30 0 JOURNL OF PPLIED SIENES Electronics and Information Engineering Vol. 30 No. Jan. 0 DOI: 0.3969/j.issn.055-897.0.0.009. 0094. 0003.... TN98.7 055-897(0)0-005-07 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 [. [-3.... [ 0-08-0 0-0- (No.4074090 No.60745) (No.008088004) E-mail: caodongcn@gmail.com E-mail: ylsong@mail.njust.edu.cn
53. [4 3.. [3. [5 84. [5-6 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.
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. [0-. 3. [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).
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)
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.
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. /.
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