斯坦福密码课程06.6-collision-resistance-Timing-attacks-on-MAC-verification

polypeptides. The precise method of calculation gets a bit abstruse, but an illustration may demystify some aspects.The procedure for calculating a BLOSUM matrix is based on a likelihood method estimating the occurrence of each possible pairwise substitution. A very simple illustration of such a calculation for a very short segment is given below to illustrate the process. The polypeptides were initially aligned using an identity scoring matrix. Only aligned blocks are used to calculate the BLOSUMs.Assume that the following 5 proteins were aligned as follows:AVAAAAVAAAAVAAAAVLAAVVAALFirst, we have to decide whether each sequence should count equally in this process. If this database were a global representation, they should. However, databases of today typically over-represent certain classes of proteins. Therefore, the first step is to reduce this over-representation and make the dataset more representative. One method of doing this is to count all the identical blocks as if they were a single block, reducing the aligned database to:AVAAAAVLAAVVAALNext, at each position, we must calculate the observed and expected pairwise substitutions. At position 1, we have:AA A-A, A-V, A-V are the observed substitutions. Without specifying the necessary calculations, one V can see that the substitution of A for A or A for V are quite likely and that A-X is not!Why is BLOSUM62 called BLOSUM62? Basically, this is because all blocks whose members shared at least 62% identity with ANY other member of that block were averaged and represented as 1 sequence. How would this work with our example?AVAAAAVAAAAVAAAAVLAAVVAAL1-4 are all 80% identical to each other. Sequence 5 is less than 62% (it is 60% identical to 1-3 and t0 #4). This means that the BLOCK used to make a BLOSUM62 would be: (note the averaging!)AVA(3/4)AAL(1/4)VVA*****ALHow does the matrix relate to structural similarity? Most biochemists group the amino acids as follows: G,A,V,L,I, M aliphatic (though some would not include G)S,T,C hydroxyl, sulfhydryl, polarN,Q amide side chainsF,W,Y aromaticH,K,R basicD,E acidicSome rather anomalous substitutions relative to these groupings are highlighted below. For example, it seems VERY surprising to me that K-E substitution is not unusual. That changes charge! This suggests that what evolution thinks is “similar” is not necessarily similar to the molecular biologist.(Of cou rse, it is also possible that K-E substitu tion in one position is also often correlated with a E-K substitution elsewhere, and that what one retains is the electrostatic interaction between charged residues. Much like G-C or C-G compensating mu tations in stem-。

1 8 0 9
In[7]:= b = {{5, 18, 11, 9, 25, 25, 5, 12, 8}, {11, 13, 2, 24, 10, 3, 5, 19, 8}}; c = Mod[inva1.b, 26]; MatrixForm[c] Out[7]//MatrixForm=
Mathematica： Eulerphi[m]
k
( m)
1 (mod m)
x a ( m )1 (mod m)
aij Z m , 矩阵模 m 可逆 设 A aij nn 为 n 阶方阵， 若存在 B bij nn , bij Z m , 使得 AB E (mod m) ，称 B 为 A 的模 m逆矩 阵，记作 B A1 (mod m)
密码的故事
战争和和平时期的间谍战
吕贝卡的故事－007的故事
基度山伯爵 （大仲马）
舞蹈人形
Conan Doyle 创作的歇洛克.福尔摩斯
这段符号的译文为 AM HERE ABE SLANE .
密码学 — Cryptography
源于希腊文字：秘密＋书写，古老神秘的学科
目的
将信息传递给己方的接收者 防止敌方知道信息的内容
HILL2密码的加密与解密
★ 假设要加密的明文是由26个字母所构成 ★ 将每个明文字母与 0 – 25 的一个数字建立
1–1对应关系，称为明文字母的表值
字母 A B C D E F G H 表值 字母
I
J
K L M
1 2
3
4 5 6
7 8 9 10 11 12 13
N O P Q R S T U V W X Y Z 表值 14 15 16 17 18 19 20 21 22 23 24 25 0

2
The Micciancio-Voulgaris Algorithm for CVP
The MV algorithm solves CVP on any n-dimensional lattice in 2O(n) time (for simplicity, we ignore polynomial factors in the input length). It is based around the (closed) Voronoi cell of the lattice, which, to recall, is the set of all points in Rn that are as close or closer to the origin than to any other lattice point: ¯ (L) = {x ∈ Rn : x ≤ x − v ∀ v ∈ L \ {0}}. V We often omit the argument L when it is clear from context. From the definition it can be seen that for any ¯ consists of all the shortest elements of t + L. For any lattice point v, define coset t + L, the set (t + L) ∩ V the halfspace Hv = {x : x ≤ x − v } = {x : 2 x, v ≤ v, v }. ¯ is the intersection of Hv over all v ∈ L \ {0}. The minimal set V of lattice vectors It is easy to see that V ¯ such that V = v∈V Hv is called the set of Voronoi-relevant vectors; we often call them relevant vectors for short. The following characterizes the relevant vectors of a lattice: Fact 2.1 (Voronoi). A nonzero lattice vector v ∈ L \ {0} is relevant if and only if ±v are the only shortest vectors in the coset v + 2L. Corollary 2.2. An n-dimensional lattice has at most 2(2n − 1) ≤ 2n+1 relevant vectors. Proof. Every relevant vector belongs to some nonzero coset of L/2L, of which there exactly 2n − 1. By the above, there are at most two relevant vectors in each such coset. 2

密码学专业主干课程摘要：一、引言二、密码学概述1.密码学定义2.密码学发展历程三、密码学专业主干课程1.密码学基础课程2.密码学进阶课程3.密码学应用课程四、课程举例与介绍1.密码学基础课程举例与介绍2.密码学进阶课程举例与介绍3.密码学应用课程举例与介绍五、结论正文：【引言】密码学是一门研究信息加密与解密、保证信息安全的学科，随着信息化时代的到来，密码学在信息安全、电子商务等领域具有重要的应用价值。

密码学专业因此应运而生，培养具备密码学理论基础和实践能力的高级人才。

本文将介绍密码学专业的主干课程，以帮助大家了解该专业的学习内容。

【密码学概述】密码学是研究加密与解密方法、破译与防护手段的一门学科。

其发展历程可追溯到古代的密码传递，如古希腊的斯巴达加密法。

随着科技的发展，现代密码学涉及到数字、编码、序列、图像等多个领域。

【密码学专业主干课程】密码学专业主干课程可以分为三类：密码学基础课程、密码学进阶课程和密码学应用课程。

【密码学基础课程】密码学基础课程主要包括：1.数学基础：高等数学、线性代数、概率论与数理统计等。

2.计算机科学基础：计算机原理、数据结构、算法分析等。

3.密码学基础：密码学原理、对称加密、非对称加密、哈希函数等。

【密码学进阶课程】密码学进阶课程主要包括：1.密码学分支：分组密码、序列密码、公钥密码、量子密码等。

2.安全协议：身份认证、加密协议、签名协议等。

3.密码学理论：信息论、复杂度理论、密码学数学基础等。

【密码学应用课程】密码学应用课程主要包括：1.网络安全：网络攻防、入侵检测、安全体系结构等。

2.应用密码学：数字签名、电子商务、移动通信安全等。

3.密码学实践：密码学实验、密码算法实现、安全系统设计等。

【课程举例与介绍】【密码学基础课程举例与介绍】1.高等数学：为密码学提供必要的数学基础，如代数、微积分等。

2.密码学原理：介绍密码学基本概念、加密解密方法等。

【密码学进阶课程举例与介绍】1.分组密码：研究将明文分成固定长度组进行加密的方法。