Hacking the Xbox

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Hacking the Xbox: An Introduction to Reverse Engineering
typically require more complex computations and are thus slower than
symmetric ciphers. Public key ciphers also tend to require longer keys for
equivalent security. As a result, if a large amount of data is to be exchanged,
public key ciphers are often used to encrypt a key for a symmetric
cipher that is used to encrypt the bulk of the data. This symmetric
cipher key can be unique to each transaction and hence it is often referred
to as a “session key.”
SHA-1 Hash
SHA-1 is the Secure Hash Algorithm recommended by the Federal
government in FIPS publication 180-1 (http://www.itl.nist.gov/
fipspubs/fip180-1.htm). Devised by the NSA and based on Ronald L.
Rivest’s MD4 message digest algorithm, SHA-1 works on messages of
Very Difficult Problems (continued)
The exact correlation between the security of RSA public key
lengths and symmetric cipher key lengths is unknown. The security
of RSA is thought to be the difficulty of factoring the
products of large prime numbers; however, there may be other
attacks yet to be discovered on the algorithm. Even so, the
effective difficulty of factoring the product of large primes is
reduced not only by advances in computing technology
(Moore’s Law), but also by advances in number theory, such
as the invention and refinement of the Quadratic Sieve and
the General Number Field Sieve.
In August 1999, a group of researches used the Number Field
Sieve to factor a 512-bit prime number in 7.4 calendar months,
including the time required to set up the factorizing run1 . In
addition, new technologies such as quantum computing
promise to enable the factorization of prime numbers in polynomial
time. I wouldn’t hold your breath, however; there is still
debate as to whether it is possible to build a quantum computer
large enough to factor an interesting prime.
As of today, RSA Security, Inc. recommends key lengths of 1024
bits for most corporate uses, and 2048 bits for “extremely valuable
keys” 2 . Bruce Schneier estimates in the second edition of
Applied Cryptography that a 2304 bit public key length gives
the equivalent security of a 128 bit symmetric key, and that a
1792 bit public key length corresponds to about a 112 bit symmetric
key.
As you read about the Xbox security scheme, keep in mind
these basic guidelines about how difficult it can be to crack
these security schemes using brute-force methods. Time after
time, messages are posted on hacking forums and bulletin
boards asking, “why don’t we start a distributed key search
effort for these keys?” Now you know the answer.
1 http://www.rsasecurity.com/rsalabs/challenges/factoring/rsa155.html
2 http://www.rsasecurity.com/rsalabs/faq/3-1-5.html