1. Public Key Based Cryptoschemes for Data Concealment in Wireless Sensor Networks Einar Mykletun, Joao Girao, Dirk Westhoff IEEE ICC 2006, 1-4244-0355-3/06 Citation: 73 Presenter: 林顥桐 Date: 2012/12/17

2. Outline Introduction A Desirable Homomorphic Cryptoscheme Public-Key Cryptoscheme Candidates Applications and Recommendation Conclusion

3. Introduction Data aggregation is untrusted between sensors and the sink Public-key based solutions provide a higher level of system security But not popular – Too costly for computationally weak devices – A faster depletion of the sensor’s energy

4. Introduction Contrast a set of candidate solutions and give recommendations for the selection of the preferred scheme

5. A Desirable Homomorphic Cryptoscheme Aggregation – Additively Homomorphic Encrytion which have the property that Enc(m1) ⊕ Enc(m1) = Enc(m1+ m2) Security – Can be proved on math – The compromise of sensor node should not assist in revealing aggregated data – Key management should be simple – Chiphertext Expansion should be moderate – Probabilistic Encryption

6. A Desirable Homomorphic Cryptoscheme WSN Lifetime – Efficient Computations – Sending ciphertexts should not require the transmission of large amounts of additional data – Electing aggregator nodes should not need to take into account security parameters The use of elliptic curve cryptoschemes

7. Outline Introduction A Desirable Homomorphic Cryptoscheme Public-Key Cryptoscheme Candidates Applications and Recommendation Conclusion

8. Public-Key Cryptoscheme Candidates Okamoto-Uchiyama(OU) – Based on the ablity of computing discrete logarithms – additive homomorphic: Enc(m1+m2) = Enc(m1) X Enc(m2) – Probabilistic encryption, and relating the computational complexity of the encryption function to the size of the plaintext L(x) = (x - 1)/p p and q are random k- bit primes, n is approximately 1024 bits, k could be 341

9. Public-Key Cryptoscheme Candidates Benaloh – A probabilistic cryptoscheme whose encryption cost is dependent on the size of the plaintext p, q are large primes

10. Public-Key Cryptoscheme Candidates Elliptic curve ElGamal encryption Scheme(EC-EG) – This is equivalent to the original ElGamal scheme, but transformed to an additive group E is an elliptic curve, p is a prime with 163bits, G is a generator

11. Public-Key Cryptoscheme Candidates Elliptic curve ElGamal encryption Scheme(EC-EG) – EC-EG is additively homomorphic and chipertexts are combined through addition, i.e. map(m1 + m2) = map(m1) + map(m2) – This mapping needs to be deterministic such that the same plaintext always maps to the same point

12. Outline Introduction A Desirable Homomorphic Cryptoscheme Public-Key Cryptoscheme Candidates Applications and Recommendation Conclusion

13. Applications Data Aggregation – The usage of additive encryption for calculating the average and for movement detection Long-term data storage – Data is kept in the nodes for later retrieval – The nodes have restricted storage capacity, it is important to reduce the amount of values that are actually stored

14. Recommendation OU – Bigger ciphertext size EC-EG – Expensive mapping function during decryption, to costly to revert

15. Conclusion The addition of ciphertexts – minimize bandwidth overhead – reduce the sensors’ energy consumption EC-EG, Benaloh, OU are better