Cryptography Reference
In-Depth Information
Table 10.3
Bit lengths and security levels of ECDSA
q
Hash output (min) Security levels
192
192
96
224
224
112
256
256
128
384
384
192
512
512
256
10.6 Discussion and Further Reading
Digital Signature Algorithms
The first practical realization of digital signatures
was introduced in the original paper by Rivest, Shamir and Adleman [143]. RSA
digital signatures have been standardized by several bodies for a long time, see,
e.g., [95]. RSA signatures were, and in many cases still are, the de facto standard
for many applications, especially for certificates on the Internet.
The Elgamal digital signature was published in 1985 in [73]. Many variants of
this scheme are possible and have been proposed over the years. For a compact
summary, see [120, Note 11.70].
The DSA algorithm was proposed in 1991 and became a US standard in 1994.
There were two possible motivations for the government to create this standard as an
alternative to RSA. First, RSA was patented at that time and having a free alternative
was attractive for US industry. Second, an RSA digital signature implementation
can also be used for encryption. This was not desirable (from the US government
viewpoint) since there were still rather strict export restrictions for cryptography
in the US at that time. In contrast, a DSA implementation can only be used for
signing and not for encryption, and it was easier to export systems that only included
signature functionality. Note that DSA refers to the digital signature
algorithm
, and
the corresponding standard is referred to as DSS, the digital signature
standard
.
Today, DSS includes not only the DSA algorithm but also ECDSA and RSA digital
signatures [126].
In addition to the algorithms discussed in this chapter, there exist several other
schemes for digital signatures. These include, e.g., the Rabin signature [140], the
Fiat-Shamir signature [76], the Pointcheval-Stern signature [134] and the Schnorr
signature [150].
Using Digital Signatures
With digital signatures, the problem of authentic public
keys is acute: How can Alice (or Bob) assure that they possess the correct public
keys for each other? Or, phrased differently, how can Oscar be prevented from in-
jecting faked public keys in order to perform an attack? We discuss this question in
detail in Chap. 13, where certificates are introduced. Certificates are based on digital
signatures and are one of the main applications of digital signatures. They bind an
identity (e.g., Alice's e-mail address) to a public key.
One of the more interesting interactions between society and cryptography is
digital signature laws. They basically assure that a cryptographic digital signature
has a legally binding meaning. For instance, an electronic contract that was digitally
