Security Level 密码算法对比

date
Mar 27, 2022
slug
crypto-security-level
status
Published
tags
Cryptography
Standard
summary
RSA 和 ECC 安全性和参数对比
type
Post
 

Intro

在做实验对比时, 需要保证 RSA 与 pbc 安全性的一致性, 也就是 RSA 和 ECC.
简单找了 NIST 标准, 查了对比.

Main

Ref.1. Table.2 表示不同密码算法在相同安全参数下的参数要求, 不过该表格里面参数没有具体表示.
notion image
notion image

第四列 RSA

k 代表 RSA 群的模N的 bit-length, 其中 N=PQ.
Ref.2. Ch5.1 RSA Key Pair Generation
This Standard specifies three choices for the length of the modulus (i.e., nlen): 1024, 2048 and 3072 bits.

第五列 ECC

f 代表点 G 的阶 order, 阶的定义参考群元素order定义.
Ref.2. Ch6.1 ECDSA Domain Parameters
q is the field size; n is the order of the point G
notion image
 

简单结论

RSA 模 N(N=PQ), ECC 点 G 的 order 为 n, 域大小(field size)为 p 的情况下安全性等价关系为:
在 pbc type-A 的曲线上, 对应的则是 RSA 1024bit 安全性, 发现原文也写了
In other words, the fastest known way to break discrete log for a general elliptic curve is to use a algorithm for a generic cyclic group, such as the Pollard rho and lambda methods, implying that the security of a 160-bit elliptic curve group and a 1024-bit finite field are roughly equivalent.

Reference

  1. NIST.Recommendation for Key Management Part 1: General
  1. NIST.Digital Signature Standard (DSS)

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