update notes

pages/CSE442T/CSE442T_L19.md

@@ -2,6 +2,18 @@
 
 ## Chapter 5: Authentication
 
+### One-Time Secure Digital Signature
+
+#### Definition 136.2 (Security of Digital Signature)
+
+A digital signature scheme is $(Gen, Sign, Ver)$ is secure if for all n.u.p.p.t. $\mathcal{A}$, there exists a negligible function $\epsilon(n)$ such that $\forall n\in\mathbb{N}$,
+
+$$
+P[(pk,sk)\gets Gen(1^n); (m,\sigma)\gets\mathcal{A}^{Sign_{sk}(\cdot)}(1^n); \mathcal{A}\textup{ did not query }m\textup{ and } Ver_{pk}(m,\sigma)=\textup{``Accept''}]\leq \frac{1}{p(n)}+\epsilon(n)
+$$
+
+A digital signature scheme is one-time secure if it is secure and the adversary makes only one query to the signing oracle.
+
 ### Lamport's One-Time Signature
 
 Given a one-way function $f$, we can create a signature scheme as follows:
@@ -82,7 +94,7 @@ $B$ inverts $f$ with prob $\geq \frac{1}{p(n)}$
 
 We now have one-time secure signature scheme.
 
-We want one-time secure signature scheme that increase the size of messages relative tothe keys.
+We want one-time secure signature scheme that increase the size of messages relative to the keys.
 
 Let $H:\{h_i:D_i\to R_i\}_{i\in I}$ be a family of CRHF if