 0 (N kc NS(ρ))) = s h ψ H U EH. ode = ns p h ξ h Ψ H Ψ H ξ h. lice h=0 I j ( NS(ρ) ) s j ξ j U j κ 0 (N kc NS(ρ)) U j ( κ 0 (N kc NS(ρ)) ) = s j ψ J U EJ. ode = ns p j ξ j Ψ J Ψ J ξ j. j=0 5 lice ode ode ob hris.. 6 ob hris ode ode U EH U EJ U h U j GHZ. N k c NS (ρ) GHZ. Eve ob hris lice. 3.3 GHZ. GHZ.. 4. ob hris P P K 0 K 0 Hadamard / /.. lice ob GHZ lice hris. lice ob P 0 K 0 K 0 D D. Z X ZX 3 (I ). D NOT D controlled-z D NOT controlled-z Φ Φ [4. lice ob LO ± = ( 0 ± ) / Φ ( 00 ) [ ( 00 ) = [ ( 0 ) ( 0 ) ( 0 ) ( 0 ) ( ) (9) Φ = ( 00 ) = [ ( 00 ) = [ ( 0 ) ( 0 ) ( 0 ) ( 0 ) ( ) (0) GHZ lice ob 3 ( hris ) lice ob.

6 57 Φ ( ) Φ ( ) Φ source Φ ± target ( Φ Φ ) XOR(XOR) [5 Φ source Φ source Φ target Φ target Φ source Φ target Φsource Φtarget Φ Φ 0 0 S. S t t. lice ob / t t. 4 lice ob lice hris.. lice ob lice ob. diamond [06 N = N N = N N p N ( N i=0 i ) p i ( p) N i N N p Eve p i Eve( p Eve ) N i () p p Eve N N N. [ P Eve N N ε e Nε ().... [7 EPR GHZ lice ob lice hris. lice ob lice hris. ob Hadamard. ( Eve) lice ob T ( lice lice hris ) lice ob h γ (T ) = ( 0 h 0 h (L) 0 h 0 h h [( 0 h 0 h (L) 0 h 0 h h ( h h (R) h h h (U) h ) Zγ γ ( h h (R) h [( 0 h 0 h 0 h h ( h h h h h (U) 0 h ) (U) 0 h ) γ h (U) h ) (L) 0 h (U) 0 h ) Xγ γ (R) h (U) h ) Xγ Z γ γ (3) (L) (R) (U) (L) (R) (U) lice. ob Hadamard NS (ρ) m 0. /.

7 : [ Julio G. Hiding messages in quantum data [J. Journal of Mathematical Physics 00 43(9): [ Qu Zhiguo hen Xiubo Luo Mingxing Niu Xinxin Yang Yixian. Quantum steganography with large payload based on entanglement swapping of X-type entangled states [J. Optics ommunications 0 84: [3 Natori S. Why quantum steganography can be stronger than classical steganography [J. Quantum omputation and Information 006(0): [4 urty M Santos D J. Protocols for quantum steganography [// The nd ielefeld Workshop on Quantum Information and omplexity. ielefeld Germany 004. [5 Martin K. Steganographic communication with quantum information [//Information Hiding Lecture Notes in omputer Science : [6 Liao Xin Wen Qiaoyan Sun Ying Zhang Jie. Multi-party covert communication with steganography and quantum secret sharing [J. The Journal of Systems and Software 00 83: [7 Zeng Guihua. Quantum private communication [M. [S.l.: Springer Press 00. [8 Hwang T Hang Li M. Multiparty quantum secret sharing based on GHZ states [J. Physica Scripta 0 84(4): [9. ID LDP [J. 0 33(): 8-. Zhao Shengmei Zhu Xiuli Xiao Yu. novel construction of quantum LDP codes based on balanced incomplete block designs [J. Journal of Electronics & Information Technology 0 33(): 8-. (in hinese) [0 Shaw run T. Quantum steganography with noisy quantum channels [J. Physical Review 0 83: 030. [ Shaw run T. Quantum steganography [E/OL. [ [ Shaw run T. Hiding Quantum information in the perfect code [E/OL. [ [3 Nielsen M huang I L. Quantum computation and quantum information [M. [S.l.: ambridge University Press 000. [4 Leung D W. Quantum Vernam cipher [J. Quantum Information and omputation 00 (3): 0-3. [5 ennett H Divncenzo D P Smolin J Wootters W K. Mixed state entanglement and quantum error correction [E/OL. [ arxiv: quant-ph/960404v 996. [6 enenti G Strini G. omputing the distance between quantum channels: usefulness of the Fano representation [J. Journal of Physics : tomic Molecular and Optical Physics 00 43(): ( : )

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