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Gottesman and Chuang Quantum Digital Signature: Difference between revisions
Gottesman and Chuang Quantum Digital Signature (edit)
Revision as of 11:04, 28 May 2019
, 28 May 2019→Pseudocode
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<u>'''Stage 1'''</u> Distribution | <u>'''Stage 1'''</u> Distribution | ||
*'''Input''' L | *'''Input''' L | ||
*'''Output''' Seller: <math>\{k_0^i, k_1^i\}</math>, <math>1\le i\ | *'''Output''' Seller: <math>\{k_0^i, k_1^i\}</math>, <math>1\le i\le M</math>, <math>\{f_{k_0^i}, f_{k_1^i}\}</math> | ||
**'''Key Generation''' | **'''Key Generation''' | ||
#For m = 0,1 | #For m = 0,1 | ||
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###Seller performs <math>k_m^i\rightarrow f_{k_m^i}</math> | ###Seller performs <math>k_m^i\rightarrow f_{k_m^i}</math> | ||
**'''Key Distribution: No Trusted Third Party Assumption | **'''Key Distribution:''' (No Trusted Third Party Assumption) | ||
#For m = 0,1 | #For m = 0,1 | ||
##For i=0,M | ##For i=0,M | ||
###For j=1,2 | ###For j=1,2 | ||
####Seller sends f_{k_m^i}^j to buyer and verifier | ####Seller sends <math>f_{k_m^i}^j</math> to buyer and verifier | ||
####Buyer performs SWAP1(f_{k_m^i}^1, f_{k_m^i}^2) | ####Buyer performs '''SWAP1'''<math>(f_{k_m^i}^1, f_{k_m^i}^2)</math> | ||
####If SWAP1= False, Buyer aborts | ####If SWAP1= '''False''', Buyer '''aborts''' | ||
####If SWAP1= True, Buyer sends f_{k_m^i}^{b}=f_{k_m^i}^2=f_{k_m^i}^1 to verifier | ####If SWAP1= '''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 f_{k_m^i}^{v}=f_{k_m^i}^2=f_{k_m^i}^1 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(f_{k_m^i}^{b},f_{k_m^i}^{v}) | ####Both perform SWAP<math>(f_{k_m^i}^{b},f_{k_m^i}^{v})</math> | ||
####If SWAP2= False, protocol aborted | ####If SWAP2= '''False''', protocol aborted | ||
####If SWAP2= True, distribution successful | ####If SWAP2= '''True''', distribution successful | ||
<u>'''Stage 2'''</u> Messaging | <u>'''Stage 2'''</u> Messaging | ||
*'''Input''' Seller: Message b, Private Key for k_b | *'''Input''' Seller: Message b, Private Key for <math>k_b</math> | ||
*'''Output''' Buyer: '''1-ACC''' (Message is valid and transferable), '''0-ACC''' (Message is valid but not transferable), '''REJ''' (Message is invlaid) | *'''Output''' Buyer: '''1-ACC''' (Message is valid and transferable), '''0-ACC''' (Message is valid but not transferable), '''REJ''' (Message is invlaid) | ||
**'''Signing:''' | **'''Signing:''' | ||
# For i=1,M | # For i=1,M | ||
# Seller sends Buyer (b,k_b^i) | # Seller sends Buyer (b,<math>k_b^i</math>) | ||
# For l = 1,2,..,L | # For l = 1,2,..,L | ||
## Buyer performs k_b^i\rightarrow f_{new} | ## Buyer performs <math>k_b^i\rightarrow f_{new}</math> | ||
## Buyer performs SWAP(f_{new},f_{k_b^i}) | ## Buyer performs '''SWAP'''<math>(f_{new},f_{k_b^i})</math> | ||
## If SWAP= False s_B=s_B+1 | ## If SWAP= False <math>s_B=s_B+1</math> | ||
#If s_B<c_1M, result '''1-ACC''' | #If <math>s_B<c_1M</math>, result '''1-ACC''' | ||
#If c_1M<s_B<c_2M, result '''0-ACC''' | #If <math>c_1M<s_B<c_2M</math>, result '''0-ACC''' | ||
#If s_B>c_2M, result '''REJ''' | #If <math>s_B>c_2M</math>, result '''REJ''' | ||
==Further Information== | ==Further Information== | ||