A New Related Message Attack on RSA

1

• A New Related Message Attack on RSA
• Oded Yacobi UCSD
• Yacov Yacobi MSR
• 4/3/2006

2
Motivation

• A new attack on RSA.
• New tools (new in cryptanalysis).

3

• Related Messages

4

• OAEP

5
OAEP

• M?G(r) r ?H(M ?G(r))

6

• Previous Result

7

• Our Result

8

• A Special Case

9

• Follow your nose

10

• Our tool the divided difference

11

• Example

12

• Adopted lemmas

13

• A new lemma

14

• A new lemma

15

• The attack

16

• Algorithm
• Pre-computation
• Real-time computation

17

• (Reminder Adopted lemmas)

18

• More about the computational complexity of the
  pre-computation

19

• Why is the special case more efficient?

20

• Finite difference continued

21

• Compare Results

of cryptogram pre- comp real- time
Coppersmith et al 2 0
Newton e
Our main result e
Our special case e 0
22
Acknowledgments and References?

• ACKNOWLEDGEMENTS
• Peter Montgomery
• Gideon Yuval