Question

For Exercises 1-27, mark the answers true or false as follows: A. True B. False In public-key cryptography, each user has two related keys, one public and one private.

Short answer

True

Step-by-step solution

Understanding the Statement

We need to determine if the given statement about public-key cryptography is correct. The statement claims that each user in this system has two related keys: one public and one private.

Core Concepts in Public-Key Cryptography

In public-key cryptography, each participant indeed possesses two distinct keys: a public key, which is shared with others, and a private key, which is kept secret. These keys are mathematically related, allowing for secure communication or data encryption.

Evaluating the Statement

Given the core concept of public-key cryptography—having a pair of related keys, one public and one private—we find that the statement provided accurately describes this aspect of cryptographic systems.

Conclusion

Since the statement correctly reflects the mechanics of public-key cryptography, where each user does have a public and a private key, we determine the statement to be true.

Key concepts

Private Key

The private key is one half of the key pair used in public-key cryptography. As the name suggests, this key is meant to be kept secret and secure. Only the owner should have access to it. The private key is pivotal for ensuring the confidentiality and integrity of the communication. Here’s how it is typically used:

• To decrypt messages sent to you that have been encrypted with your public key.
• To sign messages or transactions, thereby proving that they indeed came from you.

The security of the private key is crucial. If an unauthorized party gains access to it, they could decrypt your sensitive data or impersonate you by signing messages. That is why safeguarding your private key involves using strong passwords and secure hardware, and avoiding sharing it.

Public Key

The public key is the counterpart to the private key in a public-key cryptographic system. Unlike the private key, the public key is meant to be freely shared with others. It allows others to encrypt data that only you—the holder of the matching private key—can decrypt. Here’s how the public key functions in this system:

• Others use your public key to encrypt messages intended for you, ensuring that only you can read them when decrypted with your private key.
• Entities can verify your digital signature using your public key, confirming that you are the author of a signed message.

The distribution of the public key is what makes public-key cryptography so flexible and secure, enabling anyone to communicate privately without needing to share secret keys beforehand.

Encryption

Encryption is the process that converts plain text or data into a coded form, known as ciphertext, to prevent unauthorized access. In the context of public-key cryptography, encryption typically involves the use of a public key. Here's how encryption works:

• The sender encodes the message using the recipient's public key, ensuring that only the recipient's private key can decode or decrypt the message.
• This process ensures that even if a message is intercepted while in transit, it cannot be read by anyone other than the intended recipient who has the corresponding private key.

Encryption provides a means to secure sensitive data against unauthorized access, thus maintaining privacy and confidentiality. With growing cybersecurity threats, encryption plays a fundamental role in protecting communications.

Cryptographic Systems

At the heart of modern communication security are cryptographic systems, uniquely designed to secure information. They involve a set of cryptographic algorithms and protocols, which are methods of converting readable data into unreadable format, except by those possessing the right tools (such as keys). Public-key cryptography is one type of cryptographic system known for:

• Using two keys: public and private, to facilitate secure data exchanges without needing a shared secret.
• Verifying identities through digital signatures.
• Providing confidentiality, integrity, and authenticity in communications.

Cryptographic systems are vital in various applications, from securing emails and credit card information to ensuring trusted connections over the internet, like HTTPS. Their designs ensure that even if data is intercepted, it cannot be accessed or altered without proper keys.