Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Undeniable signature
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
=== Confirmation (i.e., avowal) protocol === Bob wishes to verify the signature, ''z'', of ''m'' by Alice under the key, ''y''. # Bob picks two random numbers: ''a'' and ''b'', and uses them to blind the message, sending to Alice: {{glossary}}{{defn|''c {{=}} m<sup>a</sup>g<sup>b</sup>''.}}{{glossary end}} # Alice picks a random number, ''q'', uses it to blind, ''c'', and then signing this using her private key, ''x'', sending to Bob: {{glossary}}{{defn|''s<sub>1</sub> {{=}} cg<sup>q</sup>'' and}}{{defn|''s<sub>2</sub>'' {{=}} ''s<sub>1</sub><sup>x</sup>''.}}{{glossary end}} Note that {{glossary}}{{defn|''s<sub>1</sub><sup>x</sup>'' {{=}} ''(cg<sup>q</sup>){{sup|x}}'' {{=}} ''(m<sup>a</sup>g<sup>b</sup>'')''{{sup|x}}g<sup>qx</sup>'' {{=}} ''(m{{sup|x}}){{sup|a}}(g{{sup|x}}){{sup|b+q}}'' {{=}} ''z{{sup|a}}y{{sup|b+q}}''.}}{{glossary end}} # Bob reveals ''a'' and ''b''. # Alice verifies that ''a'' and ''b'' are the correct blind values, then, if so, reveals ''q''. Revealing these blinds makes the exchange zero knowledge. # Bob verifies ''s<sub>1</sub>'' = ''cg<sup>q</sup>'', proving ''q'' has not been chosen dishonestly, and {{glossary}}{{defn|''s<sub>2</sub>'' {{=}} ''z<sup>a</sup>y<sup>b+q</sup>'',}}{{glossary end}} proving z is valid signature issued by Alice's key. Note that {{glossary}}{{defn|''z<sup>a</sup>y<sup>b+q</sup>'' {{=}} ''(m{{sup|x}})<sup>a</sup>(g<sup>x</sup>)<sup>b+q</sup>''.}}{{glossary end}} Alice can cheat at step 2 by attempting to randomly guess ''s<sub>2</sub>''.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)