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538 Chapter 9 • Basis of Cryptography

Understanding Asymmetric Key Sizes
Damage & Defense… and 2048 bits. The keys are this large because factoring, while still a dif-
RSA, Diffie-Hellman, and other asymmetric algorithms use larger keys
than their symmetric counterparts. Common key sizes include 1024 bits

ficult operation, is much easier to perform than the exhaustive key search
approach used with symmetric algorithms. The slowness of PKE systems is
also due to the larger key sizes. Since most computers can only handle 32
bits of precision, different “tricks” are required to emulate the 1024-bit
and 2048-bit integers. However, the additional processing time is justi-
fied, since, for security purposes, 2048-bit keys are considered secure
“forever.”

Hashing Algorithms

Hashing is a technique in which an algorithm (also called a hash function) is applied
to a portion of data to create a unique digital “fingerprint” that is a fixed-size vari-
able. If anyone changes the data by so much as one binary digit, the hash function
will produce a different output (called the hash value or a message digest) and the
recipient will know that the data has been changed. Hashing can ensure integrity
and provide authentication.The hash function cannot be “reverse-engineered”; that
is, you can’t use the hash value to discover the original data that was hashed.Thus,
hashing algorithms are referred to as one-way hashes.A good hash function will not
return the same result from two different inputs (called a collision). In other words,
the collision domain of the function should be large enough to make it extremely
unlikely to have a collision.All of the encryption algorithms studied so far, both
symmetric and asymmetric, are reversible, (i.e., they can be converted from clear-
text to ciphertext and back again, provided the appropriate keys are used).
However, there is no reversible function for hashing algorithms, so original material
cannot be recovered. For this reason, hashing algorithms are commonly referred to
as one-way hashing functions. However, irreversible encryption techniques are useful
for determining data integrity and authentication.

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