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Kể từ khi nó được sử dụng hai lần, bộ nhớ đệm nó tiết kiệm thời gian. Tuy nhiên, chúng tôi không thực sự cần các mảng. Nếu chúng ta thêm tất cả các đầu vào, sau đó kết quả xtime (), chúng ta chỉ cần một byte dung lượng lưu trữ thêm. | Chapter 5 Hash Functions Solutions in this chapter What Are Hash Functions Designs of SHS and Implementation PKCS 5 Key Derivation Putting It All Together 0 Summary 0 Solutions Fast Track 0 Frequently Asked Questions 203 204 Chapter 5 Hash Functions Introduction Secure one-way hash functions are recurring tools in cryptosystems just like the symmetric block ciphers. They are highly flexible primitives that can be used to obtain privacy integrity and authenticity. This chapter deals solely with the integrity aspects of hash functions. A hash function formally known as a pseudo random function or PRF maps an arbitrary sized input to a fixed size output through a process known as compression. This form of compression is not your typical data compression as you would see with a .zip file but a nonin-vertible mapping. Loosely speaking checksum algorithms are forms of hash functions and in many independent circles they are called just that. For example mapping inputs to hash buckets is a simple way of storing arbitrary data that is efficiently searchable. In the cryptographic sense hash functions must have two properties to be useful they must be one-way and must be collision resistant. For these reasons simple checksums and CRCs are not good hash functions for cryptography. Being one-way implies that given the output of a hash function learning anything useful about the input is nontrivial. This is an important property for a hash since they are often used in conjunction with RNG seed data and user passwords. Most trivial checksums are not one-way since they are linear functions. For short enough inputs deducing the input from the output is often a simple computation. Being collision resistant implies that given an output from the hash finding another input that produces the same output called a collision is nontrivial. There are two forms of collision resistance that we require from a useful hash function. Pre-image collision resistance Figure 5.1 states that given an
