Joint Compression and Protection

1. 47th Annual Allerton Conference on Communication, Control, and Computing University of Illinois at Urbana-Champaign Joint Compression and Protection J.Almeida, J.Barros Instituto de Telecomunicações Universidade do Porto

2. Conventional Encryption • Insensitive to the characteristics of the communication system • Compression, channel reliability, etc. • Encryption of all data • Limitations • Delay constraints, energy and power constraints, etc.

3. Reducing Encryption Complexity • Is it really necessary to cipher the complete set of data? • Ex: SPOC [Vilela et al. ‘08]. • Partial encryption algorithms • Data dependable • Trade-off between the amount of encrypted data and security. • Can source coding help? • Intrinsic security • Variable length codes are hard to cryptanalyze! • Preffix codes – Fraenkel and Klein ‘94 • Huffman codes – Gillman, Mohtashemi and Rivest ’96 • Ambiguity • C0 = {a:0, b:10, c:11}, C1 = {a:1, b:01, c:00} • C-1(0001011) = AAABC or CBBA?

4. Combining Compression and Protection Features Eavesdropper z u z Message Source Encoder Decoder u k Key Source • Encoder • Compression + encryption • Analysis-by-synthesistype of encoding • Exploit code properties to reduce size of data to encrypt. • Decoder • Decompression + decryption.

5. Combining Compression and Protection Features Eavesdropper u z u Encoder Message Source Decoder k Key Source y = xÅ t x Compression Encryption Multiplexer u z x k’ One-time pad Analysis Entropy coder t t’ k • Joint design of analysis and entropy coder blocks. • Minimize the size of t’ to reduce the computational complexity of encryption.

6. Combining Compression and Protection Features Eavesdropper u z u Message Source Encoder Decoder k Key Source k y y Demultiplexer One-time pad Entropy coder z k’ t’ y t x = y Å t Decryption Decompression u

7. The case of Huffman codes • Exploit this property for encryption • Generated keystreams will have long runs of zeros. • Runlength entropy coder reduces the amount of information we need to encrypt. • Catastrophic error propagation • C = {A: 100, B: 0, C: 111, D: 101, E: 110} • Source message: BBCBECDBBB • Encoded bitstream: 001110110111101000 • Decoded symbols: DBDDCBAB • Fliped two bits and changed several source symbols.

8. Huffman Tree and Trellis • C = { A:00, B:01, C:10, D:110, E:111 }.

9. Trellis based keystreams • Cryptogram cannot contain the trellis root states of the original codewords • Define path cost function that reflects the cost of the entropy coder • Compute the minimum path cost using greedy approach

10. Huffman Tree and Error Automaton • C = { A:00, B:01, C:10, D:110, E:111 }.

11. Error Automaton based keystreams • Transition function between automaton states • If a codeword leads to a synchronization state modify codeword • Choice can be subject to optimization regarding the efficiency of the entropy coder • Keystream is the concatenation of the sequence of modifications • Error states: {0, 1, 00, 01, 10, 11, 000} • Source message: CRYPTOGRAPHY • Cryptogram: YYOHRGOCOGA

12. Information Leakage • Assume adversary that • (a) knows the compression algorithm in use • (b) knows the encryption algorithm in use • ... assume also that the one-time pad is correctly used • Eavesdropper tries to infer x (eq. t) based on y and the algorithm • No key recovery attacks! • When do things go wrong? • When there is not enough diversity in codeword sizes

13. Information Leakage - Trellis • Eavesdropper knows that his trellis path root states are forged • Prunes the trellis • Random choices • Increases the size of data to encrypt

14. Information Leakage - Automaton • Adversary knows that the 1st codeword has size different from his observation • Loss of synchronization was induced • Ignore the size of the 1st codeword and start to decode afterwards • Use keystream to control how modifications are induce • Increases the size of data to encrypt

15. Results

16. Results

17. http://nip.dcc.fc.up.pt Conclusions • Joint compression and data protection • Abstraction from compression algorithm • Analysis-by-synthesis encoding • Reduction of size of encrypted information • Link between entropy coder and analysis block • Trade-off between security, computational and data overheads • Huffman codes • Catastrophic error propagation + RL entropy coder • Encryption algorithms based on loss of synchronization principles • Further developments • Cryptanalysis of the proposed algorithms • Study trade-offs for other entropy coders • Develop analysis algorithms for other source coders