1. intensive reading of elementary number theory or its guidance, skimming of computational number theory;

2. Algebraic number theory;

Analytic number theory is not commonly used in cryptography, so I don't need to read it carefully. I haven't seen it anyway.

4. commutative algebra;

5. Combinatorial mathematics.

Further suggestions: learning algebra, finite fields, elliptic curves. As for the books on cryptography, just read one or two classic books!

The classic cryptology book is Principles and Practice of Cryptography (by Douglas R. Stinson; Feng Dengguo translation). This textbook is concise and clear.

Introduction to Cryptography (Feng Dengguo, Pei, Science Education Press) is comprehensive, with a brief introduction of basic knowledge such as number theory in the appendix.

See:/question/95390233.html.

If you read any of them, you can put away all the cryptography books mentioned above. If the elliptic curve password is green, there is nothing to see.

Professor Wang Xiaoyun of Shandong University (who has been poached by Tsinghua) is the world's top expert in this field. If the landlord is interested in her papers and works, he might as well pay attention to it. At present, Wang Xiaoyun has been elected as an academician in the computer field!