A fundamental security property of a cryptographic hash function is that it must be a one-way function, meaning it is computationally infeasible to reverse. This property, formally known as pre-image resistance, ensures that an original input (e.g., a password) cannot be derived from its resulting hash value. Therefore, being "reversible" is explicitly NOT a feature of a cryptographic hash function. The other options are essential features: they must be deterministic (same input always produces the same output), unique in practice (collision-resistant), and useful for applications like data integrity verification and digital signatures.

A. Useful: Cryptographic hash functions are highly useful for verifying data integrity, storing passwords securely, and creating digital signatures.

B. Deterministic: A hash function must be deterministic, meaning a specific input will always generate the exact same hash output.

D. Unique: This refers to collision resistance, a critical property where it is computationally infeasible to find two different inputs that produce the same hash.

1. National Institute of Standards and Technology (NIST) Special Publication 800-107 Revision 1

Recommendation for Applications Using Approved Hash Algorithms

August 2012.

Section 4

"Properties of Hash Functions

" page 4: "Three properties are of particular importance...: pre-image resistance

second pre-image resistance

and collision resistance." Pre-image resistance is the formal term for the one-way (non-reversible) property.

2. Katz

J.

& Lindell

Y. (2014). Introduction to Modern Cryptography (2nd ed.). Chapman and Hall/CRC.

Chapter 5

Section 5.2.1

"Preimage Resistance

" page 158: Defines pre-image resistance (one-wayness) as a core security property

stating that for a given hash output y

it is infeasible to find any input x such that H(x) = y. This directly contradicts the concept of reversibility.

3. Massachusetts Institute of Technology (MIT) OpenCourseWare

6.857 Computer and Network Security

Fall 2017.

Lecture 5 Notes: Hashing

page 1: Lists the desired properties of a cryptographic hash function H as: "1. H is deterministic... 3. H is one-way (preimage resistant)... 4. H is collision-resistant." This explicitly states that being one-way (non-reversible) and deterministic are required features.