One-Way Encryption and Message Authentication

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "One-Way Encryption and Message Authentication"

Transcription

1 One-Way Encryption and Message Authentication Cryptographic Hash Functions Johannes Mittmann Zentrum Mathematik Technische Universität München (TUM) 3 rd Joint Advanced Student School (JASS) St. Petersburg, March 30 April 9, 2005 Course 1: Algorithms for IT Security Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 1 / 35

2 Outline 1 Introduction 2 Security of Hash Functions Generic Attacks in the Random Oracle Model Comparison of Security Criteria 3 Iterated Hash Functions The Merkle-Damgård Construction The Secure Hash Algorithm (SHA-1) 4 Message Authentication Codes (MACs) Nested MACs, HMAC and CBC-MAC Unconditionally Secure MACs Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 2 / 35

3 Hash Functions Introduction h : {0, 1} {0, 1} m hash function constructs short fingerprint of an arbitrarily long message x computation of h(x) should be easy small change of x should change h(x) completely it should be hard to find (second) preimages collisions Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 3 / 35

4 Introduction Applications of Hash Functions verification of data integrity authentication of data origin optimization of digital signature schemes digital timestamping schemes hashcash password protection pseudo-random numbers generation... Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 4 / 35

5 Definitions Introduction Definition A hash family is a four-tuple (X, Y, K, H), where: 1 X is a set of possible messages 2 Y is a finite set of possible message digests or authentication tags 3 K, the keyspace, is a finite set of possible keys 4 for each K K, there is a hash function h K H, h K : X Y. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 5 / 35

6 Definitions Introduction Definition A hash family is a four-tuple (X, Y, K, H), where: 1 X is a set of possible messages 2 Y is a finite set of possible message digests or authentication tags 3 K, the keyspace, is a finite set of possible keys 4 for each K K, there is a hash function h K H, h K : X Y. X finite: compression function (x, y) X Y is valid pair under the key K h K (x) = y (N, M)-hash family, where N = X, M = Y Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 5 / 35

7 Security of Hash Functions Cryptographic Properties Preimage Resistance (One-Wayness) Instance: hash function h : X Y and y Y. Find: x X such that h(x) = y. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 6 / 35

8 Security of Hash Functions Cryptographic Properties Preimage Resistance (One-Wayness) Instance: hash function h : X Y and y Y. Find: x X such that h(x) = y. Second Preimage Resistance Instance: hash function h : X Y and x X. Find: x X such that x x and h(x ) = h(x). Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 6 / 35

9 Security of Hash Functions Cryptographic Properties Preimage Resistance (One-Wayness) Instance: hash function h : X Y and y Y. Find: x X such that h(x) = y. Second Preimage Resistance Instance: hash function h : X Y and x X. Find: x X such that x x and h(x ) = h(x). Collision Resistance Instance: hash function h : X Y. Find: x, x X such that x x and h(x ) = h(x). Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 6 / 35

10 Security of Hash Functions Generic Attacks in the Random Oracle Model The Random Oracle Model mathematical model of an ideal hash function hash function h : X Y is chosen randomly from Y X only oracle access (ɛ, q)-algorithm: Las Vegas algorithm with average-case success probability ɛ and at most q oracle queries Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 7 / 35

11 Security of Hash Functions Generic Attacks in the Random Oracle Model The Random Oracle Model mathematical model of an ideal hash function hash function h : X Y is chosen randomly from Y X only oracle access (ɛ, q)-algorithm: Las Vegas algorithm with average-case success probability ɛ and at most q oracle queries Theorem (independence property) Let h Y X be chosen at random, and let X 0 X. Suppose that the values h(x) have been determined iff x X 0. Then Pr [h(x) = y] = 1 M x X \ X 0 y Y. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 7 / 35

12 Security of Hash Functions Algorithm for Preimage Generic Attacks in the Random Oracle Model Algorithm: FindPreimage(h, y, q) 1: choose X 0 X, X 0 = q 2: for all x X 0 do 3: if h(x) = y then return x 4: end for 5: return failure Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 8 / 35

13 Security of Hash Functions Generic Attacks in the Random Oracle Model Algorithm for Preimage Algorithm: FindPreimage(h, y, q) 1: choose X 0 X, X 0 = q 2: for all x X 0 do 3: if h(x) = y then return x 4: end for 5: return failure Theorem For any X 0 X with X 0 = q, the average-case success probability of FindPreimage(h, y, q) is ( ɛ = ) q. M Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 8 / 35

14 Security of Hash Functions Generic Attacks in the Random Oracle Model Algorithm for Second Preimage Algorithm: FindSecondPreimage(h, x, q) 1: y h(x) 2: choose X 0 X \ {x}, X 0 = q 1 3: for all x 0 X 0 do 4: if h(x 0 ) = y then return x 0 5: end for 6: return failure Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 9 / 35

15 Security of Hash Functions Generic Attacks in the Random Oracle Model Algorithm for Second Preimage Algorithm: FindSecondPreimage(h, x, q) 1: y h(x) 2: choose X 0 X \ {x}, X 0 = q 1 3: for all x 0 X 0 do 4: if h(x 0 ) = y then return x 0 5: end for 6: return failure Theorem For any X 0 X \ {x} with X 0 = q 1, the success probability of FindSecondPreimage(h, x, q) is ( ɛ = ) q 1. M Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 9 / 35

16 Security of Hash Functions Random (Second) Preimage Attack Generic Attacks in the Random Oracle Model 1 ɛ = ( 1 1 M ) q = 1 q M. q i=0 ( ) ( q 1 ) i i M Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 10 / 35

17 Security of Hash Functions Random (Second) Preimage Attack Generic Attacks in the Random Oracle Model 1 ɛ = ( 1 1 M ) q = 1 q M. q ɛm. q i=0 ( ) ( q 1 ) i i M Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 10 / 35

18 Security of Hash Functions Random (Second) Preimage Attack Generic Attacks in the Random Oracle Model 1 ɛ = ( 1 1 M ) q = 1 q M. q ɛm. q i=0 ( ) ( q 1 ) i i M = (ɛ, O(M))-algorithm Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 10 / 35

19 Algorithm for Collision Security of Hash Functions Generic Attacks in the Random Oracle Model Algorithm: FindCollision(h, q) 1: choose X 0 X, X 0 = q 2: for all x X 0 do y x h(x) 3: if y x = y x for some x x then return (x, x ) 4: else return failure Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 11 / 35

20 Algorithm for Collision Security of Hash Functions Generic Attacks in the Random Oracle Model Algorithm: FindCollision(h, q) 1: choose X 0 X, X 0 = q 2: for all x X 0 do y x h(x) 3: if y x = y x for some x x then return (x, x ) 4: else return failure Theorem For any X 0 X with X 0 = q, the success probability of Collision(h, q) is q 1 ( ɛ = 1 1 i ). M i=1 Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 11 / 35

21 Security of Hash Functions Birthday (Collision) Attack Generic Attacks in the Random Oracle Model 1 ɛ = q 1 i=1 = exp ( 1 i ) q 1 M i=1 ) ( q(q 1) 2M ( exp i ) ( = exp M exp ) ( q2. 2M q 1 i=1 ) i M Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 12 / 35

22 Security of Hash Functions Birthday (Collision) Attack Generic Attacks in the Random Oracle Model 1 ɛ = q 1 i=1 = exp q ( 1 i ) q 1 M i=1 ) ( 2M log q(q 1) 2M 1 1 ɛ. ( exp i ) ( = exp M exp ) ( q2. 2M q 1 i=1 ) i M Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 12 / 35

23 Security of Hash Functions Birthday (Collision) Attack Generic Attacks in the Random Oracle Model 1 ɛ = q 1 i=1 = exp q ( 1 i ) q 1 M i=1 ) ( 2M log q(q 1) 2M 1 1 ɛ. ( exp i ) ( = exp M exp ) ( q2. 2M = (ɛ, O( M))-algorithm q 1 i=1 ) i M Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 12 / 35

24 Security of Hash Functions Birthday (Collision) Attack Generic Attacks in the Random Oracle Model 1 ɛ = q 1 i=1 = exp q ( 1 i ) q 1 M i=1 ) ( 2M log q(q 1) 2M 1 1 ɛ. ( exp i ) ( = exp M exp ) ( q2. 2M = (ɛ, O( M))-algorithm q 1 i=1 ) i M Example (Birthday Paradox) ɛ = 0.5, M = 365 = q 1.17 M Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 12 / 35

25 Security of Hash Functions Generic Attacks in the Random Oracle Model Generic Attacks on Cryptographic Hash Functions attack random (second) preimage birthday (collision) algorithm (ɛ, O(M)) (ɛ, O( M)) Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 13 / 35

26 Security of Hash Functions Generic Attacks in the Random Oracle Model Generic Attacks on Cryptographic Hash Functions attack random (second) preimage birthday (collision) algorithm (ɛ, O(M)) (ɛ, O( M)) attacks are optimal in the random oracle model minimum acceptable size of a message digest: 128 bits 160-bit message digest (or larger) recommended Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 13 / 35

27 Security of Hash Functions Reduce Collision to Second Preimage Comparison of Security Criteria Algorithm: CollisionTo2ndPreimage(h) 1: choose x X uniformly at random 2: if Oracle2ndPreimage(h, x) = x and x x and h(x ) = h(x) then return (x, x ) 3: else return failure Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 14 / 35

28 Security of Hash Functions Reduce Collision to Second Preimage Comparison of Security Criteria Algorithm: CollisionTo2ndPreimage(h) 1: choose x X uniformly at random 2: if Oracle2ndPreimage(h, x) = x and x x and h(x ) = h(x) then return (x, x ) 3: else return failure Oracle2ndPreimage is (ɛ, q)-algorithm for Second Preimage = CollisionTo2ndPreimage is (ɛ, q + 2)-algorithm for Collision collision resistance = second preimage resistance Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 14 / 35

29 Security of Hash Functions Reduce Collision to Preimage Comparison of Security Criteria Algorithm: CollisionToPreimage(h) Require: OraclePreimage is (1, q)-algorithm 1: choose x X uniformly at random 2: y h(x) 3: if OraclePreimage(h, y) = x and x x then return (x, x ) 4: else return failure Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 15 / 35

30 Security of Hash Functions Reduce Collision to Preimage Comparison of Security Criteria Algorithm: CollisionToPreimage(h) Require: OraclePreimage is (1, q)-algorithm 1: choose x X uniformly at random 2: y h(x) 3: if OraclePreimage(h, y) = x and x x then return (x, x ) 4: else return failure Theorem Let h : X Y be a compression function, where X 2 Y. Suppose OraclePreimage is a (1, q)-algorithm that solves Preimage for h. Then CollisionToPreimage is a (1/2, q + 1)-algorithm for Collision, for the fixed compression function h. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 15 / 35

31 Security of Hash Functions Comparison of Security Criteria Proof. x x h(x) = h(x ) is equivalence relation on X Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 16 / 35

32 Security of Hash Functions Comparison of Security Criteria Proof. x x h(x) = h(x ) is equivalence relation on X C := X /, so C = Y Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 16 / 35

33 Security of Hash Functions Comparison of Security Criteria Proof. x x h(x) = h(x ) is equivalence relation on X C := X /, so C = Y for x X the probability of success is ( [x] 1)/ [x] Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 16 / 35

34 Security of Hash Functions Comparison of Security Criteria Proof. x x h(x) = h(x ) is equivalence relation on X C := X /, so C = Y for x X the probability of success is ( [x] 1)/ [x] Pr[success] = 1 [x] 1 = 1 X [x] X x X C C = 1 X C C X X /2 X ( C 1) = = 1 2. X Y X x C C 1 C Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 16 / 35

35 Iterated Hash Functions Iterated Hash Functions Compress : {0, 1} m+t {0, 1} m, t 1. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 17 / 35

36 Iterated Hash Functions Iterated Hash Functions Compress : {0, 1} m+t {0, 1} m, t 1. 1 preprocessing input string x, x m + t + 1 construct y = y 1 y 2 y r, x y(x) injection y i = t y = x Pad(x) padding function Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 17 / 35

37 Iterated Hash Functions Design of Iterated Hash Functions 2 processing z 0 IV, IV = m z 1 Compress(z 0 y 1 ). z r Compress(z r 1 y r ) Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 18 / 35

38 Iterated Hash Functions Design of Iterated Hash Functions 2 processing z 0 IV, 3 optional output transformation g : {0, 1} m {0, 1} l IV = m z 1 Compress(z 0 y 1 ). z r Compress(z r 1 y r ) Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 18 / 35

39 Iterated Hash Functions Design of Iterated Hash Functions 2 processing z 0 IV, 3 optional output transformation g : {0, 1} m {0, 1} l h : i=m+t+1 IV = m z 1 Compress(z 0 y 1 ). z r Compress(z r 1 y r ) {0, 1} i {0, 1} l, h(x) = g(z r ). Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 18 / 35

40 Iterated Hash Functions The Merkle-Damgård Construction The Merkle-Damgård Construction Theorem (Merkle-Damgård) Suppose Compress : {0, 1} m+t {0, 1} m is a collision resistant compression function, where t 1. Then there exists a collision resistant hash function h : {0, 1} i {0, 1} m. i=m+t+1 The number of times Compress is computed in the evaluation of h is at most 1 + n t 1 if t 2, where x = n. 2n + 2 if t = 1, Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 19 / 35

41 Iterated Hash Functions The Secure Hash Algorithm (SHA-1) The Secure Hash Algorithm (SHA-1) Ron Rivest: 128-bit hash function MD4 and strengthened version MD5 design goals: (direct) security speed simplicity and compactness collisions for MD4 (Dobbertin) and compression function of MD5 (Boer/Bosselaers) Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 20 / 35

42 Iterated Hash Functions The Secure Hash Algorithm (SHA-1) The Secure Hash Algorithm (SHA-1) Ron Rivest: 128-bit hash function MD4 and strengthened version MD5 design goals: (direct) security speed simplicity and compactness collisions for MD4 (Dobbertin) and compression function of MD5 (Boer/Bosselaers) NIST & NSA: 160-bit hash function SHA-1 Feb. 13, 2005: collisions with < 2 69 hash operations (Wang/Yin/Yu) Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 20 / 35

43 Padding Scheme Iterated Hash Functions The Secure Hash Algorithm (SHA-1) Algorithm: SHA-1-Pad(x) Require: x Ensure: y = 0 (mod 512) 1: d (447 x ) mod 512 2: l the binary representation of x, where l = 64 3: return y x 1 0 d l x l Figure: MD-Strengthening Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 21 / 35

44 SHA-1 Iterated Hash Functions The Secure Hash Algorithm (SHA-1) BC ( B)D, B C D, f t (B, C, D) = BC BD CD, B C D, 5A827999, if 0 t 19, 6ED9EBA1, if 20 t 39, K t = 8F1BBCDC, if 40 t 59, CA62C1D6, if 60 t 79. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 22 / 35

45 SHA-1 Iterated Hash Functions The Secure Hash Algorithm (SHA-1) BC ( B)D, B C D, f t (B, C, D) = BC BD CD, B C D, 5A827999, if 0 t 19, 6ED9EBA1, if 20 t 39, K t = 8F1BBCDC, if 40 t 59, CA62C1D6, if 60 t 79. Cryptosystem: SHA-1(x) 1: y SHA-1-Pad(x) 2: denote y = M 1 M 2 M n, where each M i is a 512-bit block 3: H , H 1 EFCDAB89, H 2 98BADCFE 4: H , H 4 C3D2E1F0... Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 22 / 35

46 Iterated Hash Functions The Secure Hash Algorithm (SHA-1) Cryptosystem: SHA-1(x)... (continued) 1: for i 1 to n do 2: denote M i = W 0 W 1 W 15, where each W i is a word 3: for t 16 to 79 do W t (W t 3 W t 8 W t 14 W t 16 ) 1 4: A H 0, B H 1, C H 2 5: D H 3, E H 4 6: for t 0 to 79 do 7: temp (A 5) + f t (B, C, D) + E + W t + K t 8: E D, D C 9: C B 30 10: B A, A temp 11: end for 12: H 0 H 0 + A, H 1 H 1 + B, H 2 H 2 + C 13: H 3 H 3 + D, H 4 H 4 + E 14: end for 15: return H 0 H 1 H 2 H 3 H 4 Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 23 / 35

47 Message Authentication Codes (MACs) Message Authentication Codes (MACs) MAC = keyed hash function h K + security properties Alice and Bob share secret key K (x, h K (x)) is transmitted over insecure channel Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 24 / 35

48 Message Authentication Codes (MACs) Message Authentication Codes (MACs) MAC = keyed hash function h K + security properties Alice and Bob share secret key K (x, h K (x)) is transmitted over insecure channel (Existential) Forgery Instance: valid pairs (x 1, y 1 ),..., (x q, y q ) under unknown key K. Find: valid pair (x, y) such that x {x 1,..., x q }. (ɛ, q)-forger: forgery with worst-case success probability ɛ Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 24 / 35

49 Message Authentication Codes (MACs) Example (Iterated hash function h K with IV = K) Compress : {0, 1} m+t {0, 1} m. Given: (x, h K (x)) y = x Pad(x), y = rt. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 25 / 35

50 Message Authentication Codes (MACs) Example (Iterated hash function h K with IV = K) Compress : {0, 1} m+t {0, 1} m. Given: (x, h K (x)) y = x Pad(x), y = rt. x = x Pad(x) w. y = x Pad(x) w Pad(x ), y = r t, r > r. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 25 / 35

51 Message Authentication Codes (MACs) Example (Iterated hash function h K with IV = K) Compress : {0, 1} m+t {0, 1} m. Given: (x, h K (x)) y = x Pad(x), y = rt. x = x Pad(x) w. y = x Pad(x) w Pad(x ), y = r t, r > r. z r+1 Compress(h K (x) y r+1 ). z r Compress(z r 1 y r ). h K (x ) = z r. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 25 / 35

52 Message Authentication Codes (MACs) Example (Iterated hash function h K with IV = K) Compress : {0, 1} m+t {0, 1} m. Given: (x, h K (x)) y = x Pad(x), y = rt. x = x Pad(x) w. y = x Pad(x) w Pad(x ), y = r t, r > r. z r+1 Compress(h K (x) y r+1 ). z r Compress(z r 1 y r ). h K (x ) = z r. = (1, 1) forger Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 25 / 35

53 Nested MACs Message Authentication Codes (MACs) Nested MACs, HMAC and CBC-MAC Hash families (X, Y, L, H) and (Y, Z, K, G), X < Y Z. (X, Z, M, G H) nested MAC, M = K L, G H = { (g h) (K,L) : g K G, h L H }. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 26 / 35

54 Nested MACs Message Authentication Codes (MACs) Nested MACs, HMAC and CBC-MAC Hash families (X, Y, L, H) and (Y, Z, K, G), X < Y Z. (X, Z, M, G H) nested MAC, M = K L, G H = { (g h) (K,L) : g K G, h L H }. Theorem Let (X, Z, M, G H) be a nested MAC. Suppose there does not exist an (ɛ 1, q + 1)-collision attack for a h L H (L secret), and there does not exist an (ɛ 2, q)-forger for a g K G. Further suppose there exists an (ɛ, q)-forger for (g h) (K,L) G H. Then ɛ ɛ 1 + ɛ 2. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 26 / 35

55 HMAC Message Authentication Codes (MACs) Nested MACs, HMAC and CBC-MAC 512-bit key K. ipad = , opad = 5C5C 5C. (512-bit) Cryptosystem: HMAC(x, K) HMAC K (x) = SHA-1((K opad) SHA-1((K ipad) x)) Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 27 / 35

56 Message Authentication Codes (MACs) Nested MACs, HMAC and CBC-MAC CBC-MAC (P, C, K, E, D) endomorphic cryptosystem, P = C = {0, 1} t. K K, e K E. Cryptosystem: CBC-MAC(x, K) 1: denote x = x 1 x n, x i = t 2: y initial value 3: for i 1 to n do y i e K (y i 1 x i ) 4: return y n Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 28 / 35

57 Message Authentication Codes (MACs) Unconditionally Secure MACs Unconditionally Secure MACs a key is used to produce only one authentication tag impersonation: (ɛ, 0)-forger substitution: (ɛ, 1)-forger deception probability Pd q : maximum value of ɛ such that (ɛ, q)-forger exists (q = 0, 1) Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 29 / 35

58 Message Authentication Codes (MACs) Unconditionally Secure MACs Example X = Y = Z 3, K = Z 3 Z 3, H = { h (a,b) : (a, b) K } h (a,b) (x) = ax + b (mod 3). Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 30 / 35

59 Message Authentication Codes (MACs) Unconditionally Secure MACs Example X = Y = Z 3, K = Z 3 Z 3, H = { h (a,b) : (a, b) K } h (a,b) (x) = ax + b (mod 3). key (0, 0) (0, 1) (0, 2) (1, 0) (1, 1) (1, 2) (2, 0) (2, 1) (2, 2) Figure: Authentication Matrix Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 30 / 35

60 Message Authentication Codes (MACs) Unconditionally Secure MACs Example X = Y = Z 3, K = Z 3 Z 3, H = { h (a,b) : (a, b) K } h (a,b) (x) = ax + b (mod 3). = Pd 0 = Pd 1 = 1 3 key (0, 0) (0, 1) (0, 2) (1, 0) (1, 1) (1, 2) (2, 0) (2, 1) (2, 2) Figure: Authentication Matrix Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 30 / 35

61 Message Authentication Codes (MACs) Unconditionally Secure MACs Computation of Deception Probabilities payoff(x, y) = Pr [y = h K0 (x)] = {K K : h K (x) = y}. K Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 31 / 35

62 Message Authentication Codes (MACs) Unconditionally Secure MACs Computation of Deception Probabilities payoff(x, y) = Pr [y = h K0 (x)] = {K K : h K (x) = y}. K Pd 0 = max {payoff(x, y) : x X, y Y}. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 31 / 35

63 Message Authentication Codes (MACs) Unconditionally Secure MACs Computation of Deception Probabilities payoff(x, y) = Pr [y = h K0 (x)] = {K K : h K (x) = y}. K Pd 0 = max {payoff(x, y) : x X, y Y}. payoff(x, y ; x, y) = Pr [ y = h K0 (x ) y = h K0 (x) ] = Pr [y = h K0 (x ) y = h K0 (x)] Pr [y = h K0 (x)] = {K K : h K (x ) = y, h K (x) = y}. {K K : h K (x) = y} Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 31 / 35

64 Message Authentication Codes (MACs) Unconditionally Secure MACs Computation of Deception Probabilities payoff(x, y) = Pr [y = h K0 (x)] = {K K : h K (x) = y}. K Pd 0 = max {payoff(x, y) : x X, y Y}. payoff(x, y ; x, y) = Pr [ y = h K0 (x ) y = h K0 (x) ] = Pr [y = h K0 (x ) y = h K0 (x)] Pr [y = h K0 (x)] = {K K : h K (x ) = y, h K (x) = y}. {K K : h K (x) = y} V = {(x, y) : {K K : h K (x) = y} 1}. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 31 / 35

65 Message Authentication Codes (MACs) Unconditionally Secure MACs Computation of Deception Probabilities payoff(x, y) = Pr [y = h K0 (x)] = {K K : h K (x) = y}. K Pd 0 = max {payoff(x, y) : x X, y Y}. payoff(x, y ; x, y) = Pr [ y = h K0 (x ) y = h K0 (x) ] = Pr [y = h K0 (x ) y = h K0 (x)] Pr [y = h K0 (x)] = {K K : h K (x ) = y, h K (x) = y}. {K K : h K (x) = y} V = {(x, y) : {K K : h K (x) = y} 1}. Pd 1 = max { payoff(x, y ; x, y) : x x X, y, y Y, (x, y) V }. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 31 / 35

66 Message Authentication Codes (MACs) Strongly Universal Hash Families Unconditionally Secure MACs Definition Let (X, Y, K, H) be an (N, M)-hash family. This hash family is strongly universal, if { K K : h K (x) = y, h K (x ) = y } = K M 2 for all x, x X such that x x, and for all y, y Y. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 32 / 35

67 Message Authentication Codes (MACs) Strongly Universal Hash Families Unconditionally Secure MACs Definition Let (X, Y, K, H) be an (N, M)-hash family. This hash family is strongly universal, if { K K : h K (x) = y, h K (x ) = y } = K M 2 for all x, x X such that x x, and for all y, y Y. Lemma Let (X, Y, K, H) be a strongly universal (N, M)-hash family. Then {K K : h K (x) = y} = K M x X y Y. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 32 / 35

68 Message Authentication Codes (MACs) Unconditionally Secure MACs Proof. Let x, x X such that x x, and let y Y. {K K : h K (x) = y} = y Y { K K : h K (x) = y, h K (x ) = y } = y Y K M 2 = K M. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 33 / 35

69 Message Authentication Codes (MACs) Unconditionally Secure MACs Proof. Let x, x X such that x x, and let y Y. {K K : h K (x) = y} = y Y { K K : h K (x) = y, h K (x ) = y } = y Y K M 2 = K M. Theorem Let (X, Y, K, H) be a strongly universal (N, M)-hash family. Then (X, Y, K, H) is an authentication code with Pd 0 = Pd 1 = 1 M. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 33 / 35

70 Message Authentication Codes (MACs) Unconditionally Secure MACs Proof. Let x X and y Y. payoff(x, y) = {K K : h K (x) = y} K = K /M K = 1 M. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 34 / 35

71 Message Authentication Codes (MACs) Unconditionally Secure MACs Proof. Let x X and y Y. payoff(x, y) = {K K : h K (x) = y} K = K /M K = 1 M. Now let x, x X such that x x, and let y, y Y, where (x, y) V. payoff(x, y ; x, y) = {K K : h K (x ) = y, h K (x) = y} {K K : h K (x) = y} = K /M2 K /M = 1 M. Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 34 / 35

72 Message Authentication Codes (MACs) Unconditionally Secure MACs Proof. Let x X and y Y. payoff(x, y) = {K K : h K (x) = y} K = K /M K = 1 M. Now let x, x X such that x x, and let y, y Y, where (x, y) V. payoff(x, y ; x, y) = {K K : h K (x ) = y, h K (x) = y} {K K : h K (x) = y} = K /M2 K /M = 1 M. = Pd 0 = Pd 1 = 1 M Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 34 / 35

73 Thanks for listening! References For further reading: Douglas R. Stinson Cryptography: Theory and Practice 2 nd ed., Chapman & Hall/CRC, Bruce Schneier Applied Cryptography: Protocols, Algorithms, and Source Code in C John Wiley & Sons, Inc., Bart van Rompay Analysis and Design of Cryptographic Hash Functions, MAC Algorithms and Block Ciphers Ph. D. thesis, Katholieke Universiteit Leuven, Johannes Mittmann (TU München) One-Way Encryption JASS 2005 IT Security 35 / 35

Cryptographic Hash Functions Message Authentication Digital Signatures

Cryptographic Hash Functions Message Authentication Digital Signatures Cryptographic Hash Functions Message Authentication Digital Signatures Abstract We will discuss Cryptographic hash functions Message authentication codes HMAC and CBC-MAC Digital signatures 2 Encryption/Decryption

More information

Message Authentication Codes. Lecture Outline

Message Authentication Codes. Lecture Outline Message Authentication Codes Murat Kantarcioglu Based on Prof. Ninghui Li s Slides Message Authentication Code Lecture Outline 1 Limitation of Using Hash Functions for Authentication Require an authentic

More information

Overview of Cryptographic Tools for Data Security. Murat Kantarcioglu

Overview of Cryptographic Tools for Data Security. Murat Kantarcioglu UT DALLAS Erik Jonsson School of Engineering & Computer Science Overview of Cryptographic Tools for Data Security Murat Kantarcioglu Pag. 1 Purdue University Cryptographic Primitives We will discuss the

More information

Cryptographic hash functions and MACs Solved Exercises for Cryptographic Hash Functions and MACs

Cryptographic hash functions and MACs Solved Exercises for Cryptographic Hash Functions and MACs Cryptographic hash functions and MACs Solved Exercises for Cryptographic Hash Functions and MACs Enes Pasalic University of Primorska Koper, 2014 Contents 1 Preface 3 2 Problems 4 2 1 Preface This is a

More information

Introduction to Computer Security

Introduction to Computer Security Introduction to Computer Security Hash Functions and Digital Signatures Pavel Laskov Wilhelm Schickard Institute for Computer Science Integrity objective in a wide sense Reliability Transmission errors

More information

Signature Schemes. CSG 252 Fall 2006. Riccardo Pucella

Signature Schemes. CSG 252 Fall 2006. Riccardo Pucella Signature Schemes CSG 252 Fall 2006 Riccardo Pucella Signatures Signatures in real life have a number of properties They specify the person responsible for a document E.g. that it has been produced by

More information

HASH CODE BASED SECURITY IN CLOUD COMPUTING

HASH CODE BASED SECURITY IN CLOUD COMPUTING ABSTRACT HASH CODE BASED SECURITY IN CLOUD COMPUTING Kaleem Ur Rehman M.Tech student (CSE), College of Engineering, TMU Moradabad (India) The Hash functions describe as a phenomenon of information security

More information

Network Security. Gaurav Naik Gus Anderson. College of Engineering. Drexel University, Philadelphia, PA. Drexel University. College of Engineering

Network Security. Gaurav Naik Gus Anderson. College of Engineering. Drexel University, Philadelphia, PA. Drexel University. College of Engineering Network Security Gaurav Naik Gus Anderson, Philadelphia, PA Lectures on Network Security Feb 12 (Today!): Public Key Crypto, Hash Functions, Digital Signatures, and the Public Key Infrastructure Feb 14:

More information

Outline. Computer Science 418. Digital Signatures: Observations. Digital Signatures: Definition. Definition 1 (Digital signature) Digital Signatures

Outline. Computer Science 418. Digital Signatures: Observations. Digital Signatures: Definition. Definition 1 (Digital signature) Digital Signatures Outline Computer Science 418 Digital Signatures Mike Jacobson Department of Computer Science University of Calgary Week 12 1 Digital Signatures 2 Signatures via Public Key Cryptosystems 3 Provable 4 Mike

More information

Hash Functions. Integrity checks

Hash Functions. Integrity checks Hash Functions EJ Jung slide 1 Integrity checks Integrity vs. Confidentiality! Integrity: attacker cannot tamper with message! Encryption may not guarantee integrity! Intuition: attacker may able to modify

More information

Message Authentication

Message Authentication Message Authentication message authentication is concerned with: protecting the integrity of a message validating identity of originator non-repudiation of origin (dispute resolution) will consider the

More information

CERIAS Tech Report 2007-20

CERIAS Tech Report 2007-20 CERIAS Tech Report 2007-20 DYNAMIC CRYPTOGRAPHIC HASH FUNCTIONS by William Speirs Center for Education and Research in Information Assurance and Security, Purdue University, West Lafayette, IN 47907-2086

More information

Authentication requirement Authentication function MAC Hash function Security of

Authentication requirement Authentication function MAC Hash function Security of UNIT 3 AUTHENTICATION Authentication requirement Authentication function MAC Hash function Security of hash function and MAC SHA HMAC CMAC Digital signature and authentication protocols DSS Slides Courtesy

More information

Lecture 10: CPA Encryption, MACs, Hash Functions. 2 Recap of last lecture - PRGs for one time pads

Lecture 10: CPA Encryption, MACs, Hash Functions. 2 Recap of last lecture - PRGs for one time pads CS 7880 Graduate Cryptography October 15, 2015 Lecture 10: CPA Encryption, MACs, Hash Functions Lecturer: Daniel Wichs Scribe: Matthew Dippel 1 Topic Covered Chosen plaintext attack model of security MACs

More information

Communications security

Communications security University of Roma Sapienza DIET Communications security Lecturer: Andrea Baiocchi DIET - University of Roma La Sapienza E-mail: andrea.baiocchi@uniroma1.it URL: http://net.infocom.uniroma1.it/corsi/index.htm

More information

lundi 1 octobre 2012 In a set of N elements, by picking at random N elements, we have with high probability a collision two elements are equal

lundi 1 octobre 2012 In a set of N elements, by picking at random N elements, we have with high probability a collision two elements are equal Symmetric Crypto Pierre-Alain Fouque Birthday Paradox In a set of N elements, by picking at random N elements, we have with high probability a collision two elements are equal N=365, about 23 people are

More information

Length extension attack on narrow-pipe SHA-3 candidates

Length extension attack on narrow-pipe SHA-3 candidates Length extension attack on narrow-pipe SHA-3 candidates Danilo Gligoroski Department of Telematics, Norwegian University of Science and Technology, O.S.Bragstads plass 2B, N-7491 Trondheim, NORWAY danilo.gligoroski@item.ntnu.no

More information

Cryptography and Network Security Chapter 11

Cryptography and Network Security Chapter 11 Cryptography and Network Security Chapter 11 Fifth Edition by William Stallings Lecture slides by Lawrie Brown (with edits by RHB) Chapter 11 Cryptographic Hash Functions Each of the messages, like each

More information

CIS 6930 Emerging Topics in Network Security. Topic 2. Network Security Primitives

CIS 6930 Emerging Topics in Network Security. Topic 2. Network Security Primitives CIS 6930 Emerging Topics in Network Security Topic 2. Network Security Primitives 1 Outline Absolute basics Encryption/Decryption; Digital signatures; D-H key exchange; Hash functions; Application of hash

More information

Introduction to Cryptography CS 355

Introduction to Cryptography CS 355 Introduction to Cryptography CS 355 Lecture 30 Digital Signatures CS 355 Fall 2005 / Lecture 30 1 Announcements Wednesday s lecture cancelled Friday will be guest lecture by Prof. Cristina Nita- Rotaru

More information

Computer Security: Principles and Practice

Computer Security: Principles and Practice Computer Security: Principles and Practice Chapter 20 Public-Key Cryptography and Message Authentication First Edition by William Stallings and Lawrie Brown Lecture slides by Lawrie Brown Public-Key Cryptography

More information

1 Digital Signatures. 1.1 The RSA Function: The eth Power Map on Z n. Crypto: Primitives and Protocols Lecture 6.

1 Digital Signatures. 1.1 The RSA Function: The eth Power Map on Z n. Crypto: Primitives and Protocols Lecture 6. 1 Digital Signatures A digital signature is a fundamental cryptographic primitive, technologically equivalent to a handwritten signature. In many applications, digital signatures are used as building blocks

More information

Digital Signatures. Murat Kantarcioglu. Based on Prof. Li s Slides. Digital Signatures: The Problem

Digital Signatures. Murat Kantarcioglu. Based on Prof. Li s Slides. Digital Signatures: The Problem Digital Signatures Murat Kantarcioglu Based on Prof. Li s Slides Digital Signatures: The Problem Consider the real-life example where a person pays by credit card and signs a bill; the seller verifies

More information

Symmetric Crypto MAC. Pierre-Alain Fouque

Symmetric Crypto MAC. Pierre-Alain Fouque Symmetric Crypto MAC Pierre-Alain Fouque Birthday Paradox In a set of D elements, by picking at random D elements, we have with high probability a collision two elements are equal D=365, about 23 people

More information

Public Key Cryptography Overview

Public Key Cryptography Overview Ch.20 Public-Key Cryptography and Message Authentication I will talk about it later in this class Final: Wen (5/13) 1630-1830 HOLM 248» give you a sample exam» Mostly similar to homeworks» no electronic

More information

CIS433/533 - Computer and Network Security Cryptography

CIS433/533 - Computer and Network Security Cryptography CIS433/533 - Computer and Network Security Cryptography Professor Kevin Butler Winter 2011 Computer and Information Science A historical moment Mary Queen of Scots is being held by Queen Elizabeth and

More information

Designing Hash functions. Reviewing... Message Authentication Codes. and message authentication codes. We have seen how to authenticate messages:

Designing Hash functions. Reviewing... Message Authentication Codes. and message authentication codes. We have seen how to authenticate messages: Designing Hash functions and message authentication codes Reviewing... We have seen how to authenticate messages: Using symmetric encryption, in an heuristic fashion Using public-key encryption in interactive

More information

Table of Contents. Bibliografische Informationen http://d-nb.info/996514864. digitalisiert durch

Table of Contents. Bibliografische Informationen http://d-nb.info/996514864. digitalisiert durch 1 Introduction to Cryptography and Data Security 1 1.1 Overview of Cryptology (and This Book) 2 1.2 Symmetric Cryptography 4 1.2.1 Basics 4 1.2.2 Simple Symmetric Encryption: The Substitution Cipher...

More information

Cryptography Lecture 8. Digital signatures, hash functions

Cryptography Lecture 8. Digital signatures, hash functions Cryptography Lecture 8 Digital signatures, hash functions A Message Authentication Code is what you get from symmetric cryptography A MAC is used to prevent Eve from creating a new message and inserting

More information

Practice Questions. CS161 Computer Security, Fall 2008

Practice Questions. CS161 Computer Security, Fall 2008 Practice Questions CS161 Computer Security, Fall 2008 Name Email address Score % / 100 % Please do not forget to fill up your name, email in the box in the midterm exam you can skip this here. These practice

More information

Lecture 6 - Cryptography

Lecture 6 - Cryptography Lecture 6 - Cryptography CSE497b - Spring 2007 Introduction Computer and Network Security Professor Jaeger www.cse.psu.edu/~tjaeger/cse497b-s07 Question 2 Setup: Assume you and I don t know anything about

More information

Data integrity and data origin authentication

Data integrity and data origin authentication Network Security Elements of Applied Cryptography Hash functions and data integrity Manipulation Detection Code (MDC) Message Authentication Code (MAC) Data integrity and origin authentication Data integrity

More information

Cryptosystems. Bob wants to send a message M to Alice. Symmetric ciphers: Bob and Alice both share a secret key, K.

Cryptosystems. Bob wants to send a message M to Alice. Symmetric ciphers: Bob and Alice both share a secret key, K. Cryptosystems Bob wants to send a message M to Alice. Symmetric ciphers: Bob and Alice both share a secret key, K. C= E(M, K), Bob sends C Alice receives C, M=D(C,K) Use the same key to decrypt. Public

More information

Message Authentication Code

Message Authentication Code Message Authentication Code Ali El Kaafarani Mathematical Institute Oxford University 1 of 44 Outline 1 CBC-MAC 2 Authenticated Encryption 3 Padding Oracle Attacks 4 Information Theoretic MACs 2 of 44

More information

Recommendation for Applications Using Approved Hash Algorithms

Recommendation for Applications Using Approved Hash Algorithms NIST Special Publication 800-107 Recommendation for Applications Using Approved Hash Algorithms Quynh Dang Computer Security Division Information Technology Laboratory C O M P U T E R S E C U R I T Y February

More information

Message Authentication Codes

Message Authentication Codes 2 MAC Message Authentication Codes : and Cryptography Sirindhorn International Institute of Technology Thammasat University Prepared by Steven Gordon on 28 October 2013 css322y13s2l08, Steve/Courses/2013/s2/css322/lectures/mac.tex,

More information

Public Key Cryptography. c Eli Biham - March 30, 2011 258 Public Key Cryptography

Public Key Cryptography. c Eli Biham - March 30, 2011 258 Public Key Cryptography Public Key Cryptography c Eli Biham - March 30, 2011 258 Public Key Cryptography Key Exchange All the ciphers mentioned previously require keys known a-priori to all the users, before they can encrypt

More information

Digital Signatures. (Note that authentication of sender is also achieved by MACs.) Scan your handwritten signature and append it to the document?

Digital Signatures. (Note that authentication of sender is also achieved by MACs.) Scan your handwritten signature and append it to the document? Cryptography Digital Signatures Professor: Marius Zimand Digital signatures are meant to realize authentication of the sender nonrepudiation (Note that authentication of sender is also achieved by MACs.)

More information

Lecture 15 - Digital Signatures

Lecture 15 - Digital Signatures Lecture 15 - Digital Signatures Boaz Barak March 29, 2010 Reading KL Book Chapter 12. Review Trapdoor permutations - easy to compute, hard to invert, easy to invert with trapdoor. RSA and Rabin signatures.

More information

CS155. Cryptography Overview

CS155. Cryptography Overview CS155 Cryptography Overview Cryptography Is n A tremendous tool n The basis for many security mechanisms Is not n The solution to all security problems n Reliable unless implemented properly n Reliable

More information

Outline. CSc 466/566. Computer Security. 8 : Cryptography Digital Signatures. Digital Signatures. Digital Signatures... Christian Collberg

Outline. CSc 466/566. Computer Security. 8 : Cryptography Digital Signatures. Digital Signatures. Digital Signatures... Christian Collberg Outline CSc 466/566 Computer Security 8 : Cryptography Digital Signatures Version: 2012/02/27 16:07:05 Department of Computer Science University of Arizona collberg@gmail.com Copyright c 2012 Christian

More information

CS 758: Cryptography / Network Security

CS 758: Cryptography / Network Security CS 758: Cryptography / Network Security offered in the Fall Semester, 2003, by Doug Stinson my office: DC 3122 my email address: dstinson@uwaterloo.ca my web page: http://cacr.math.uwaterloo.ca/~dstinson/index.html

More information

Final Exam. IT 4823 Information Security Administration. Rescheduling Final Exams. Kerberos. Idea. Ticket

Final Exam. IT 4823 Information Security Administration. Rescheduling Final Exams. Kerberos. Idea. Ticket IT 4823 Information Security Administration Public Key Encryption Revisited April 5 Notice: This session is being recorded. Lecture slides prepared by Dr Lawrie Brown for Computer Security: Principles

More information

1 Signatures vs. MACs

1 Signatures vs. MACs CS 120/ E-177: Introduction to Cryptography Salil Vadhan and Alon Rosen Nov. 22, 2006 Lecture Notes 17: Digital Signatures Recommended Reading. Katz-Lindell 10 1 Signatures vs. MACs Digital signatures

More information

Network Security. Computer Networking Lecture 08. March 19, 2012. HKU SPACE Community College. HKU SPACE CC CN Lecture 08 1/23

Network Security. Computer Networking Lecture 08. March 19, 2012. HKU SPACE Community College. HKU SPACE CC CN Lecture 08 1/23 Network Security Computer Networking Lecture 08 HKU SPACE Community College March 19, 2012 HKU SPACE CC CN Lecture 08 1/23 Outline Introduction Cryptography Algorithms Secret Key Algorithm Message Digest

More information

Crittografia e sicurezza delle reti. Digital signatures- DSA

Crittografia e sicurezza delle reti. Digital signatures- DSA Crittografia e sicurezza delle reti Digital signatures- DSA Signatures vs. MACs Suppose parties A and B share the secret key K. Then M, MAC K (M) convinces A that indeed M originated with B. But in case

More information

Lecture 9 - Message Authentication Codes

Lecture 9 - Message Authentication Codes Lecture 9 - Message Authentication Codes Boaz Barak March 1, 2010 Reading: Boneh-Shoup chapter 6, Sections 9.1 9.3. Data integrity Until now we ve only been interested in protecting secrecy of data. However,

More information

How encryption works to provide confidentiality. How hashing works to provide integrity. How digital signatures work to provide authenticity and

How encryption works to provide confidentiality. How hashing works to provide integrity. How digital signatures work to provide authenticity and How encryption works to provide confidentiality. How hashing works to provide integrity. How digital signatures work to provide authenticity and non-repudiation. How to obtain a digital certificate. Installing

More information

Lecture 9: Application of Cryptography

Lecture 9: Application of Cryptography Lecture topics Cryptography basics Using SSL to secure communication links in J2EE programs Programmatic use of cryptography in Java Cryptography basics Encryption Transformation of data into a form that

More information

CSCE 465 Computer & Network Security

CSCE 465 Computer & Network Security CSCE 465 Computer & Network Security Instructor: Dr. Guofei Gu http://courses.cse.tamu.edu/guofei/csce465/ Public Key Cryptogrophy 1 Roadmap Introduction RSA Diffie-Hellman Key Exchange Public key and

More information

1 Message Authentication

1 Message Authentication Theoretical Foundations of Cryptography Lecture Georgia Tech, Spring 200 Message Authentication Message Authentication Instructor: Chris Peikert Scribe: Daniel Dadush We start with some simple questions

More information

Digital Signature For Text File

Digital Signature For Text File Digital Signature For Text File Ayad Ibrahim Abdulsada Dept. of Computer Science, College of Education, University of Basrah, Basrah, Iraq. E-mail: mraiadibraheem@yahoo.com Abstract: Digital signatures

More information

CRYPTOGRAPHY IN NETWORK SECURITY

CRYPTOGRAPHY IN NETWORK SECURITY ELE548 Research Essays CRYPTOGRAPHY IN NETWORK SECURITY AUTHOR: SHENGLI LI INSTRUCTOR: DR. JIEN-CHUNG LO Date: March 5, 1999 Computer network brings lots of great benefits and convenience to us. We can

More information

Secure Shell SSH provides support for secure remote login, secure file transfer, and secure TCP/IP and X11 forwarding. It can automatically encrypt,

Secure Shell SSH provides support for secure remote login, secure file transfer, and secure TCP/IP and X11 forwarding. It can automatically encrypt, Secure Shell SSH provides support for secure remote login, secure file transfer, and secure TCP/IP and X11 forwarding. It can automatically encrypt, authenticate, and compress transmitted data. The main

More information

Cryptography & Network Security

Cryptography & Network Security Cryptography & Network Security Lecture 1: Introduction & Overview 2002. 3. 27 chlim@sejong.ac.kr Common Terms(1) Cryptography: The study of mathematical techniques related to aspects of information security

More information

Message authentication

Message authentication Message authentication -- Hash based MAC unctions -- MAC unctions based on bloc ciphers -- Authenticated encryption (c) Levente Buttyán (buttyan@crysys.hu) Secret preix method MAC (x) = H( x) insecure!

More information

Introduction. Digital Signature

Introduction. Digital Signature Introduction Electronic transactions and activities taken place over Internet need to be protected against all kinds of interference, accidental or malicious. The general task of the information technology

More information

Remotely Keyed Encryption Using Non-Encrypting Smart Cards

Remotely Keyed Encryption Using Non-Encrypting Smart Cards THE ADVANCED COMPUTING SYSTEMS ASSOCIATION The following paper was originally published in the USENIX Workshop on Smartcard Technology Chicago, Illinois, USA, May 10 11, 1999 Remotely Keyed Encryption

More information

Implementation and Comparison of Various Digital Signature Algorithms. -Nazia Sarang Boise State University

Implementation and Comparison of Various Digital Signature Algorithms. -Nazia Sarang Boise State University Implementation and Comparison of Various Digital Signature Algorithms -Nazia Sarang Boise State University What is a Digital Signature? A digital signature is used as a tool to authenticate the information

More information

Common Pitfalls in Cryptography for Software Developers. OWASP AppSec Israel July 2006. The OWASP Foundation http://www.owasp.org/

Common Pitfalls in Cryptography for Software Developers. OWASP AppSec Israel July 2006. The OWASP Foundation http://www.owasp.org/ Common Pitfalls in Cryptography for Software Developers OWASP AppSec Israel July 2006 Shay Zalalichin, CISSP AppSec Division Manager, Comsec Consulting shayz@comsecglobal.com Copyright 2006 - The OWASP

More information

CUNSHENG DING HKUST, Hong Kong. Computer Security. Computer Security. Cunsheng DING, HKUST COMP4631

CUNSHENG DING HKUST, Hong Kong. Computer Security. Computer Security. Cunsheng DING, HKUST COMP4631 Cunsheng DING, HKUST Lecture 08: Key Management for One-key Ciphers Topics of this Lecture 1. The generation and distribution of secret keys. 2. A key distribution protocol with a key distribution center.

More information

2. Cryptography 2.4 Digital Signatures

2. Cryptography 2.4 Digital Signatures DI-FCT-UNL Computer and Network Systems Security Segurança de Sistemas e Redes de Computadores 2010-2011 2. Cryptography 2.4 Digital Signatures 2010, Henrique J. Domingos, DI/FCT/UNL 2.4 Digital Signatures

More information

DIGITAL SIGNATURES 1/1

DIGITAL SIGNATURES 1/1 DIGITAL SIGNATURES 1/1 Signing by hand COSMO ALICE ALICE Pay Bob $100 Cosmo Alice Alice Bank =? no Don t yes pay Bob 2/1 Signing electronically Bank Internet SIGFILE } {{ } 101 1 ALICE Pay Bob $100 scan

More information

Capture Resilient ElGamal Signature Protocols

Capture Resilient ElGamal Signature Protocols Capture Resilient ElGamal Signature Protocols Hüseyin Acan 1, Kamer Kaya 2,, and Ali Aydın Selçuk 2 1 Bilkent University, Department of Mathematics acan@fen.bilkent.edu.tr 2 Bilkent University, Department

More information

Fundamentals of Computer Security

Fundamentals of Computer Security Fundamentals of Computer Security Spring 2015 Radu Sion Intro Encryption Hash Functions A Message From Our Sponsors Fundamentals System/Network Security, crypto How do things work Why How to design secure

More information

SECURITY IN NETWORKS

SECURITY IN NETWORKS SECURITY IN NETWORKS GOALS Understand principles of network security: Cryptography and its many uses beyond confidentiality Authentication Message integrity Security in practice: Security in application,

More information

MACs Message authentication and integrity. Table of contents

MACs Message authentication and integrity. Table of contents MACs Message authentication and integrity Foundations of Cryptography Computer Science Department Wellesley College Table of contents Introduction MACs Constructing Secure MACs Secure communication and

More information

Cryptography and Network Security Chapter 12

Cryptography and Network Security Chapter 12 Cryptography and Network Security Chapter 12 Fifth Edition by William Stallings Lecture slides by Lawrie Brown (with edits by RHB) Chapter 12 Message Authentication Codes At cats' green on the Sunday he

More information

Talk announcement please consider attending!

Talk announcement please consider attending! Talk announcement please consider attending! Where: Maurer School of Law, Room 335 When: Thursday, Feb 5, 12PM 1:30PM Speaker: Rafael Pass, Associate Professor, Cornell University, Topic: Reasoning Cryptographically

More information

Network Security (2) CPSC 441 Department of Computer Science University of Calgary

Network Security (2) CPSC 441 Department of Computer Science University of Calgary Network Security (2) CPSC 441 Department of Computer Science University of Calgary 1 Friends and enemies: Alice, Bob, Trudy well-known in network security world Bob, Alice (lovers!) want to communicate

More information

Evaluation of Digital Signature Process

Evaluation of Digital Signature Process Evaluation of Digital Signature Process Emil SIMION, Ph. D. email: esimion@fmi.unibuc.ro Agenda Evaluation of digital signatures schemes: evaluation criteria; security evaluation; security of hash functions;

More information

1 Domain Extension for MACs

1 Domain Extension for MACs CS 127/CSCI E-127: Introduction to Cryptography Prof. Salil Vadhan Fall 2013 Reading. Lecture Notes 17: MAC Domain Extension & Digital Signatures Katz-Lindell Ÿ4.34.4 (2nd ed) and Ÿ12.0-12.3 (1st ed).

More information

MTAT.07.003 Cryptology II. Digital Signatures. Sven Laur University of Tartu

MTAT.07.003 Cryptology II. Digital Signatures. Sven Laur University of Tartu MTAT.07.003 Cryptology II Digital Signatures Sven Laur University of Tartu Formal Syntax Digital signature scheme pk (sk, pk) Gen (m, s) (m,s) m M 0 s Sign sk (m) Ver pk (m, s)? = 1 To establish electronic

More information

INTERACTIVE TWO-CHANNEL MESSAGE AUTHENTICATION BASED ON INTERACTIVE-COLLISION RESISTANT HASH FUNCTIONS

INTERACTIVE TWO-CHANNEL MESSAGE AUTHENTICATION BASED ON INTERACTIVE-COLLISION RESISTANT HASH FUNCTIONS INTERACTIVE TWO-CHANNEL MESSAGE AUTHENTICATION BASED ON INTERACTIVE-COLLISION RESISTANT HASH FUNCTIONS ATEFEH MASHATAN 1 AND DOUGLAS R STINSON 2 Abstract We propose an interactive message authentication

More information

Provable-Security Analysis of Authenticated Encryption in Kerberos

Provable-Security Analysis of Authenticated Encryption in Kerberos Provable-Security Analysis of Authenticated Encryption in Kerberos Alexandra Boldyreva Virendra Kumar Georgia Institute of Technology, School of Computer Science 266 Ferst Drive, Atlanta, GA 30332-0765

More information

Security and Authentication Primer

Security and Authentication Primer Security and Authentication Primer Manfred Jantscher and Peter H. Cole Auto-ID Labs White Paper WP-HARDWARE-025 Mr. Manfred Jantscher Visiting Master Student, School of Electrical and Electronics Engineering,

More information

The Keyed-Hash Message Authentication Code (HMAC)

The Keyed-Hash Message Authentication Code (HMAC) FIPS PUB 198-1 FEDERAL INFORMATION PROCESSING STANDARDS PUBLICATION The Keyed-Hash Message Authentication Code (HMAC) CATEGORY: COMPUTER SECURITY SUBCATEGORY: CRYPTOGRAPHY Information Technology Laboratory

More information

Secure Network Communication Part II II Public Key Cryptography. Public Key Cryptography

Secure Network Communication Part II II Public Key Cryptography. Public Key Cryptography Kommunikationssysteme (KSy) - Block 8 Secure Network Communication Part II II Public Key Cryptography Dr. Andreas Steffen 2000-2001 A. Steffen, 28.03.2001, KSy_RSA.ppt 1 Secure Key Distribution Problem

More information

An Efficient and Secure Key Management Scheme for Hierarchical Access Control Based on ECC

An Efficient and Secure Key Management Scheme for Hierarchical Access Control Based on ECC An Efficient and Secure Key Management Scheme for Hierarchical Access Control Based on ECC Laxminath Tripathy 1 Nayan Ranjan Paul 2 1Department of Information technology, Eastern Academy of Science and

More information

7! Cryptographic Techniques! A Brief Introduction

7! Cryptographic Techniques! A Brief Introduction 7! Cryptographic Techniques! A Brief Introduction 7.1! Introduction to Cryptography! 7.2! Symmetric Encryption! 7.3! Asymmetric (Public-Key) Encryption! 7.4! Digital Signatures! 7.5! Public Key Infrastructures

More information

Improved Online/Offline Signature Schemes

Improved Online/Offline Signature Schemes Improved Online/Offline Signature Schemes Adi Shamir and Yael Tauman Applied Math. Dept. The Weizmann Institute of Science Rehovot 76100, Israel {shamir,tauman}@wisdom.weizmann.ac.il Abstract. The notion

More information

Network Security. Abusayeed Saifullah. CS 5600 Computer Networks. These slides are adapted from Kurose and Ross 8-1

Network Security. Abusayeed Saifullah. CS 5600 Computer Networks. These slides are adapted from Kurose and Ross 8-1 Network Security Abusayeed Saifullah CS 5600 Computer Networks These slides are adapted from Kurose and Ross 8-1 Public Key Cryptography symmetric key crypto v requires sender, receiver know shared secret

More information

Chapter 11 Security+ Guide to Network Security Fundamentals, Third Edition Basic Cryptography

Chapter 11 Security+ Guide to Network Security Fundamentals, Third Edition Basic Cryptography Chapter 11 Security+ Guide to Network Security Fundamentals, Third Edition Basic Cryptography What Is Steganography? Steganography Process of hiding the existence of the data within another file Example:

More information

Dr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall 2010

Dr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall 2010 CS 494/594 Computer and Network Security Dr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall 2010 1 Introduction to Cryptography What is cryptography?

More information

Efficient construction of vote-tags to allow open objection to the tally in electronic elections

Efficient construction of vote-tags to allow open objection to the tally in electronic elections Information Processing Letters 75 (2000) 211 215 Efficient construction of vote-tags to allow open objection to the tally in electronic elections Andreu Riera a,,joseprifà b, Joan Borrell b a isoco, Intelligent

More information

Elliptic Curve Hash (and Sign)

Elliptic Curve Hash (and Sign) Elliptic Curve Hash (and Sign) (and the 1-up problem for ECDSA) Daniel R. L. Brown Certicom Research ECC 2008, Utrecht, Sep 22-24 2008 Dan Brown (Certicom) Elliptic Curve Hash (and Sign) ECC 2008 1 / 43

More information

Software Implementation of Gong-Harn Public-key Cryptosystem and Analysis

Software Implementation of Gong-Harn Public-key Cryptosystem and Analysis Software Implementation of Gong-Harn Public-key Cryptosystem and Analysis by Susana Sin A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master

More information

1 Construction of CCA-secure encryption

1 Construction of CCA-secure encryption CSCI 5440: Cryptography Lecture 5 The Chinese University of Hong Kong 10 October 2012 1 Construction of -secure encryption We now show how the MAC can be applied to obtain a -secure encryption scheme.

More information

RSA Attacks. By Abdulaziz Alrasheed and Fatima

RSA Attacks. By Abdulaziz Alrasheed and Fatima RSA Attacks By Abdulaziz Alrasheed and Fatima 1 Introduction Invented by Ron Rivest, Adi Shamir, and Len Adleman [1], the RSA cryptosystem was first revealed in the August 1977 issue of Scientific American.

More information

Digital Signatures. What are Signature Schemes?

Digital Signatures. What are Signature Schemes? Digital Signatures Debdeep Mukhopadhyay IIT Kharagpur What are Signature Schemes? Provides message integrity in the public key setting Counter-parts of the message authentication schemes in the public

More information

Network Security CS 5490/6490 Fall 2015 Lecture Notes 8/26/2015

Network Security CS 5490/6490 Fall 2015 Lecture Notes 8/26/2015 Network Security CS 5490/6490 Fall 2015 Lecture Notes 8/26/2015 Chapter 2: Introduction to Cryptography What is cryptography? It is a process/art of mangling information in such a way so as to make it

More information

Chapter 6. Hash Functions. 6.1 The hash function SHA1

Chapter 6. Hash Functions. 6.1 The hash function SHA1 Chapter 6 Hash Functions A hash function usually means a function that compresses, meaning the output is shorter than the input. Often, such a function takes an input of arbitrary or almost arbitrary length

More information

Hash Function JH and the NIST SHA3 Hash Competition

Hash Function JH and the NIST SHA3 Hash Competition Hash Function JH and the NIST SHA3 Hash Competition Hongjun Wu Nanyang Technological University Presented at ACNS 2012 1 Introduction to Hash Function Hash Function Design Basics Hash function JH Design

More information

EXAM questions for the course TTM4135 - Information Security May 2013. Part 1

EXAM questions for the course TTM4135 - Information Security May 2013. Part 1 EXAM questions for the course TTM4135 - Information Security May 2013 Part 1 This part consists of 5 questions all from one common topic. The number of maximal points for every correctly answered question

More information

Recommendation for Applications Using Approved Hash Algorithms

Recommendation for Applications Using Approved Hash Algorithms NIST Special Publication 800-107 Revision 1 Recommendation for Applications Using Approved Hash Algorithms Quynh Dang Computer Security Division Information Technology Laboratory C O M P U T E R S E C

More information

Massachusetts Institute of Technology Handout 13 6.857: Network and Computer Security October 9, 2003 Professor Ronald L. Rivest.

Massachusetts Institute of Technology Handout 13 6.857: Network and Computer Security October 9, 2003 Professor Ronald L. Rivest. Massachusetts Institute of Technology Handout 13 6.857: Network and Computer Security October 9, 2003 Professor Ronald L. Rivest Quiz 1 1. This quiz is intended to provide a fair measure of your understanding

More information

Cryptography and Network Security Chapter 11. Fourth Edition by William Stallings

Cryptography and Network Security Chapter 11. Fourth Edition by William Stallings Cryptography and Network Security Chapter 11 Fourth Edition by William Stallings Chapter 11 Message Authentication and Hash Functions At cats' green on the Sunday he took the message from the inside of

More information

Authentication and Encryption: How to order them? Motivation

Authentication and Encryption: How to order them? Motivation Authentication and Encryption: How to order them? Debdeep Muhopadhyay IIT Kharagpur Motivation Wide spread use of internet requires establishment of a secure channel. Typical implementations operate in

More information

Cryptography Overview

Cryptography Overview Cryptography Overview Cryptography Is n A tremendous tool n The basis for many security mechanisms Is not n The solution to all security problems n Reliable unless implemented properly n Reliable unless

More information

Chapter 7 Transport-Level Security

Chapter 7 Transport-Level Security Cryptography and Network Security Chapter 7 Transport-Level Security Lectured by Nguyễn Đức Thái Outline Web Security Issues Security Socket Layer (SSL) Transport Layer Security (TLS) HTTPS Secure Shell

More information