7. Key Length Public key length Kim Hyoung-Shick.

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Presentation transcript:

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 logarithm 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 f s () –given s and y, it is easy to compute an x such that f s (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

How much does it cost to factor a large number? Number Length (bits) MachinesMemory 4301trivial ,0004 Gb ,000, Gb x 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