1 / 6

Digital Signatures

Digital Signatures. CSCI381 Fall 2005 GWU. Definition. P : set of plaintext S : set of signatures K : keyspace private function: sig k : P  S public function: ver K : P X S  {true, false} ver K (m, s) = true iff sig K (m) = s; else ver K (m, s) = false

jakeem-mooney
Download Presentation

Digital Signatures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Digital Signatures CSCI381 Fall 2005 GWU

  2. Definition • P: set of plaintext • S: set of signatures • K: keyspace • private function: sigk: P S • public function: verK: P X S {true, false} • verK(m, s) = true iff sigK(m) = s; else verK(m, s) = false • {m, sigK(m)} is a signed message CS284/Spring05/GWU/Vora/Signatures

  3. El Gamal Digital Signature • For a key K= (p, , , a);  = a mod p; a private • Choose random k invertible in Zp-1 • sigK(x, k) = (=k mod p, =(x-a)k-1 mod p-1) • verK(x, (G, D)) = true  GGD=x mod p • Depends on security of the DL problem: Find a given p, ,  CS284/Spring05/GWU/Vora/Signatures

  4. Digital Signature Example • K= (p=11, =2, =5, a=4);  = a mod p; a private • Choose random k=3 invertible in Zp-1 • sigK(x=7, k=3) = (=k mod p, =(x-a)k-1 mod p-1) = (8, 5) • verK(x, (G, D)) = true  GGD=x mod p (7 mod 11) CS284/Spring05/GWU/Vora/Signatures

  5. DSA Uses SHA(x) instead of X CS284/Spring05/GWU/Vora/Signatures

  6. Discrete Log in Elliptic Curves As before, only group is no longer Zp* The problem is to determine a given P and Q = aP in the elliptic curve group The best-known algorithm for breaking DL over Zp* takes less time than that for breaking DL over an elliptic curve group of the same size CS284/Spring05/GWU/Vora/Signatures

More Related