### Table 4: An example of chameleon hash generation based on claw-free permutations

### Table 1. Proven lower bounds on security in the random-oracle model relative to roots (for RSA) or factorization (for Rabin/Williams). 1996 Bellare/Rogaway proved tight security for RSA and outlined a proof for unstructured Rabin/Williams, but specifically prohibited principal Rabin/ Williams and required large B. 1999 Kurosawa/Ogata claimed tight security for principal B = 0 Rabin/Williams (starred entries in the table), but the Kurosawa/Ogata proof has a fatal flaw and the theorem appears unsalvageable. 2003 Katz/Wang introduced a new proof allowing B as small as 1 for claw-free permutation pairs, but claw-free permutation pairs are not general enough to cover Rabin/Williams. This paper generalizes the Katz/Wang idea to cover Rabin/ Williams, and introduces a new security proof covering fixed unstructured B = 0 Rabin/Williams.

2008

Cited by 3

### Table 5.5: Dense cubic graphs

### Table 5.5: Dense cubic graphs

### TABLE 4 Radius of connected cubic graphs on 14 vertices

### TABLE 1. Counts of cubic graphs with additional properties. The percentages show Kotzig graphs among the hamiltonian graphs.

### Table 3. Vital statistics of the largest-known cubic broadcast networks.

"... In PAGE 5: ... For the origin of these bounds, see Section 3. Table3 shows the properties of the largest cubic broadcast graphs for T 12. All of these graphs are transitive.... ..."

### Table 3. Vital statistics of the largest-known cubic broadcast networks.

"... In PAGE 6: ... For the origin of these bounds, see Section 3. Table3 shows the properties of the largest cubic broadcast graphs for T n14 12. All of these graphs are transitive.... ..."