1 / 6

Tut 6 Qn 5, TB Pg. 192

Tut 6 Qn 5, TB Pg. 192. (a). Consider the signing equation s = a -1 (m-kr) (mod p-1). Show that the verification α m ≡ ( α a ) s r r (mod p) is a valid verification procedure. Substituting, r = α k (mod p) s = a -1 (m-kr) (mod p-1) Fermat’s Little Theorem:

alec
Télécharger la présentation

Tut 6 Qn 5, TB Pg. 192

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. Tut 6Qn 5, TB Pg. 192 (a). Consider the signing equation s = a-1(m-kr) (mod p-1). Show that the verification αm≡ (αa)srr (mod p) is a valid verification procedure.

  2. Substituting, r = αk (mod p) s = a-1(m-kr) (mod p-1) Fermat’s Little Theorem: αk mod (p-1) (mod p) = αk (mod p) RHS, (αa)srr (mod p) ≡ (αa) a-1(m-kr) (mod p-1)αk (mod p) r (mod p) ≡ ((αa) a-1(m-kr) (mod p-1)) (mod p) (αkr) (mod p) ≡ (α(m-kr) (mod p-1)) (mod p) (αkr) (mod p) ≡ α(m-kr) (αkr) (mod p) ≡ αm (mod p) = LHS

  3. (b). Consider the signing equation s = am + kr (mod p-1). Show that the verification αs≡ (αa)mrr (mod p) is a valid verification procedure.

  4. Substituting, r = αk (mod p) s = am + kr (mod p-1) Fermat’s Little Theorem: αk mod (p-1) (mod p) = αk (mod p) RHS, (αa)mrr (mod p) ≡ (αa)mαk (mod p) r (mod p) ≡ αam (mod p) (αkr) (mod p) ≡ αam + kr (mod p) ≡ αs (mod p) = LHS

  5. (c). Consider the signing equation s = ar + km (mod p-1). Show that the verification αs≡ (αa)rrm (mod p) is a valid verification procedure.

  6. Substituting, r = αk (mod p) s = ar + km (mod p-1) Fermat’s Little Theorem: αk mod (p-1) (mod p) = αk (mod p) RHS, (αa)rrm (mod p) ≡ αar.αk (mod p) m (mod p) ≡ αar.αkm (mod p) ≡ αar + km (mod p) ≡ αs (mod p) = LHS

More Related