Bài giảng Mật mã học: Tổng quan về mật mã học - Huỳnh Trọng Thưa

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Bài giảng "Mật mã học: Tổng quan về mật mã học" cung cấp cho người học các kiến thức: Introduction, information security and cryptography, cryptographic goals, one-way functions, basic terminology and concepts,... Mời các bạn cùng tham khảo.

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Tổng quan về mật mã học Huỳnh Trọng Thưa htthua@ptithcm.edu.vn
Introduction • Cryptography was used as a tool to protect national secrets and strategies. • 1960s (computers and communications systems) -> means to protect information and to provide security services. 2
Introduction (cont.) • 1970s: DES (Feistel, IBM) - the most well-known cryptographic mechanism in history • 1976: public-key cryptography (Difﬁe and Hellman) • 1978: RSA (Rivest et al.) - ﬁrst practical public-key encryption and signature scheme • 1991: the ﬁrst international standard for digital signatures (ISO/IEC 9796) was adopted. 3
Information security and cryptography • Some information security objectives – Privacy or conﬁdentiality – Data integrity – Entity authentication or identiﬁcation – Message authentication – Signature – Authorization – Validation – Access control 4
Information security and cryptography (cont.) • Some information security objectives – Certiﬁcation – Timestamping – Witnessing – Receipt – Conﬁrmation – Ownership – Anonymity – non-repudiation – Revocation 5
Information security and cryptography (cont.) • Cryptography is the study of mathematical techniques related to aspects of information security such as conﬁdentiality, data integrity, entity authentication, and data origin authentication. • Cryptography is not the only means of providing information security, but rather one set of techniques. 6
Cryptographic goals • Conﬁdentiality • Data integrity • Authentication • Non-repudiation Cryptography is about the prevention and detection of cheating and other malicious activities. 7
A taxonomy of cryptographic primitives 8
Background on functions • Function:  f:XY  f(x)=y • Ex: f(1) = 1 f(2) = 4 f(3) = 9  X = {1, 2, 3,... , 10} f(4) = 5 f(5) = 3 f(6) = 3 f(7) = 5 f(8) = 9 f(9) = 4  f(x)= rx, where rx is the remainder f(10) = 1. when x2 is divided by 11.  image of f is the set Y = {1, 3, 4, 5, 9} 9
1-1 functions • A function is 1 − 1 (injection - đơn ánh) if each element in Y is the image of at most one element in X • A function is onto (toàn ánh) if each element in Y is the image of at least one element in X, i.e Im(f)=Y • If a function f: X → Y is 1−1 and Im(f)=Y, then f is called a bijection (song ánh). 10
Inverse function • f:XY and g:YX; g(y)=x where f(x)=y • g obtained from f, called the inverse function of f, g = f−1. • Ex: Let X = {a, b, c, d, e}, and Y = {1, 2, 3, 4, 5} 11
One-way functions • A function f from a set X to a set Y is called a one-way function if f(x) is “easy” to compute for all x ∈ X but for “essentially all” elements y ∈ Im(f) it is “computationally infeasible” to ﬁnd any x ∈ X such that f(x)= y. – Ex: X = {1, 2, 3,... , 16}, f(x)= rx for all x ∈ X where rx is the remainder when 3x is divided by 17. 12
Permutations (Hoán vị) • Let S be a ﬁnite set of elements. – A permutation p on S is a bijection from S to itself (i.e., p: S→S). • Ex: S = {1, 2, 3, 4, 5}. A permutation p: S→S is deﬁned as follows: p(1) = 3,p(2) = 5,p(3) = 4,p(4) = 2,p(5) = 1. 13
Involutions (Ánh xạ đồng phôi) • Let S be a ﬁnite set and let f be a bijection from S to S (i.e., f : S→S).  The function f is called an involution if f = f−1.  f(f(x)) = x for all x ∈S. 14
Basic terminology and concepts • M denotes a set called the message space. – An element of M is called a plaintext message – Ex: M may consist of binary strings, English text, computer code, etc. • C denotes a set called the ciphertext space. – C consists of strings of symbols from an alphabet of deﬁnition, which may differ from the alphabet of deﬁnition for M. – An element of C is called a ciphertext. 15
Encrypt and decrypt transformations (Các phép biến đổi) • K denotes a set called the key space. An element of K is called a key. • Each element e ∈ K uniquely determines a bijection from M to C, denoted by Ee. • Ee is called an encryption function or an encryption transformation • For each d ∈ K, Dd denotes a bijection from C to M (i.e., Dd : C→M). Dd is called a decryption function or decryption transformation. 16
Encrypt and decrypt transformations (cont.) • Ee : e ∈ K ; Dd : d ∈ K – for each e ∈ K there is a unique key d ∈ K such that Dd = Ee-1; – that is, Dd(Ee(m)) = m for all m ∈ M. • The keys e and d in the preceding deﬁnition are referred to as a key pair and some times denoted by (e, d). • To construct an encryption scheme requires one to select – a message space M, – a ciphertext space C, – a key space K, – a set of {Ee : e ∈ K}, and a corresponding set of {Dd:d ∈ K}. 17
Ex of encryption scheme • Let M = {m1,m2,m3} and C = {c1,c2,c3}. – There are precisely 3! = 6 bijections from M to C. – The key space K = {1, 2, 3, 4, 5, 6} has six elements in it, each specifying one of the transformations. 18
Communication participants • Entity or party: sender, receiver, adversary 19
Channels • A channel is a means of conveying information from one entity to another. • An unsecured channel is one from which parties other than those for which the information is intended can reorder, delete, insert, or read. • A secured channel is one from which an adversary does not have the ability to reorder, delete, insert, or read. 20