学术报告:Provably Secure Cryptographic Primitives Based on NTRU
发布时间: 2018-12-10 浏览次数: 13
 

Speaker: Wang Mingqiang, School of Mathematics, Shandong University, Jinan, China

  

Title:Provably Secure Cryptographic Primitives Based on NTRU

  

Time: 3:10, December 11, 2018

  

Place:Room A407

  

Abstract:

Crypto-primitives based on NTRU have many advantages, such as moderate key sizes, high efficiency and potential of resisting attacks from quantum computers. However, the securities of classical encryption and signatures based on NTRU are all heuristic. The known schemes having security proofs based on NTRU are all limited. Whether we can release these constraints and design them in more general rings are still open problems.

   We give provably security encryption, signature, IBE and IBS based on NTRU over any cyclotomic rings. Securities of our schemes are based on either Ring-LWE problems (NTRUEncrypt and IBE) or Ring-SIS problems (NTRUSign and IBS), more precisely, securities are guarantees by worst-case approximate Ideal-SIVP problems. The parameters of our NTRUEncrypts are less dependent on the choices of plaintext spaces, meanwhile, our decryption errors are much smaller. We also get a ring-based left-over hash lemma for all cyclotomic fields, which is very useful for designs of many crypto-primitives, for example, NTRUSign, IBE and IBS.We give a concrete construction of Collision Resistance Preimage Sampleable Functions (CRPSF) over any cyclotomic ring and then used GPV’s results to design our NTRUSign. Also, based on the CRPSF we construct, we design provably secure IBE (which is provably secure under adaptive chosen-plaintext and adaptive chosen-identity attacks) and IBS (which is existentially unforgeable against adaptively chosen message and adaptively chosen identity attacks) over any cyclotomic ring.