Cryptography Reference
In-Depth Information
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Figure 4.3. Digital Signatures in Asymmetric Key Cryptography
breaking approach of public key encryption was first introduced by Diffie and Hellman
in their seminal paper titled “New Directions in Cryptography” (Diffie and Hellman
1976). However, they were unable to come up with a concrete mathematical proof of
their proposed scheme. In 1978, three researchers (Rivest, Shamir, and Adleman) came
up with a convincing algorithm that conceptualized public key encryption and called
it the RSA algorithm (Rivest et al. 1978). Furthermore, the notion of a digital signa-
ture was introduced with the establishment of public key cryptographic systems. In this
scheme, each end user uses his private key to encrypt a message, resulting in a digital
signature. Likewise, the signature is verified using the end user's public key (Figure 4.3).
Therefore, Alice uses her private key [
Apr ] to encrypt a message that results in a digi-
tal signature. Any recipient of digital signature can verify the signature by using Alice's
public key [
(
)
k
Apu ]. Hence, each end user is able to provide authenticity using the
concept of digital signatures.
In 1984, ElGamal proposed a public key encryption scheme that was closely related
to the Diffie-Hellman key agreement protocol (Elgamal 1985). In this scheme, the plain
text message is mapped to a single group element while the cipher text is mapped to
two group elements. Hence, the cipher text is longer than the plain-text message. At
that time, the notion of having a larger cipher text compared to plain text was a difficult
concept for the cryptographic community to digest. Also, in either of the schemes (RSA
or Elgamal's signature scheme), two important questions arise:
(
)
k
• How and from what source does Bob retrieve Alice's public key?
• If Bob receives Alice's public key from Alice, how can Bob verify the binding
between Alice's unique identity and the public key?
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