Lattice Cryptography

Lattice Cryptography

(permanently under construction!)

Navigation Bar

• Home

• Cryptography
  • CCA Encrypt
  • Functional Encryption
  • FHE
  • Group Sign
  • Hashing
  • Homomorphic Crypto
  • IBE
  • ZK and Id protocols
  • Key Exchange
  • Encryption
  • Sampling
  • Signatures
  • Foundation
  • Threshold Crypto

• Lattice Algorithms
  • Enumeration
  • Sieving
  • Voronoi
  • Basis Reduction
  • SIS/LWE

CCA-secure Encryption

The problem of designing a lattice-based encryption scheme secure against Chosen Ciphertext Attack (CCA) was first solved by Peikert and Waters in (2). The most efficient construction known to date is the one of (1). CCA secure encryption schemes can also be obtained using a generic transformation from Identity Based Encryption (IBE) described in Chosen-Ciphertext Security from Identity-Based Encryption.

1. Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller
   (Micciancio & Peikert, Eurocrypt 2012)

2. Lossy Trapdoor Functions and Their Applications
   (Peikert & Waters, SIAM J. Computing, 2011 / STOC 2008)

Transformations from CPA-secure to CCA-secure encryption (in the random oracle model)

3. Tightly Secure Ring-LWE Based Key Encapsulation with Short Ciphertexts
   (Albrecht, Orsini, Paterson, Peer & Smart, ESORICS 2017)

4. A Modular Analysis of the Fujisaki-Okamoto Transformation
   (Hofheinz, Hövelmanns & Kiltz, TCC 2017)

Additional improvements and variants:

5. An efficient CCA-secure cryptosystem over ideal lattices from identity-based encryption
   (Yang, Wu, Zhang & Chen - Comp. Math. Appl, 2012)

6. NTRUCCA: How to Strengthen NTRUEncrypt to Chosen-Ciphertext Security in the Standard Model
   (Steinfeld, Ling, Pieprzyk, Tartary & Wang - PKC 2012)

7. Improved Efficiency of MP12
   (Fang, Li, Lu & Sun - IWSEC 2015)

8. CCA Secure Public Key Encryption Scheme Based on LWE Without Gaussian Sampling
   (Sun, Li, Lu, Fang, Inscrypt 2015)

9. High Performance Lattice-based CCA-secure Encryption
   (ElBansarkhani & Buchmann - ePrint 2015/42)

10. Post-quantum Key Exchange - A New Hope
    (Alkim, Ducas, Pöppelmann & Schwabe, USENIX Security 2016)
    webpage

11. NewHope without reconciliation
    (Alkim, Ducas, Pöppelmann & Schwabe, ePrint 2016/1157)

12. Frodo: Take off the Ring! Practical, Quantum-Secure Key Exchange from LWE
    (Bos, Costello, Ducas, Mironov, Naehrig, Nikolaenko, Raghunathan, Stebila, CCS 2016)
    webpage

13. Saber on ARM CCA-secure module lattice-based key encapsulation on ARM
    (Karmakar, Mera, Roy & Verbauwhede - ePrint 2018/682)

14. HILA5 Pindakaas: On the CCA security of lattice-based encryption with error correction
    (Bernstein, Bruinderink, Lange & Panny, Africacrypt 2018)

15. CRYSTALS – Kyber: a CCA-secure module-lattice-based KEM
    (Bos, Ducas, Kiltz, Lepoint, Lyubashevsky, Schanck, Schwabe & Stehlé, EuroS&P 2018)
    webpage

16. Practical CCA2-Secure and Masked Ring-LWE Implementation
    (Oder, Schneider, Pöppelmann & Güneysu, CHES 2018