【大学受験対策】英語長文問題61（暗号学）333語＋和訳・解答解説

In an increasingly digital world, the ability to protect information has become essential. From online banking to private messaging apps, cryptography—the science of encoding and decoding information—plays a vital role in securing our data. Behind the sleek interface of modern technology lies a deeply mathematical foundation that makes such protection possible.

At its core, cryptography relies heavily on number theory, a branch of mathematics concerned with the properties and relationships of integers. In particular, prime numbers are central to many encryption systems. The most widely used method, known as RSA encryption, is based on the difficulty of factoring large numbers into their prime components. While multiplying two large prime numbers is relatively simple, reversing the process—finding the original primes from the product—is extremely time-consuming, even for the fastest computers. This asymmetry creates a secure barrier against hackers attempting to break encrypted data.

Beyond number theory, other areas of mathematics, such as algebra, probability, and modular arithmetic, also contribute to cryptographic algorithms. For instance, modular arithmetic—a system of arithmetic for integers where numbers “wrap around” after reaching a certain value—is fundamental in constructing secure keys and digital signatures. These mathematical tools ensure that only authorized parties can access or alter protected information.

In recent years, the rise of quantum computing has posed a new challenge to traditional encryption methods. Quantum machines operate on principles entirely different from classical computers and may eventually be capable of solving problems—like prime factorization—much more efficiently. As a result, mathematicians and computer scientists are now racing to develop quantum-resistant algorithms, many of which involve even more advanced mathematical concepts such as lattice-based cryptography.

Cryptography is not just about secrecy; it’s about trust. Whether you’re making a purchase, sending a message, or accessing personal records, you depend on unseen mathematical structures to ensure that your data remains private and authentic. For students who enjoy solving puzzles or exploring the logic behind patterns, cryptography offers a fascinating and highly relevant application of mathematics that continues to evolve with every technological leap.

Q1. What function of modular arithmetic is emphasised in encryption systems?

1. It eliminates entirely the need for prime numbers in key generation.
2. It enables computers to factor large integers almost instantly for decryption.
3. It is mainly used to model random traffic patterns across communication networks.
4. It supports building secret keys and validating digital signatures against tampering.

Q2. Why does the passage describe cryptography as fundamentally linked to trust?

1. Daily online activities rely on hidden maths ensuring data privacy and authenticity.
2. Governments mandate cryptographic standards primarily to reduce internet connection costs.
3. Trust comes only from public awareness of every algorithm’s underlying code details.
4. People distrust encryption because its mathematical basis remains untested by researchers.

Q3. Which statement is NOT supported by the information in the passage?

1. Digital communication and banking heavily depend on cryptographic protections today.
2. Current supercomputers easily factor RSA keys within minutes under normal conditions.
3. RSA security relies on difficulty reversing multiplication of very large primes.
4. Quantum progress motivates research into lattice‑based algorithms resisting future attacks.