Digital signature in automatic analyses for confidentiality against active adversaries

1. Digital signature in automatic analyses for confidentiality against active adversaries Ilja Tšahhirov, Peeter Laud

2. Goal of the analysis • Problem statement • Given the protocol (set of programs making calculations and exchanging messages) • It works with some secret data • No active adversary should be able to learn anything about the secret data • Automatically determine whether the protocol is secure or not.

3. Original technique • Published in: Peeter Laud. Symmetric encryption in automatic analyses for confidentiality against active adversaries. 2004 IEEE Symposium on Security and Privacy, pages 71-85, May 2004. • Automatic analyzer present • Programming language • Single cryptographic primitive – symmetric encryption • Definition of the adversary • Definition of the security • Protocol transformations

4. Programming language • Instruction set P :: = k:=gen_key | y:=(x1,…,xm) | x:= πim(y) | x:=encrk(y) | y:=decrk(x) | x:=random | send(x) | x:=receivel | check(x=y) | x:=constant(b) | x:=y | kp:=gen_key_pair | pk:=public_key(kp) | sm:=signkp(m) | testpk(sm) | m:=get_signed_message(sm) • The only cryptographic primitive in original analysis – symmetric encryption • Our contribution is adding the digital signature primitive support (commands in bold) to the language.

5. Adversary • Adversary is active - it schedules the participants and relays messages between them • Can modify, create new, or not deliver sent messages

6. Security definition The protocol is considered secure if the secret message is computationally independent from the adversary’s view.

7. Security against chosen-ciphertextattacks • No PPT adversary should be able to distinguish second black box from the first Without querying the second algorithm with the outputs from the first

8. Protocol transformations - encryption • During the analysis protocols are transformed • Protocols working with the first black box can be replaced to use the second (under certain conditions)

9. Information flow analysis • If some participant of the protocol contains a statement of the form x:=E(x1,…,xn) there is an information flow from the variable xi to the variable x. • The protocol is deemed secure if M * y holds for no y affecting the adversary’s view. • The protocol transformation described above breaks some of those links.

10. Unforgeability under adaptive chosen message attack • The property we require signature scheme to satisfy • Adversary making queries to the signature oracle should not be able to create a valid signature for the message that has not previously been signed by it

11. Protocol transformations – digital signature • Signature operations are replaced with checking whether the signed message being tested belongs to the set of the actually signed messages.

12. Running example • Transmit the public key and signature from A to B AgeneratesKPA A: public_key(KPA) AB: enc(KAB: public_key(KPA)) AB: enc(KAB:sign(KPA:M)) B verifies the signature B: OK • KABis a long-term key shared between Aand B.

13. Data dependencies

14. Control dependencies

15. Criterion for security No path from M to any Si  The system is secure

16. Security does not follow

17. Encryptions replaced

18. Security stilldoes not follow

19. Case handling – Case 1

20. Case 1 - Replacing the signature test

21. Case 1 – in statement handling.

22. Case 1 – checkstatement handling Sub-protocol is secure (result of check can be statically determined)

23. Case 2 Sub-protocol is secure (test statement always fails)

24. Conclusions and future work • Conclusions • The presented technique can be used in automated analysis of the cryptographic protocols • Technique is published in Nordsec 2005 proceedings, p 29-41. • Future work • Implementation of the automated analyser • Introducing the support for other cryptographic primitives