Peter, a security professional, was hired by an organization and was instructed to secure the application and its content from unauthorized access. In this process, Peter implemented a public- key cryptosystem that uses modular arithmetic and elementary number theory for Internet encryption and user authentication. Which of the following algorithms was employed by Peter in the above scenario?

The scenario describes the implementation of a public-key cryptosystem used for both encryption and user authentication, which is based on modular arithmetic and elementary number theory. The RSA (Rivest-Shamir-Adleman) algorithm perfectly fits this description. RSA's security relies on the computational difficulty of factoring the product of two large prime numbers, a core concept in number theory. It operates using modular exponentiation. RSA is a versatile asymmetric algorithm widely used on the internet for securely transmitting data (encryption) and for verifying user identities through digital signatures (authentication).

B. MD6: This is a cryptographic hash function, not a public-key cryptosystem. It is used for creating a fixed-size digest of data for integrity checks, not for encryption or authentication via key pairs.
C. DSA: The Digital Signature Algorithm (DSA) is a public-key cryptosystem used exclusively for creating digital signatures for authentication. It cannot be used for encryption, which is a stated requirement in the scenario.
D. SHA-2: The Secure Hash Algorithm 2 (SHA-2) is a family of cryptographic hash functions. Like MD6, it is used for data integrity and is not an asymmetric cryptosystem designed for encryption.

1. Katz, J., & Lindell, Y. (2014). Introduction to Modern Cryptography (2nd ed.). CRC Press. In Chapter 10, the text describes public-key encryption schemes, and Section 11.5 details the RSA algorithm, its reliance on number-theoretic problems (factoring), and its construction using modular arithmetic.

2. National Institute of Standards and Technology (NIST). (2013). FIPS PUB 186-4: Digital Signature Standard (DSS). Section 6.1, "RSA Digital Signature Algorithm," specifies RSA for signature generation and verification. The introduction also contrasts it with DSA, which is solely for signatures. (Page 1, Section 1).

3. Lehman, E., Leighton, F. T., & Meyer, A. R. (2010). Mathematics for Computer Science (MIT OpenCourseWare). Chapter 8, "Number Theory," Section 8.11, "The RSA Cryptosystem," details the mathematical foundation of RSA, including its use of modular arithmetic and Euler's theorem for both encryption and digital signatures. (Pages 268-272).

4. Moriarty, K., et al. (2016). RFC 8017: PKCS #1: RSA Cryptography Specifications Version 2.2. Internet Engineering Task Force (IETF). This official standard document explicitly defines schemes for both encryption (Section 7) and signatures (Section 8) using the RSA algorithm.