diff --git a/_includes/guide_transactions.md b/_includes/guide_transactions.md
index 0c205890..4c4df8cc 100644
--- a/_includes/guide_transactions.md
+++ b/_includes/guide_transactions.md
@@ -595,12 +595,25 @@ such as CoinJoin or merge avoidance, to make it extremely difficult to
 use the block chain by itself to reliably track how users receive and
 spend their satoshis.
 
-Avoiding key reuse in combination with P2PH or P2SH addresses also
-prevents anyone from seeing the user's ECDSA public key until he spends
-the satoshis sent to those addresses. This, combined with the block
-chain, provides security against hypothetical future attacks which may
-allow reconstruction of private keys from public keys in a matter of
-hours, days, months, or years (but not any faster).
+Avoiding key reuse can also provide security against attacks which might
+allow reconstruction of private keys from public keys (hypothesized) or
+from signature comparisons (possible today under certain circumstances
+described below, with more general attacks hypothesized).
+
+1. Unique (non-reused) P2PH and P2SH addresses protect against the first
+   type of attack by keeping ECDSA public keys hidden (hashed) until the
+   first time satoshis sent to those addresses are spent, so attacks
+   are effectively useless unless they can reconstruct private keys in
+   less than the hour or two it takes for a transaction to be well
+   protected by the block chain.
+
+2. Unique (non-reused) private keys protect against the second type of
+   attack by only generating one signature per private key, so attackers
+   never get a subsequent signature to use in comparison-based attacks.
+   Existing comparison-based attacks are only practical today when 
+   insufficient entropy is used in signing or when the entropy used
+   is exposed by some means, such as a
+   [side-channel attack](https://en.wikipedia.org/wiki/Side_channel_attack).
 
 So, for both privacy and security, we encourage you to build your
 applications to avoid public key reuse and, when possible, to discourage