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Introduction
In this article, we will discuss a signature scheme and the various terms required to understand the topic, like the RSA signature scheme and the difference between conventional and digital signatures. This article will also discuss the methods to help prevent attacks by forging signatures.
The tradition of using a signature as an identity is used everywhere. A signature is used while withdrawing money from the bank, signing a letter, or a contract. A handwritten signature on a document is a standard way to specify the person responsible for it. So what is a signature scheme? A signature scheme is the signing of a message in electronic or digital form. A signed message can be easily transmitted over a network channel.
Conventional Signature and Digital Signature
In this section of the article, What is a Signature Scheme, we will discuss the differences between conventional and digital signatures, given as follows -
Signing a Document
The traditional way of signing a physical document is the conventional method of authenticating a document. On the other hand, a digital signature is not signed physically; therefore, the algorithm used here must bind the signature to the document.
Question of Verification
A conventional or a physical signature is verified by being compared to other authentic signatures. For example - the passport renewal process requires comparing signatures to authenticate the documents. This method is not very secure, as signatures can be easily forged. In contrast, digital signatures can be easily verified by using verification algorithms. This prevents the forgery of signatures.
Copy of Signature
A copy of a handwritten signature can be distinguished from the original signature. In comparison, a copied digital signature is identical to the authentic signature. This calls for unique prevention methods to prevent a digital signature from being reused.
Let us understand this with the help of an example - If ‘Ninja A’ signs a digital message that authorizes Ninja B to withdraw some money from Ninja A’s bank account. This authorization is only valid once; therefore, the message should have the date and time details mentioned to prevent it from being reused.
Components of a Signature Scheme
The signature scheme consists of two components: a signing and a verification algorithm.
For example - ‘Ninja A’ signs a text using a private signing algorithm; this algorithm depends on a private key. Now, the resulting signature is verified using a verification algorithm. Given the message and its purported signature on the same message, the verification algorithm can return the output as true or false depending on whether it is a valid signature for the given message.
Formal Definition of Signature Scheme
In this section of the article, What is a Signature Scheme, we will discuss the formal definition of a Signature Scheme. A signature scheme is five tuples (A, B, C, D, E), where the following conditions must be satisfied -
A is a set of finite possible messages.
B is a set of finite possible signatures.
C is the keyspace. It is a set of finite possible keys.
For each private key that belongs to C, there exists a signing algorithm that belongs to D and a corresponding verification algorithm, E. Each signature algorithm: A → B and verification algorithm: A x B → {true, false} are functions such that the following equation is satisfied for every message that belongs to A and every signature that belongs to B: Verification algorithm (messages, signatures). This should be true if the signature satisfies the signing algorithm of the respective message and false if not.
Here, a pair of messages belonging to A and a signature to B is called a signed message.
Note that for every private key that belongs to C, the signing and verification algorithms should be polynomial-time functions. The signing and verification algorithms must be private and public, respectively.
The whole point of this explanation is to make you understand that if a message exists, it must be computationally feasible for anyone other than the sender to compute a signature such that the verification output returns true. If an attacker tries to compute a pair of messages and their corresponding signature such that the verifying algorithm returns true, given that the sender did not previously sign the message, the signature is forged.
A forced signature is valid even if it is produced by anyone other than the sender.
RSA Signature Scheme
RSA cryptosystem is used to provide digital signatures, known as the RSA signature scheme or Rivet-Shamir-Adleman scheme.
Let us understand this with an example - Ninja A signs a message using the RSA decryption rule. Now, Ninja A is the only person who knows who can make this signature because the sync between the decryption rule and the signing algorithm is private. Here, the RSA encryption rule is used by the verification algorithm. Anyone can verify this signature as the RSA encryption rule is public.
RSA cryptosystem is, however, not secure. To secure the information and prevent the document from forgery, the messages in the document must contain enough redundancy so that a forged signature of that kind doesn’t correspond to a meaningful message even with the slightest of possibilities.
Another way to prevent these attacks is to use hash functions in conjunction with the signature schemes that will omit this method of attack.
Frequently Asked Questions
What are the two components of a signature scheme?
The signature scheme consists of two components: a signing and a verification algorithm.
What is a signature scheme?
A signature scheme is the signing of a message in electronic or digital form. A signed message can be easily transmitted over a network channel.
What are the three fundamental differences between Conventional Signature and Digital Signature?
The three fundamental differences between conventional signatures and digital signatures are the signing of a document, the question of verification, and copy.
What is the full form of the RSA Signature Scheme?
The full form of the RSA signature scheme is the Rivet-Shamir-Adleman scheme.
Is the RSA cryptosystem secure?
In many instances, IoT manufacturers use the RSA cryptosystem insecurely, therefore, no, it is not secure.
Conclusion
This article discussed what a signature scheme is. Discussed the various terms required to understand the topic, like the RSA signature scheme, and discussed the fundamental differences between conventional and digital signatures and how we can prevent attackers from forging a signature. If you want to dig deeper, here are some related articles -
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