用户: Guoh064/现代密码学 (英)/Sept 13th

About grades:

•	Totally 3 tests, each test is 30%.
•	2 projects, 15% totally. (e.g. attack Matsumoto–Imai.)

Office Hour: Thursday from 18:00 to 19:00, Jinchunyuan 131;

e-mail: jtding@mail.tsinghua.edu.cn

1Symmetric cryptography

Modern cryptography? Symmetry cryptography.

Sender and receiver; AES;

Ceasar; Enigma; U-boat;

plaintext, ciphertext;

1960-70s, large computer network.

symmetric cryptography needs key exchange.

PQC: 1994, Shor; 2000, I Chuang, factoring $15 = 3 \times 5$ using quantum computer.

2015, NSA; 2016, NIST calls for PQC standard;

2022 July 5th, KYBER, Dilithium, FALCON, Sphinc;

Lattice is versatile;

MPC, FHE;

$x \mapsto x + c (mod 26)$ . We need bijective map.

$g cd (5, 26) = 1$ , so 5 is good. $5 \times 21 \equiv 5 \times (- 5) \equiv - 25 \equiv 1 (mod 26)$

Permutation (Shuffle).

e, t, ..., frequency check.

make two letters to two letters table. makes 26 to 26*26!

mathematical function for shuffling!

using computers to help. encoding!

$Z_{p}$ , $GF (p)$

$GF (p)^{n}$ , we have vector spaces on $GF (2)$ .

DES: 64-dimension vector space. $A 1∣∣ A 2 \mapsto A 1∣∣ A 2 + f (A 1, K 1) \mapsto A 2 + f (A 1, K 1) ∣∣ A 1$

$f$ must be highly nonlinear.

Encryption and Decryption share the same steps

usage of de Jonquières map.

S-boxes of $2^{8}$ elements shuffle.

attacks: linear attack and algebraic attack.