EEC-484/584 Computer Networks Lecture 16 Wenbing Zhao

2 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Outline Reminder –Quiz#5 4/30 4-6pm –Final Revised Wiki Page due 5/5 midnight –Presentation: request for waiver will be handled FCFS Waiver request must have a revision summary and a url to your revised wiki page Cipher modes Public key algorithm Digital signature Message digest and secure hash functions Public key infrastructure

3 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Stream Cipher Mode To be insensitive to transmission error, an arbitrarily large sequence of output blocks, called the keystream, is treated like a one-time pad and XORed with the plaintext to get the ciphertext –It works by encrypting an IV, using a key to get an output block –The output block is then encrypted, using the key to get a second output block –This block is then encrypted to get a third block, and so on

4 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Stream Cipher Mode Encryption Decryption The keystream is independent of the data –It can be computed in advance –It is completely insensitive to transmission errors

5 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Stream Cipher Mode It is essential never to use the same (key, IV) pair twice with a stream cipher because doing so will generate the same keystream each time Using the same keystream twice exposes the ciphertext to a keystream reuse attack Stream cipher mode is also called output feedback mode

6 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Keystream Reuse Attack Plaintext block, P0, is encrypted with the keystream to get P0 XOR K0 Later, a second plaintext block, Q0, is encrypted with the same keystream to get Q0 XOR K0 An intruder who captures both ciphertext blocks can simply XOR them together to get P0 XOR Q0, which eliminates the key The intruder now has the XOR of the two plaintext blocks If one of them is known or can be guessed, the other can also be found In any event, the XOR of two plaintext streams can be attacked by using statistical properties of the message

7 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Counter Mode To allow random access to encrypted data –The IV plus a constant is encrypted, and the resulting ciphertext XORed with the plaintext –By stepping the IV by 1 for each new block, it is easy to decrypt a block anywhere in the file without first having to decrypt all of its predecessors

8 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Public-Key Algorithms Distributing keys => the weakest link in most cryptosystems –No matter how strong a cryptosystem was, if an intruder could steal the key, the system was worthless –Cryptologists always took for granted that the encryption key and decryption key were the same Diffie and Hellman (1976) proposed a radically new kind of cryptosystem: encryption and decryption keys were different –D(E(P)) = P –It is exceedingly difficult to deduce D from E –E cannot be broken by a chosen plaintext attack

9 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Public-Key Algorithms Public-key cryptography: –Encryption algorithm and the encryption key can be made public How to establish a secure channel –Alice and Bob have never had previous contact –Alice sends Bob E B (P) (message P encrypted using Bob’s public encryption key E B ) –Bob receives the encrypted message and retrieves the plaintext by using his private key P = D B (E B (P)) –Bobs then sends a reply E A (R) to Alice

10 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao RSA Rivest, Shamir, Adleman, 1978: a good method for public-key cryptography RSA method: –Choose two large primes, p and q (typically 1024 bits) –Compute n = p  q and z = ( p-1 )  ( q-1 ) –Choose a number relatively prime to z and call it d –Find e such that e  d = 1 mod z To encrypt a message, P, Compute C = P e (mod n) To decrypt C, compute P = C d (mod n) The public key consists of the pair (e, n) The private key consists of the pair (d, n)

11 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao RSA An example of the RSA algorithm –P = 3, q = 11 => n = 33 and z = 20 –A suitable value for d = 7 –e can be found by solving the eq. 7e = 1 (mod 20) => e = 3 –C = P 3 (mod 33), P = C 7 (mod 33)

12 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Digital Signatures Requirement on digital signatures: one party can send a signed message to another party in such a way that the following conditions hold: –The receiver can verify the claimed identity of the sender –The sender cannot later repudiate the contents of the message –The receiver cannot possibly have concocted the message himself

13 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Symmetric-Key Signatures Big Brother (BB): a central authority that knows everything and whom everyone trusts –Each user chooses a secret key and shares it with BB Digital signatures with Big Brother

14 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Public-Key Signatures Digital signatures using public-key cryptography –Requires E(D(P)) = P (in addition to D(E(P)) = P)

15 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Message Digests Message digest (MD): using a one-way hash function that takes an arbitrarily long piece of plaintext and from it computes a fixed-length bit string –Given P, it is easy to compute MD(P) –Given MD(P), it is effectively impossible to find P –Given P no one can find P’ such that MD(P’) = MD(P) –A change to the input of even 1 bit produces a very different output

16 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Hash Functions: MD5 and SHA-1 Hash function: mangling bits in a sufficiently complicated way that every output bit is affected by every input bit MD5 is the fifth in a series of message digests designed by Ronald Rivest (1992) –MD5 generates a 128-bit fixed value SHA-1: Secure Hash Algorithm 1, developed by National Security Agency (NSA) and blessed by NIST –SHA-1 generates 160-bit message digest

17 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Digital Signatures Using Message Digests

18 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Message Authentication Code MACs are used between two parties that share a secret key in order to validate information transmitted between these parties The MAC mechanism that is based on cryptographic hash functions is called HMAC. Basic idea: –Append the key to the plaintext and generate a digest using a hash function –Ship the plaintext together with the digest

19 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Management of Public Keys Problem statement Certificates X.509 Public key infrastructure

20 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Problems with Public-Key Management If Alice and Bob do not know each other, how do they get each other’s public keys to start the communication process ? –It is essential Alice gets Bob’s public key, not someone else’s A way for Trudy to subvert public-key encryption

21 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Certificates Certification Authority (CA): an organization that certifies public keys –It certifies the public keys belonging to people, companies, or even attributes –CA does not need to be on-line all the time (in ideal scenarios) A possible certificate and its signed hash

22 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao X.509 Devised and approved by ITU The basic fields of an X.509 certificate

23 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Public-Key Infrastructures A Public-Key Infrastructure (PKI) is needed for reasons of –Availability, Scalability, Ease of management A PKI has multiple components –Users, CAs, Certificates, Directories A PKI provides a way of structuring these components and define standards for the various documents and protocols –A simple form of PKI is hierarchical CAs

24 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Public-Key Infrastructures Hierarchical PKI A chain of trust/certification path: A chain of certificates going back to the root

25 Spring Semester 2008EEC-484/584: Computer NetworksWenbing Zhao Public-Key Infrastructures Revocation: sometimes certificates can be revoked, due to a number of reasons Reinstatement: a revoked certificate could conceivably be reinstated Each CA periodically issues a CRL (Certificate Revocation List) giving the serial numbers of all certificates that it has revoked –A user who is about to use a certificate must now acquire the CRL to see if the certificate has been revoked Having to deal with revocation (and possibly reinstatement) eliminates one of the best properties of certificates, namely, that they can be used without having to contact a CA