Gottesman and Chuang Quantum Digital Signature: Difference between revisions

Line 62: Line 62:
###For j=1,2
###For j=1,2
####Seller sends <math>f_{k_m^i}^j</math> to buyer and verifier
####Seller sends <math>f_{k_m^i}^j</math> to buyer and verifier
####Buyer performs '''SWAP'''<math>(f_{k_m^i}^1, f_{k_m^i}^2)</math>
####Buyer performs '''SWAP TEST'''<math>(f_{k_m^i}^1, f_{k_m^i}^2)</math>
####If SWAP= '''False''', Buyer '''aborts'''
####If SWAP TEST= '''False''', Buyer '''aborts'''
####If SWAP= '''True''', Buyer sends <math>f_{k_m^i}^{b}=f_{k_m^i}^2=f_{k_m^i}^1</math> to verifier
####If SWAP TEST= '''True''', Buyer sends <math>f_{k_m^i}^{b}=f_{k_m^i}^2=f_{k_m^i}^1</math> to verifier
####Verifier performs similar steps and sends <math>f_{k_m^i}^{v}=f_{k_m^i}^2=f_{k_m^i}^1</math> to buyer
####Verifier performs similar steps and sends <math>f_{k_m^i}^{v}=f_{k_m^i}^2=f_{k_m^i}^1</math> to buyer
####Both perform '''SWAP'''<math>(f_{k_m^i}^{b},f_{k_m^i}^{v})</math>  
####Both perform '''SWAP TEST'''<math>(f_{k_m^i}^{b},f_{k_m^i}^{v})</math>  
####If SWAP= '''False''', protocol aborted
####If SWAP TEST= '''False''', protocol aborted
####If SWAP= '''True''', distribution successful
####If SWAP TEST= '''True''', distribution successful


<u>'''Stage 2'''</u> Messaging
<u>'''Stage 2'''</u> Messaging
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# For l = 1,2,..,L
# For l = 1,2,..,L
## Buyer performs <math>k_b^i\rightarrow f_{new}</math>
## Buyer performs <math>k_b^i\rightarrow f_{new}</math>
## Buyer performs '''SWAP'''<math>(f_{new},f_{k_b^i})</math>
## Buyer performs '''SWAP TEST'''<math>(f_{new},f_{k_b^i})</math>
## If SWAP= False, <math>s_B=s_B+1</math>
## If SWAP TEST= False, <math>s_B=s_B+1</math>
#If <math>s_B<c_1M</math>, result '''1-ACC'''
#If <math>s_B<c_1M</math>, result '''1-ACC'''
#If <math>c_1M<s_B<c_2M</math>, result '''0-ACC'''
#If <math>c_1M<s_B<c_2M</math>, result '''0-ACC'''
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