{"id":4583,"date":"2023-06-16T02:03:21","date_gmt":"2023-06-16T02:03:21","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=4583"},"modified":"2024-10-18T20:53:32","modified_gmt":"2024-10-18T20:53:32","slug":"cryptography-apply-it-2","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/cryptography-apply-it-2\/","title":{"raw":"Cryptography: Apply It 2","rendered":"Cryptography: Apply It 2"},"content":{"raw":"

Cryptographic Chronicles: Embarking on Zuri's Journey to Safeguard Data Cont.<\/h2>\r\nWhile symmetric-key methods like substitution and transposition ciphers can be effective, they have their limitations. One of the biggest issues is the need for a secure method to exchange the key between parties. This is where Zuri's understanding of public key cryptography will come in handy.\r\n

Public key Cryptography<\/h3>\r\nPublic key cryptography involves two keys: a public key, which can be freely distributed and used by anyone to encrypt messages, and a private key, kept secret by the recipient and used to decrypt the messages. This is a simple representation of the system; real-world usage involves complex mathematical operations.\r\n\r\n
[ohm2_question hide_question_numbers=1]9539[\/ohm2_question]<\/section>Part of Zuri's new role also involves understanding the processes that ensure message authenticity. One such process is the use of digital signatures.\r\n\r\nIf Alice sends a digitally signed message to Zuri, which key should Zuri use to verify the digital signature and read the message?\r\n\r\n
[ohm2_question hide_question_numbers=1]9540[\/ohm2_question]<\/section>
Digital signatures are created by the sender encrypting the message with their private key. This means anyone with the sender's public key can decrypt it.<\/section>Public key cryptography is generally more secure than symmetric key methods, but it also has disadvantages.\r\n\r\n
[ohm2_question hide_question_numbers=1]9541[\/ohm2_question]<\/section>As Zuri continues to dive deeper into the world of cryptography, she encounters the concept of one-way functions and their importance in secure communication. She'll also explore modular arithmetic, a crucial component of public key cryptography.\r\n

One-way functions and Modular Arithmetic<\/h3>\r\nOne of Zuri's colleagues presents her with a question related to one-way functions, often used in generating cryptographic hashes. He gives her a simple function: [latex]f(x) = x \\text{ mod } 17[\/latex], and asks her to compute [latex]f(89)[\/latex].\r\n\r\n
[ohm2_question hide_question_numbers=1]9542[\/ohm2_question]<\/section>Excellent work, you've navigated various forms of cryptographic methods alongside Zuri. You've delved into substitution and transposition ciphers, unpacked public key cyprtography, and grappled with modular arithmetic. This knowledge will be pivotal in your understanding of cybersecurity principles. Keep up the great work!","rendered":"

Cryptographic Chronicles: Embarking on Zuri’s Journey to Safeguard Data Cont.<\/h2>\n

While symmetric-key methods like substitution and transposition ciphers can be effective, they have their limitations. One of the biggest issues is the need for a secure method to exchange the key between parties. This is where Zuri’s understanding of public key cryptography will come in handy.<\/p>\n

Public key Cryptography<\/h3>\n

Public key cryptography involves two keys: a public key, which can be freely distributed and used by anyone to encrypt messages, and a private key, kept secret by the recipient and used to decrypt the messages. This is a simple representation of the system; real-world usage involves complex mathematical operations.<\/p>\n