Post-Quantum Code-Based Cryptography

Transcription

1 Big Data Photonics UCLA Post-Quantum Code-Based Cryptography Valérie Gauthier Umaña Assistant Professor

2 Cryptography Alice 1

3 Cryptography Alice Bob 1

4 Cryptography Alice Bob 1

5 Cryptography Alice Bob 1

6 Publick Key Cryptography 2

7 Post Quantum Cryptography 1977, Rivest, Shamir and Adleman - First PKC (RSA) Almost 40 year later, the security of PKC used in practice depends on only two problems: Integer Factorization Problem Discrete Logarithm Problem 3

8 Post Quantum Cryptography 1977, Rivest, Shamir and Adleman - First PKC (RSA) 1994, Peter Shor s algorithm solve these two problems in a polynomial time using a Quantum Computer Almost 40 year later, the security of PKC used in practice depends on only two problems: Integer Factorization Problem Discrete Logarithm Problem 3

9 Post Quantum Cryptography 1977, Rivest, Shamir and Adleman - First PKC (RSA) 1994, Peter Shor s algorithm solve these two problems in a polynomial time using a Quantum Computer Almost 40 year later, the security of PKC used in practice depends on only two problems: Integer Factorization Problem Discrete Logarithm Problem GOAL: Find cryptographic primitives resisting quantum computers attacks: Post-Quantum Cryptography 3

10 Demand for secure embedded devices Internet of Things (IoT) Now Days Demand Long life-time/security User interaction/low latency Limited resources/memory Goal: Alternative public-key cryptosystems resistant to quantum computing attacks Cryptographic primitives resistant to quantum computing attacks Efficient implementations for low-cost embedded devices 4

11 Error-CorrectingCodes 5

12 Error-CorrectingCodes Add redundancy to the message (k<n) Use the structure of the redundancy to recover the message 5

13 Encoding Decoding Scheme 6

14 Encoding G: Generator matrix, c= m G 7

15 Encoding G: Generator matrix, c= m G 7

16 Encoding G: Generator matrix, c= m G 7

17 McEliece scryptosystem 1978: Berlekamp, McEliece and van Tilburg showed that the associated decision problem of the decoding random linear code problem is NP-complete 1978, Robert McEliece proposed the first PKC based on error-correcting codes Main Idea: Choose a code with generator matrix G0 (Goppa Code) and a polynomial time decoding algorithm ɣ that can correct up to t errors. Find a permutation matrix P and an invertible matrix S to disguise the algebraic structure of the code by computing G=SG0P 8

18 McEliece spkc 9

19 Code based Cryptology Main Problem: Very BIG key size Goals: Use other codes to find variants of McEliece s Cryptosystem to reduce the key size. Main Advantage: Find cryptographic primitives based on these variants. Fast encryption and decryption Resist Post-Quantum Attacks 10

20 McEliece PKC Distinguisher Structures Attacks Choose a code with generator matrix G0 (Goppa Code) and a polynomial time decoding algorithm ɣ that can correct up to t errors. Find a permutation matrix P and an invertible matrix S to disguise the algebraic structure of the code by computing G=SG0P A Distinguisher for High Rate McEliece Cryptosystems Faugère, Gauthier, Otmani, Perret and Tillich,

21 McEliece PKC Distinguisher Structures Attacks Choose a code with generator matrix G0 (Goppa Code) and a polynomial time decoding algorithm ɣ that can correct up to t errors. Find a permutation matrix P and an invertible matrix S to disguise the algebraic structure of the code by computing G=SG0P Structural Attacks A Distinguisher for High Rate McEliece Cryptosystems Faugère, Gauthier, Otmani, Perret and Tillich, 2013 Barreto and Misoczki, 2009 Berger, Cayrel, Gaborit and Otmani, 2009 Gauthier Leander: 2010 StructuralDistinguisher-Based Attack Wieschebrink, 2006 Bogdanov and Lee (hommomorphic), 2011 Baldi, Bianchi, Chiaraluce, Rosenthal, Schipani, 2012 Couvreur, Gaborit, Otmani, Tillich and Gauthier, 2014 Baldi, Bianchi, Chiaraluce, Rosenthal, Schipani, 2014 Couvreur, Otmani, Tillich and Gauthier,

22 NIST Announcement (February 2016) 12

23 Universidad del Rosario Nova Et Vetera New Bachelor, Master and PhD program in Applied Mathematics and Computer Science Come and collaborate with us! 29 June 9 July 2016 Colegio Mayor de Nuestra Señora del Rosario, founded in

24 Valérie Gauthier Umaña 29 June 9 July 2016 Colegio Mayor de Nuestra Señora del Rosario, founded in