格签名重要论文简介7-Falcon

Falcon: Fast-Fourier Lattice-based Compact Signatures over NTRU Specification v1.2 — 01/10/2020十月

简介:紧致的格签名方案.
关键词:hash-and-sign,FFT,NTRU,ROM

1主要贡献

NIST第三轮格签名算法，有具体实现代码

2技术综述

• GPV08mode(hash-and-sign)
• NTRU ¹
• 快速傅里叶变换/采样技术²
• 压缩与解压缩算法
• ROM,QROM

3签名方案

3.1**

输出公私钥 s k , p k sk,pk sk,pk

3.2签名

说明：
1.加盐，hash
2.原像采样 → \rightarrow →快速傅里叶采样 → ( s 1 , s 2 ) \rightarrow (s_1,s_2) →(s1​,s2​)
3.压缩 s 2 s_2 s2​, Compress ( s 2 ) (s_2) (s2​)
4.签名 σ : ( r , s ) \sigma : (r,s) σ:(r,s)

3.2验证

说明:
1.hash消息和盐
2.解码签名
3.计算 s 1 s_1 s1​
4.范数验证
ps: 这个拒绝不是拒绝采样的拒绝, 拒绝采样的拒绝用在签名阶段.

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1. Damien Stehlé and Ron Steinfeld. Making NTRU as secure as worst-case problems over ideal lattices.
   In Kenneth G. Paterson, editor, EUROCRYPT 2011, volume 6632 of LNCS, pages 27–47, Tallinn,
   Estonia, May 15–19, 2011. Springer, Heidelberg, Germany. 6, 12 ↩︎

2. Léo Ducas and Thomas Prest. Fast fourier orthogonalization. In Sergei A. Abramov, Eugene V. Zima,and Xiao-Shan Gao, editors, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC 2016, Waterloo, ON, Canada, July 19-22, 2016, pages 191–198. ACM,2016. 6, 14 ↩︎