From e09a183984ad92729c40b1ed51d2e9f6388ca9ba Mon Sep 17 00:00:00 2001
From: mdw <mdw>
Date: Wed, 31 Oct 2001 09:33:59 +0000
Subject: [PATCH] Fix bugs.

---
 auth-mac.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/auth-mac.tex b/auth-mac.tex
index 8b4eb8a..cd3defa 100644
--- a/auth-mac.tex
+++ b/auth-mac.tex
@@ -107,7 +107,7 @@
   
   If $F_K\colon \{0, 1\}^* \to \{0, 1\}^L$ is a $(t, q, \epsilon)$-secure
   PRF, then it's also a $(t', q_T, q_V, \epsilon')$-secure MAC, with $q = q_T
-  + q_V + 1$, $t = t' + O(q)$, and $\epsilon \le \epsilon' + (q_V + 1)
+  + q_V + 1$, $t = t' + O(q)$, and $\epsilon' \le \epsilon + (q_V + 1)
   2^{-L}$.  The constant hidden by the $O(\cdot)$ is small and depends on the
   model of computation.
   
@@ -152,7 +152,7 @@
   $A$ does when it's given a random function.  But we know that the
   probability of it successfully guessing the MAC for a message for which it
   didn't query $T$ can be at most $(q_V + 1) 2^{-L}$.  So
-  \[ \Adv{prf}{F}(D) \le \Succ{suf-cma}{F}(A) - (q_V + 1) 2^{-L}. \]
+  \[ \Adv{prf}{F}(D) \ge \Succ{suf-cma}{F}(A) - (q_V + 1) 2^{-L}. \]
   Let $q = q_T + q_V + 1$; then counting, rearranging, maximizing yields
   \[ \InSec{suf-cma}(F; t, q_T, q_V) \le
      \InSec{prf}(F; t + O(q), q) + (q_V + 1)2^{-L}. \]%
-- 
2.11.0

