Hyung Seok Cho, M.D., Jin Hyoung Kim, M.D., Ph.D., Doh Lee, M.D., Ph.D.
7. Key Length Public key length Kim Hyoung-Shick.
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Transcript of 7. Key Length Public key length Kim Hyoung-Shick.
7. Key Length
Public key length
Kim Hyoung-Shick
Contents
1. Introduction
2. Results
Contents
1. Introduction
2. Results
- Is factoring hard ?
- Is factoring in NP ?
- Is factoring NP-complete ?
Questions
- RSA are based on the factoring problem.
- Elgamal are based on the discrete logarit
hm problem.
Today’s dominant public key systems
- Finding key
- Solving the base problem
Brute-force Attack
• One-way function: f() is one way if– For any x, y = f(x) is easy to compute– For any (or almost all) y, it is hard to find an
x such that f(x) = y
• Trapdoor one-way function fs() – given s and y, it is easy to compute an x suc
h that fs(x) = y
Building Public Key Systems
• Quadratic sieve – below 110 bits
• General number field sieve – above
110 bits
• Special number field sieve –
special form
Factoring Algorithm
• RSA Laboratories continues its
sponsorship of the RSA Factoring
Challenge
• To help users of the RSA public-key
cryptosystem in choosing suitable key
lengths for an appropriate level of
security.
New RSA Factoring Challenge
http://www.rsasecurity.com/rsalabs/challenges/factoring/index.html
How much does it cost to factor a large number?
Number Length (bits)
Machines Memory
430 1 trivial
760 215,000 4 Gb
1020 342,000,000 170 Gb
1620 1.6 x 1015 120 Tb
For one year, the machines column is the number of 500 MHz Pentium
New Records
- Factorization of RSA-155 digit (512 bit) by distributed computing, 1999
Recommended Key Length
(Recommendation by RSA Laboratories, RSA Data
Security, Inc.'s research arm)
768-bit and 1024-bit keys as the minimum for
achieving reliable security
• Distributed computing
• DNA computing
• Quantum computing
Future Attacks