Assessing cryptographic key strength in software on the cloud

This web site is to accompany the paper

Using the Cloud to Determine Key Strengths by T. Kleinjung, A.K. Lenstra, D. Page and N.P. Smart

Please read the paper for the basic ideas behind our use of the cloud to determine an economic model for the key strength of different algorithms.

Currently we only present dollar costs computed in 2011 on Amazon's E2C. As people improve the software, Amazon changes its pricing model, we change to a different cloud provider, and computers improve we will update the tables to show progression over time.

All histograms are presented in a logarithmic scale (bar the one for DES).

You can download our code used to perform the experiments from here.

We do not (currently) include the code for performing the RSA experiments due to its size and complexity.

You are welcome to improve it; please contact us if you would like your improvements incorporated into our code base. We can then run the experiments again and determine new numbers. The idea is then, over time, we see how the economic cost of key recovery for various algorithms changes. This will enable us to determine the economic strength of the different main algorithm choices in cryptography.

At the bottom of this page you can find a revision history.

DES

Dollar Cost

Cost of DES Key Recovery on E2C

14k

11k

19k

16k

29k

28k

10k

15k

ASAP

Vanilla C

SSE

2011, 2012

AES/SHA-256/SHA-512

Log₁₀(Dollar Cost)	Cost of AES Key Recovery and SHA-256/SHA-512 Collision on E2C
	26	26	26	26	63	63
	AES-128		SHA-256		SHA-512
	2011, 2012

RSA

Log₁₀(Dollar Cost)	Cost of RSA Key Recovery on E2C
	7	7	7	6	9	8	8	7	17	17	17	17
	Sieve		Matrix		Sieve		Matrix		Sieve		Matrix
	RSA-896				RSA-1024				RSA-2048
	2011, 2012

ECC

Log₁₀(Dollar Cost)	Cost of ECC Key Recovery on E2C
	8	8	12	12	17	17	24	24	42	42	17	17	22	22	27	27	46	46
	p-131		p-163		p-191		p-239		p-359		p192		p224		p256		p384
	Certicom Challenges										NIST/SECG
	2011, 2012

Assessing cryptographic key strength in software on the cloud

DES

AES/SHA-256/SHA-512

RSA

ECC

Revision History

May 2011

May 2012