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# Public Key Cryptography

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Public Key Cryptography,Rivest, Shamir & Adleman ,Diffe-Hellman Key Exchange Algorithm,Digital Signature Standard,Euclid Algorithm,Euler Theorem,Euler Totient Function

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### Public Key Cryptography

1. 1. Security Concept Part-2 Mr.Gopal Sakarkar Mr. Gopal Sakarkar
2. 2. Public Key Cryptography • It is used two keys for encryption and for decryption. – a public-key, which may be known by anybody, and can be used to encrypt messages – a private-key, known only to the recipient, used to decrypt Mr. Gopal Sakarkar messages • It has six ingredient 1 Plain text 2 Encryption algorithm 3 Public and private keys 4 Ciphertext 5 Decryption algorithm
3. 3. Mr. Gopal Sakarkar
4. 4. Public-Key Characteristics • Public-Key algorithms rely on two keys where: – it is computationally infeasible to find decryption key knowing only algorithm & encryption key – it is computationally easy to en/decrypt messages when the relevant (en/decrypt) key is known – either of the two related keys can be used for encryption, with the other used for decryption (for some algorithms) Mr. Gopal Sakarkar
5. 5. Public key Cryptosystem : Authentication and secrecy Mr. Gopal Sakarkar
6. 6. Requirement of Public key Cryptography 1. It is easy for party B to generate a pair of keys (public key PUb , Mr. Gopal Sakarkar Private key PRb). 2. It is easy for a sender A , knowing the public key and message to be encrypt. C=E(PUb, M) 3. It is easy for receiver B to decrypt the resulting ciphertext using the private key . M=D(PRb,C)=D[PRb,E(PUb,M)] 4. It is infeasible for an any person , to know the public key PUb to determine the private key PRb. 5. It is infeasible for any person to know the public key PUb and a ciphertext C to recover the original message M. 6. Two keys can be applied in either order M=DP[PUb, E(PRb,M)] = D[PRb,E(PUb, M)]
7. 7. Exercise • Explain the difference between conventional and public key encryption. • What are the different requirements for public key cryptography . Mr. Gopal Sakarkar
8. 8. Related Links • http://docs.sun.com/source/816-6154-10/contents.htm Mr. Gopal Sakarkar
9. 9. RSA • Invented by Rivest, Shamir & Adleman of MIT in Mr. Gopal Sakarkar 1977 • It is a best known & widely used public-key scheme. • It is a block cipher algorithm in which palintext and ciphertext integers between 0 to n-1 for some n. • A typical size for n is 1024 bits or 309 decimal digits.
10. 10. RSA Algorithm Mr. Gopal Sakarkar
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13. 13. An Example • Let p= 3 and q=5, • n= 3 X 5 =15 • Q(n)= (3-1) * (5-1) = 2 x 4= 8 • Select e such that gcd(Q(n), e) =1 where, 1<e<Q(n) • Say e=3 (any prime number) • Calculate d , such that d e mod Q(n)=1 • 8k+1= 9, 17,25, 33, 41……..where k=1,2,3,4…. • Now check which number is divisible by 3. • 33 is divisible by 3 .So, d=33/3=11. //9 is also divisible by 3. • Now k1=(3,15) and K2=(11,15) • Take plan text M =13 , where (M<n) • Encryption C= 133 mod 15 =7 • Decryption D= 711 mod 15 =13 Mr. Gopal Sakarkar Video
14. 14. Exercise • Perform encryption and decryption using the RSA algorithm for the following 1. p=3, q=11, e=7, M=5 2. P=5,q=11, e=3 , M=9 • Explain various Asymmetric Encryption Algorithms . • Draw an algorithm, flowchart for implementing the RSA Algo. Mr. Gopal Sakarkar
15. 15. Diffie –Hellman Key Exchange Mr. Gopal Sakarkar in 1976 • It is used by two users to securely exchange a key that can be used for subsequent encryption of messages. a public-key distribution scheme – cannot be used to exchange an arbitrary message – rather it can establish a common key – known only to the two participants value of key depends on the participants (and their private and public key information) based on mathematical principles security relies on the difficulty of computing discrete logarithms (similar to factoring) – hard
16. 16. Diffe-Hellman Key Exchange Algorithm Global Public Elements q = prime number(300 decimal, i.e. 1024 bits)  = Integer User A key Generation Select private Xa , Xa < q Calculate public Ya , Ya= Xa mod q User B Key Generation Select private Xb , Xb < q Calculate public Yb , Yb= Xb mod q Mr. Gopal Sakarkar
17. 17. Diffe-Hellman Key Exchange Algorithm Generation of secret key by user A K=(Yb)Xa mod q Generation of secret key by user B K=(Ya)Xb mod q Mr. Gopal Sakarkar Video
18. 18. • users Alice & Bob who wish to swap keys: • agree on prime q=353 and =3 • select random secret keys: – A chooses xA=97, B chooses xB=233 • compute respective public keys: – yA=397 mod 353 = 40 (Alice) – yB=3233 mod 353 = 248 (Bob) • compute shared session key as: xA mod 353 = 24897 = 160 (Alice) Mr. Gopal Sakarkar – KAB= yB – KAB= yA xB mod 353 = 40233 = 160 (Bob)
19. 19. Diffie –Hellman Key Exchange Mr. Gopal Sakarkar
20. 20. Exercise users Alice & Bob who wish to swap keys: agree on prime q=5 and =7 select random secret keys: – A chooses xA= 8, B chooses xB= 13 Mr. Gopal Sakarkar
21. 21. Exercise Using diffie- hellman key exchange techniques ,Find A’s public key YA and B’s public key YB . If, q=71 and = 7 , XA =5 and XB = 12 Draw an algorithm, flowchart and write C++ program to implement Diffe-Hellman Key Exchange Algorithm Mr. Gopal Sakarkar
23. 23. • Send your all PPT, Posters, IEEE papers on KnowledgeWealth at Facebook Mr. Gopal Sakarkar
24. 24. Digital Signature Encryption, message authentication and digital signatures are all tools of modern cryptography. A signature is a technique for non-repudiation based on the public key cryptography. The creator of a message can attach a code, the signature, which guarantees the source and integrity of the message. Mr. Gopal Sakarkar
25. 25. Digital signature process Mr. Gopal Sakarkar
26. 26. Properties of Signatures Similar to handwritten signatures, digital signatures must fulfill the following: Recipients must be able to verify them  Signers must not be able to repudiate them later In addition, digital signatures cannot be constant and must be a function of the entire document it signs Mr. Gopal Sakarkar
27. 27. Types of Signatures Direct digital signature – involves only the communicating parties  Assumed that receiver knows public key of sender.  Signature may be formed by (1) encrypting entire message with sender’s private key or (2) encrypting hash code of message with sender’s private key.  Further encryption of entire message + signature with receiver’s public key or shared private key ensures confidentiality. Mr. Gopal Sakarkar
28. 28. The message with sender’s private key Mr. Gopal Sakarkar
29. 29. The hash code of message with sender’s private key Mr. Gopal Sakarkar
30. 30. Types of Signatures Arbitrated digital signature – involves a trusted third party or arbiter  Every signed message from sender, X, to receiver, Y, goes to an arbiter (authority), A, first. A subjects message + signature to number of tests to check origin & content  A date the message and sends it to Y with indication that it has been verified to its satisfaction Mr. Gopal Sakarkar
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32. 32. Digital Signature Standard Public-key technique. User applies the Secure Hash Algorithm (SHA) to the message to produce Mr. Gopal Sakarkar message digest. User’s private key is applied to message digest using DSA to generate signature.
33. 33. Digital Signature Standard Mr. Gopal Sakarkar Exp:LIC Doc
34. 34. DSA/DSS Key Generation have shared global public key values (p,q,g): – choose a large prime p with 2L-1 < p < 2L where L= 512 to 1024 bits and is a multiple of 64 – choose q with 2159 < q < 2160 such that q is a 160 bit prime divisor of (p-1) Mr. Gopal Sakarkar – choose g = h(p-1)/q where 1<h<p-1 and h(p-1)/q mod p > 1 users choose private key & compute public key: – choose x<q //Private Key – compute y = gx mod p //Public Key
35. 35. DSA Signature Creation to sign a message M the sender: – generates a random signature key k, k<q – k must be random, be destroyed after use, and never be reused Mr. Gopal Sakarkar then computes signature pair: r = (gk mod p)mod q s = [k-1(H(M)+ xr)] mod q sends signature (r,s) with message M
36. 36. DSA Signature Verification having received M & signature (r,s) to verify a signature, recipient computes: w = s-1 mod q u1= [H(M)w ]mod q u2= (rw)mod q v = [(gu1 yu2)mod p ]mod q Mr. Gopal Sakarkar if v=r then signature is verified
37. 37. DSA creates a 320 bits signature with 512-1024 bit data Mr. Gopal Sakarkar security. smaller and faster than RSA a digital signature scheme only security depends on difficulty of computing discrete logarithms Summary
38. 38. Number theory Mr. Gopal Sakarkar
39. 39. Group The .is generic can be addition, multiplication ,substraction etc.  a set of elements or “numbers” , denoted by {G,.} • Rules: – associative law: (a.b).c = a.(b.c) – Closure : if a and b belong to G then a.b also in G – identity e: e.a = a.e = a – inverses a-1: a.a-1 = e • if commutative a.b = b.a – then forms an abelian group Mr. Gopal Sakarkar
40. 40. Ring • a set of “numbers” denoted by {R,+, X} • with two operations (addition and multiplication) which form: • an abelian group with addition operation and multiplication: – has closure :is a and b belong to R , then ab is also in R – is associative : a(bc)=(ab)c for all a,b,c in R – distributive over addition: a(b+c) = ab + ac (a+b)c = ac + bc • if multiplication operation is commutative, it forms a commutative ring i.e. ab = ba for all a, b in R Mr. Gopal Sakarkar
41. 41. Prime Factorisation • to factor a number n is to write it as a product of other numbers: n=a x b x c • note that factoring a number is relatively hard compared to multiplying the factors together to generate the number • the prime factorisation of a number n is when its written as a product of primes – eg. 91=7x13 ; 3600=24x32x52 Mr. Gopal Sakarkar
42. 42. Modular Arithmetic • define modulo operator “a mod n” to be remainder when a is divided by n Mr. Gopal Sakarkar eg. 11 mod 7=4 • congruent modulo Two integer a and b are said to be congruent modulo n if, a mod n = b mod n eg. 75 mod 10 = 85 mod 10
43. 43. Divisors • say a non-zero number b divides a if for some m have a=mb (a,b,m all integers) • that is b divides into a with no remainder • denote this b|a • and say that b is a divisor of a • eg. all of 1,2,3,4,6,8,12,24 divide 24 Mr. Gopal Sakarkar
44. 44. Modular Arithmetic Operations Mr. Gopal Sakarkar Properties of Modular Arithmetic (a+b) mod n = [a mod n + b mod n] mod n <proof> (a-b) mod n = [a mod n - b mod n] mod n (a X b) mod n = [a mod n X b mod n] mod n Eg. (11 + 15 ) mod 8 = [11 mod 8 + 15 mod 8] mod 8
45. 45. Modulo 8 Addition Example + 0 1 2 3 4 5 6 7 0 0 1 2 3 4 5 6 7 1 1 2 3 4 5 6 7 0 2 2 3 4 5 6 7 0 1 3 3 4 5 6 7 0 1 2 4 4 5 6 7 0 1 2 3 5 5 6 7 0 1 2 3 4 6 6 7 0 1 2 3 4 5 7 7 0 1 2 3 4 5 6 Mr. Gopal Sakarkar
46. 46. Exercise 1.Draw a flowchart and an algorithm and write a C ++ program for Modulo of n Addition. 2. Proved that (a-b) mod n and (a X b) mod n . Mr. Gopal Sakarkar
47. 47. Greatest Common Divisor (GCD) • GCD (a,b) of a and b is the greatest number that divides evenly into both a and b – eg GCD(60,24) = 12  The positive integer c is said to be the greatest common divisor of a and b if 1. C is a divisor of a and of b 2. Any divisor of a and b is a divisor of c It is denoted by gcd(a,b)= max[k, such that k/a and k/b] Mr. Gopal Sakarkar
48. 48. Find the gcd of 36 and 15 a/b gives a remainder of r b/r gives a remainder of s r/s gives a remainder of t ... w/x gives a remainder of y x/y gives no remainder H/w gcd(25,10) Mr. Gopal Sakarkar
49. 49. Exercise 1. Draw a flowchart and an algorithm and write a C++ program to find the GCD of numbers. Mr. Gopal Sakarkar
50. 50. Euclid Algorithm In mathematics, the Euclidean algorithm (also called Euclid's algorithm) is an efficient method for computing the greatest common divisor (GCD), also known as the greatest common factor (GCF) or highest common factor (HCF). It is named after the Greek mathematician Euclid (in BC 300) The greatest common divisor g is the largest natural number that divides both a and b without leaving a remainder . Mr. Gopal Sakarkar
51. 51. Euclidean Algorithm • an efficient way to find the GCD(a,b) • uses theorem that: – GCD(a,b) = GCD(b, a mod b) • Euclidean Algorithm to compute GCD(a,b) is: EUCLID(a,b) 1. A = a; B = b 2. if B = 0 return ; A = gcd(a, b) 3. R = A mod B 4. A = B 5. B = R 6. goto 2 Mr. Gopal Sakarkar
52. 52. Euler Theorem Swiss mathematician noted both for his work in analysis and algebra, including complex numbers and logarithms, and his introduction of much of the basic notation in mathematics. Mr. Gopal Sakarkar
53. 53. Relatively Prime Numbers • Two numbers a, b are relatively prime if have no common divisors apart from 1 – eg. 8 & 15 are relatively prime since factors of 8 are 1,2,4,8 and of 15 are 1,3,5,15 and 1 is the only common factor. Mr. Gopal Sakarkar
54. 54. Euler Totient Function ø(n) • It is define as the number of positive integer less than n and relatively prime to n. • Since a number less than or equal to and relatively prime to a given number is called a totative. • A totient function can be simply defined as the number Mr. Gopal Sakarkar of totatives of n. • For example, there are eight totatives of 24 (1, 5, 7, 11, 13, 17, 19, and 23), so ø(24)=8
55. 55. Euler Totient Function ø(n) Eg. Determine ø(35) Now find out list of all positive integer less than 35 that are Mr. Gopal Sakarkar relatively prime to it: 1,2,3,4,6,8,9,11,12,13,16,17,18,19,22, 23,24,26,27,29,31,32,33,34 Science there are 24 numbers so, ø(35)=24
56. 56. Euler's Theorem • Theorem : Euler’s theorem states that for every a and n ,and if they are relatively prime then, aø(n) ≡ 1 (mod n) • The theorem may be used to easily reduce large powers modulo Mr. Gopal Sakarkar n. • consider finding the last decimal digit of 7222, i.e. 7222 (mod 10). • Note that 7 and 10 are relatively prime, and φ(10) = 4. • So Euler's theorem yields 74 ≡ 1 (mod 10), • and we get 7222 ≡ 74x55 + 2 ≡ (74)55x72 ≡ 155x72 ≡ 49 ≡ 49 (mod 10) = 9 Exp of Totient RSA
57. 57. Euler's Theorem Cont….. In general, when reducing a power of a modulo n (where a and n are relatively prime), one needs to work modulo φ(n) in the exponent of a: if x ≡ y (mod φ(n)), then ax ≡ ay (mod n) Mr. Gopal Sakarkar
58. 58. Mr. Gopal Sakarkar Video
59. 59. Story behind CRT An old woman goes to market and a horse steps on her basket and crashes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had? Problems of this kind are all examples of what universally became known as the Chinese Remainder Theorem. Mr. Gopal Sakarkar
60. 60. Chinese Remainder Theorem • Find a number x such that it has remainders of 0 when divided by 2, and 3 when divided by 5. i.e. X= a mod n and X =b mod m, Where , gcd(n, m) =1 Mr. Gopal Sakarkar Video
61. 61. Chinese Remainder Theorem • used to speed up modulo computations • it working modulo to product of numbers – eg. mod M = m1m2..mk • Chinese Remainder Theorem lets us work in each moduli mi separately • since computational cost is proportional to size, this is faster than working in the full modulus M. • This can be useful when M is 150 digits or more. Mr. Gopal Sakarkar
62. 62. CRT statement Let m1, m2, …, mk be pairwise relatively prime integers. That is, gcd(mi, mj) = 1 for 1 i , j k. Let aiZmi for 1i k and set M=m1m2…mk. Then there exists a unique A Zm, such that ai A mod mi for i = 1…k. then A can be computed as: k A a c M   ( )mod 1 i i Mr. Gopal Sakarkar i  Where 1 ( mod )& / i i i i i i c M M m M M m     for 1ik.
63. 63. 1 2 1 1 ... ... i i i k M m m m m m        k A a c m   ( )mod  c a c a c a r m a m        Mr. Gopal Sakarkar Proof: A is a solution – Since for any ji 1 – Therefore, 1mod ( mod ) 0mod i i i i i j m c M M m m       1 i i i 1 1 2 2 ... mod k k i i
64. 64. Properties: Mr. Gopal Sakarkar (A+B) mod M  ((a1 + b1) mod m1, …, (ak + bk)mod mk) (A-B) mod M  ((a1 - b1) mod m1, …, (ak - bk)mod mk) (AB) mod M  ((a1  b1) mod m1, …, (ak  bk)mod mk) If X1= Y1mod n and X2=Y2 mod n then X1+X2 = Y1+Y2 mod n and X1- X2 = Y1-Y2 mod n
65. 65. Tutorial-1 “Study of Chinese Reminder Theorem ” Submission: submission of tutorial 1 is on and before 21/8/2013. Mr. Gopal Sakarkar
66. 66. Today’s Agenda • Message Digests • Hash Functions • Message Authentication • Secure Hash Function Mr. Gopal Sakarkar
67. 67. Message digests • A technique used to establish whether text sent over a network has been tampered or not. • It consists of a mathematical rule which, when applied to a piece of text, generates a relatively short number, usually between 128 and 512 bits. • This number is then sent with the text to a recipient who reapplies the mathematical rule to the text and compares the result with the original number. • If they are the same then there is a very high probability that the message has not been tampered with during the sending process; if it does differ it is virtually certain that the message has been tampered with. • It is not useful for active attack. Mr. Gopal Sakarkar
68. 68. Mr. Gopal Sakarkar MD4 – A one-way hash function that produces a 128-bit hash, or message digest. – If as little as a single bit value in the file is modified, the MD4 checksum for the file will change. – Forgery of a file in a way that will cause MD4 to generate the same result as that for the original file is considered extremely difficult. MD5 – An improved, and more complex, version of MD4 – circa 1992 – 128-bit hash – "almost broken" by Hans Dobbertin circa 1995 – Fully broken by collision attack Wang et. al. 2004 Data Encryption Standard (DES) – Symmetric, feistel cipher – Key size (in bits): 112 or 168 – Time to crack (assume a machine could try 255 keys per second - NIST): 4.6 billion years Advanced Encryption Standard (AES) – Symmetric, block cipher – Key size (in bits): 128, 192, 256 – Time to crack (assume a machine could try 255 keys per second - NIST): 149 trillion years Secure Hash Algorithm (SHA) – produces a 160-bit hash, longer than MD5. – The algorithm is slightly slower than MD5, but the larger message digest makes it more secure against brute-force collision and inversion attacks.
69. 69. For Further Reading • http://www.faqs.org/rfcs/rfc1321.html • http://www.java2s.com/Code/Java/Spring/MessageDigestExample.h Mr. Gopal Sakarkar tm • http://docs.sun.com/app/docs/doc/816-4863/6mb20lvls?a=view
70. 70. Checksums • A checksum or hash sum is a fixed-size data computed from an arbitrary block of digital data for the purpose of detecting accidental errors that may have been introduced during its transmission or storage. • The integrity of the data can be checked at any later time by recomputing the checksum and comparing it with the stored one. • If the checksums do not match, the data was almost certainly altered (either intentionally or unintentionally). Mr. Gopal Sakarkar
71. 71. Checksum Applications • First, checksum value can be used to check data integrity when data is sent through telecommunication networks such as Internet . • Second, checksum value can be used to check data integrity of stored data to see if the data has been modified or changed in any way over time. • Third, checksum values can be used to verify data burned to CDROM, CD-R (Compact Disc-Recordable), OR DVD, DVD-R. Mr. Gopal Sakarkar
73. 73. Message Authentication • Message authentication is a mechanism or service used to verify the integrity of a message . • Most common techniques for message authentication are 1.Message Authentication Code (MAC) 2. Secure Hash Function. Mr. Gopal Sakarkar
74. 74. Message Authentication Code • It is used to generate a fix –size block of data. • Let A and B share a common secret key K. • When A has to send to B , it calculate the MAC as a function of the message and the key : MAC= C(K,M). • The message M pulse MAC are transmitted to the intended Mr. Gopal Sakarkar recipient. • The received MAC is compared to the calculated MAC. • Eg: Find out how many times r is occurred in the given message. • Now , here counting a occurrence of alphabet is a function i.e C( ) and r is acting as secret key K.
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76. 76. Hash functions • Reduce arbitrary message to fixed size Mr. Gopal Sakarkar – h = H(M) • Usually assume that the hash function is public and not keyed • Hash used to detect changes to message • Can use in various ways with message • Most often to create a digital signature
77. 77. Hash Functions • Take an input from a large domain and return an output Mr. Gopal Sakarkar in a smaller range. • Easy to compute. • Eg: Collect the alphabets , which is available at odd position in word of the message M. i.e. h = H(M)
78. 78. Basic Uses of Hash Functions Mr. Gopal Sakarkar
79. 79. • Use a “Keyed Hash” 1010100101010 1010101010101 1010101000101 0101001010001 1010010101010 Shared Secret HA 100010 010101 100011 Mr. Gopal Sakarkar
80. 80. Requirements for Hash Functions • Can be applied to any sized message M • Produces fixed-length output h • Is easy to compute h=H(M) for any message M • Given h is infeasible to find x s.t. H(x)=h Mr. Gopal Sakarkar – one-way property • Given x is infeasible to find y s.t. H(y)=H(x) – weak collision resistance • Is infeasible to find any x,y s.t. H(y)=H(x) – strong collision resistance
81. 81. • For example, a simple hashing algorithm would be to add up all digits in a number, and take the remainder when divided by 7. Let the hashing function be f(x) • f(13) = (1+3) % 7 = 4 • f(26) = (2+6) % 7 = 1 • f(78) = (7+8) % 7 = 1 Mr. Gopal Sakarkar
82. 82. Digital Signature Mr. Gopal Sakarkar
83. 83. For Further Reading • http://www.faqs.org/rfcs/rfc3174.html • http://cboard.cprogramming.com/cplusplus-programming/110600-working-bits-sha- Mr. Gopal Sakarkar 1-a.html • http://www.codeproject.com/KB/recipes/csha1.aspx • Bit-Commitment with Secure Hashes – http://citeseer.nj.nec.com/halevi96practical.html • SHA-1 Specification – http://www.itl.nist.gov/fipspubs/fip180-1.htm • MD5 Specification (rfc1321) – http://andrew2.andrew.cmu.edu/rfc/rfc1321.html • Keyed Hashes: HMAC – http://www-cse.ucsd.edu/users/mihir/papers/hmac.html
84. 84. Secure Hash Algorithm Mr. Gopal Sakarkar 1993 – The hash function SHA-0 was issued as a federal standard by NIST 1995 – SHA-1 published as the successor to SHA-0 2002 – SHA-2 variants SHA-256, SHA-384, and SHA-512 published 2004 – SHA-224 published * No known weaknesses have been found with the SHA-2 variants (at this time)
85. 85. Secure Hash Algorithm cont… SHA-1, SHA-256, SHA-384, and SHA-512 All four of the algorithms are iterative, one-way hash functions process a message to produce a condensed representation called a Mr. Gopal Sakarkar message digest These algorithms enable the determination of a message’s integrity – any change to the message will, with a very high probability, result in a different message digest – This property is useful in the generation and verification of digital signatures and message authentication codes, and in the generation of random numbers (bits).
86. 86. Flavors of SHA Mr. Gopal Sakarkar SHA-0 SHA-1* SHA-224* SHA-256* SHA-384* SHA-512* *FIPS-approved algorithm for generating a condensed representation of a message (message digest)
87. 87. The Algorithm Each algorithm can be described in two stages: Mr. Gopal Sakarkar – preprocessing Preprocessing involves padding a message, parsing the padded message into m-bit blocks, and setting initialization values to be used in the hash computation – hash computation The hash computation generates a message schedule from the padded message and uses that schedule, along with functions, constants, and word operations to iteratively generate a series of hash values – The final hash value generated by the hash computation is used to determine the message digest.
89. 89. Step 2. Appending Length -now calculate the original length of message and add it to the end of the message, Mr. Gopal Sakarkar after padding. Exp.: let original message is 1000 bits and we add padding of 472 bits to make the length of message 64 bits less than 1536 , here the length is consider as 1000 1472 bits. Original Message P a dPdaidndgi n1g-5 1 2 + Length Original Message P a dPdaidndgi n1g-5 1 2 Lengt h -the length is expressed as a 64 bit value and these 64 bits are appending to the of original message + padding
90. 90. Step 3: Divide the Input Now divide the input message into block, each of the length 512 bits. Data to be hashed Block 1 Block 2 Block 3 Block n 512 bits 512 bits 512 bits 512 bits Mr. Gopal Sakarkar
91. 91. Step 4: Initialize chaining variable - Now , five chaining variables A to E are initialized , each of 32 bits number. -in SHA we want to produce a message digest of length 160 bits , for that we have five chaining variables(5 X 32= 160 bits.) Step 5: Copy the chaining variables. -now copy the chaining variable A-E into variable a-e. -The combination of a-e treated as single register for storing the temporary intermediate as well as final result. Mr. Gopal Sakarkar A a B b C c D d E e
92. 92. Step 6: Divide a block -now divide the current block 512 bits into 16 sub blocks , each of 32 bits. Step 7: Round and Iterations -SHA consists of four rounds , each round containing 20 iteration -This make it total of 80 iterations -Mathematical representation is: abcde= (e + Process P + S^5 (a) +W [t] + K[t]) ,a , S^30 (b) ,c,d Where, abcde= The registers Process P = The logical operation S ^t = Circular –left shift of the 32 bit sub block by t bits W[t] = A 32 bit derived from the current 32 bit sub block K[t] = one of the five additive constant Mr. Gopal Sakarkar
93. 93. Secure Hashes Algorithm Mr. Gopal Sakarkar • One-Way – Given f(x), hard to find x. • Collision-Free – Hard to find x and y so that f(x)=f(y) • Hard to bias output – Hard to generate a set {xi} so that we can differentiate between f({xi}) and f(U) where U is a uniformly distributed input.
94. 94. Uses for SHA • Message Authentication Checksums – Prevent an attacker from changing messages • Faster Digital Signatures • Faster Bit-Commitment Schemes Mr. Gopal Sakarkar
95. 95. Related References • http://www.packetizer.com/security/sha1/ • http://www.itl.nist.gov/fipspubs/fip180-1.htm(IMP) Mr. Gopal Sakarkar
96. 96. Tutorial 2 “Study and implementation of various Hashing functions ”-Exercise 1. Write a comparison between MD5 and SHA-1 2. Explain the various authentication requirements for context communication across a network. 3. Differentiate between Message Encryption, Message Authentication Code, and Hash Function. 4. Explain various applications of MAC. 5. Explain in details working of SHA 512. Submission: Submit the Tutorial-2 on and before 28/8/2013. Mr. Gopal Sakarkar
97. 97. Exercise Download a DES and AES encryption software For further Reading http://www.progressive-coding.com/tutorial.php#aes_description Mr. Gopal Sakarkar
98. 98. Today’s Agenda Intrusion Detection Techniques Intrusion Intrusion Techniques Intrusion Detection Mr. Gopal Sakarkar
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101. 101. Intruders Intruders: Intruder is a person whose objetive is to gain Mr. Gopal Sakarkar access to system or to increase the range of privilege accessible on a system either via network or local Classes of intruders: • Masquerader : An individual who is not authorized to use the computer (outsider) • Misfeasor : A legitimate user who accesses unauthorized data, programs, or resources (insider) • Clandestine user : An individual who grab supervisory control of the system and uses this control to avoid auditing and access controls or to suppress audit collection (either)
102. 102. Intrusion Techniques Aim to gain access and/or increase privileges on a Mr. Gopal Sakarkar system Basic attack methodology – target acquisition and information gathering – initial access – enlarge the privilege, – covering tracks Key goal often is to acquire passwords So then exercise access rights of owner
103. 103. Intrusion Detection System Need also to detect intrusions so can – block if detected quickly – act as deterrent(prevention) – collect info to improve security Assume intruder will behave differently to a legitimate user – but will have imperfect distinction between Mr. Gopal Sakarkar
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107. 107. Approaches to Intrusion Detection Statistical anomaly detection Mr. Gopal Sakarkar – threshold – profile based Rule-based detection – anomaly – penetration identification
108. 108. Audit Records It is a fundamental tool for intrusion detection native audit records – part of all common multi-user O/S – already present for use – may not have info wanted in desired form detection-specific audit records – created specifically to collect wanted info – at cost of additional overhead on system Mr. Gopal Sakarkar
109. 109. Statistical Anomaly Detection Mr. Gopal Sakarkar Threshold detection – count occurrences of specific event over time – if exceed reasonable value assume intrusion – alone is a crude & ineffective detector Profile based – characterize past behavior of users – detect significant deviations from this – profile usually multi-parameter
110. 110. Rule-Based Intrusion Detection Observe events on system & apply rules to decide if activity Mr. Gopal Sakarkar is suspicious or not Rule-based anomaly detection – analyze historical audit records to identify usage patterns & auto-generate rules for them – then observe current behavior & match against rules to see if conforms – like statistical anomaly detection does not require prior knowledge of security flaws
111. 111. Rule-Based Intrusion Detection Rule-based penetration identification – uses expert systems technology – with rules identifying known penetration, weakness patterns, or suspicious behavior – compare audit records or states against rules – rules usually machine & O/S specific – rules are generated by experts who interview & codify knowledge of security admins – quality depends on how well this is done Mr. Gopal Sakarkar
112. 112. Distributed Intrusion Detection Traditional focus is on single systems but typically have networked systems More effective defense has these working together to detect intrusions issues – dealing with varying audit record formats – integrity & confidentiality of networked data – centralized or decentralized architecture Mr. Gopal Sakarkar
113. 113. Distributed Intrusion Detection Mr. Gopal Sakarkar
114. 114. Tutorial-3 Last date of submission : 6/09/2013 Survey of Current Network Intrusion Detection Techniques Explain various metrics useful for profile-based detection. Explain various techniques for learning others passwords. Discuss and explain the various intrusion attacks in real life world . Mr. Gopal Sakarkar
115. 115. Viruses and Malicious Programs • Computer “Viruses” and related programs have the ability to replicate themselves on an ever increasing number of computers. They originally spread by people sharing floppy disks. Now they spread primarily over the Internet (a “Worm”). Other “Malicious Programs” may be installed by hand on a single machine. they may also be built into widely distributed commercial software packages. these are very hard to detect before the payload activates (Trojan Horses, Trap Doors, and Logic Bombs). Mr. Gopal Sakarkar
116. 116. Taxanomy of Malicious Programs Mr. Gopal Sakarkar
117. 117. Definitions • Virus - code that copies itself into other programs. • A “Bacteria” replicates until it fills all disk space, or CPU cycles. • Payload - harmful things the malicious program does, after it has had Mr. Gopal Sakarkar time to spread. • Worm - a program that replicates itself across the network (usually riding on email messages or attached documents (e.g., macro viruses). • Trojan Horse - instructions in an otherwise good program that cause bad things to happen (sending your data or password to an attacker over the net). • Logic Bomb - malicious code that activates on an event (e.g., date). • Trap Door (or Back Door) - undocumented entry point written into code for debugging that can allow unwanted users. • Easter Egg - extraneous code that does something “cool.” A way for programmers to show that they control the product.
118. 118. Virus Phases • Dormant phase - the virus is idle • Propagation phase - the virus places an identical copy of itself into other programs • Triggering phase – the virus is activated to perform the function for which it was intended • Execution phase – the function is performed Mr. Gopal Sakarkar
119. 119. A Compression Virus 2. Virus first compresses 3. Copy of virus is prepended to uninfected file P2 to P2’, which is 5. The uncompressed original program is executed Mr. Gopal Sakarkar 1.Program P1 is infected compressed program.. wWithhe nv itrhuiss CprVogram invoke ,control passes to its virus. shorter than original size. 4. The compress version of infected program P1’ is uncompressed..
120. 120. Types of Viruses • Parasitic Virus - attaches itself to executable files as part of their code. Runs whenever the host program runs. • Memory-resident Virus - Lodges in main memory as part of the residual Mr. Gopal Sakarkar operating system. • Boot Sector Virus - infects the boot sector of a disk, and spreads when the operating system boots up (original DOS viruses). • Stealth Virus - explicitly designed to hide from Virus Scanning programs. • Polymorphic Virus - mutates with every new host to prevent signature detection.
121. 121. Antivirus Approaches • 1st Generation, Scanners: searched files for any of a library of known virus “signatures.” Checked executable files for length changes. • 2nd Generation, Heuristic Scanners: looks for more general signs than specific signatures (code segments common to many viruses). Checked files for checksum or hash changes. • 3rd Generation, Activity Traps: stay resident in memory and look for certain patterns of software behavior (e.g., scanning files). • 4th Generation, Full Featured: combine the best of the Mr. Gopal Sakarkar techniques above.
122. 122. Advanced Antivirus Techniques Mr. Gopal Sakarkar
123. 123. Summary • Intruder’s aim to gain access and/or increase privileges on a system • There are two type of detection techniques Mr. Gopal Sakarkar statistical anomaly detection rule-based detection • Taxanomy of Malicious Programs • Advanced Antivirus Techniques
124. 124. Tutorial-4 last date of submission: 13/9/2013 • Explain in detail classification of Viruses. Mr. Gopal Sakarkar
125. 125. • Authentication • e-mail security • PGP,S/MIME. • Firewalls Mr. Gopal Sakarkar
126. 126. Authentication Password file User Mr. Gopal Sakarkar exrygbzyf kgnosfix ggjoklbsz … … kiwifruit hash function
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128. 128. Password based authentication Mr. Gopal Sakarkar • Setup – User chooses password – Hash of password stored in password file • Authentication – User logs into system, supplies password – System computes hash, compares to file • Attacks – Online dictionary attack • Guess passwords and try to log in – Offline dictionary attack • Steal password file, try to find p with hash(p) in file
129. 129. Dictionary Attack – some numbers • Typical password dictionary – 1,000,000 entries of common passwords • people's names, common pet names, and ordinary words. – Suppose you generate and analyze 10 guesses per second – Dictionary attack in at most 1,00,000 seconds = 28 hours, or 14 hours on average • If passwords were random – Assume six-character password • Upper- and lowercase letters, digits, 32 punctuation characters • 689,869,781,056 password combinations. • Exhaustive search requires 1,093 years on average Mr. Gopal Sakarkar
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136. 136. Web Authentication Mr. Gopal Sakarkar Browser • Problems Malicious or weak-security website • Phishing • Common password problem • Pharming – DNS compromise – Malware on client machine • Spyware • Session hijacking, fabricated transactions Server password cookie
137. 137. Password Phishing Problem • User cannot reliably identify fake sites • Captured password can be used at target site Mr. Gopal Sakarkar Bank A Fake Site pwdA pwdA
138. 138. Defense: Password Hashing • Generate a unique password per site – HMACfido:123(banka.com)  Q7a+0ekEXb – HMACfido:123(siteb.com)  OzX2+ICiqc • Hashed password is not usable at any other site – Protects against password phishing – Protects against common password problem Mr. Gopal Sakarkar Bank A Site B pwdA pwdB =
139. 139. Tutorial -5 Last date of submission : 20/9/203 • Explain in details working of client-server based architecture. Mr. Gopal Sakarkar
140. 140. Today’s Agenda • Email Overview : SMTP, POP , MIME • Secure E-Mail Standard : PGP, S/MIME • Firewall Mr. Gopal Sakarkar
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142. 142. RFC 822 • Published in 1982 • Support for text format only. • Messages are viewed as having an envelope and contents. • Envelop having transmission and delivery information. • Contents has the object to be delivered. Mr. Gopal Sakarkar
143. 143. RFC 822 Mail Format • A message consists of some number of header line ( the header) followed by unrestricted text (the body). • A blank line is used for separation. • Lines no longer than 1000 char • Message body - plain US-ASCII text • Message header lines - plain US-ASCII text • Limit on message length Mr. Gopal Sakarkar
144. 144. RFC Example Date: Tue,25 feb 1985 13:45:97 From: someone@techtarget.com To: someoneelse@techtarget.com Subject: A demonstration of the RFC 822 message Mr. Gopal Sakarkar format. This is the message body , which is delimited from the message heading by a blank line. Blank line for Separation
145. 145. • http://www.rfc-editor.org/rfc/rfc822.txt Mr. Gopal Sakarkar
146. 146. MIME • MIME refers to an official Internet standard that specifies how messages must be formatted so that they can be exchanged between different email systems. • MIME permits the inclusion of virtually any type of file or document in an email message. • Specifically, MIME messages can contain – text – images – audio – video – application-specific data. • spreadsheets • word processing documets Mr. Gopal Sakarkar
147. 147. MIME Features • Support of character sets other than ASCII • Support of non-text content in e-mail messages • Support for compound documents Mr. Gopal Sakarkar
148. 148. MIME Example From: John Doe <example@example.com> To: g.sakarkar@gmail.com Subject: Hello Word MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="XXXXboundary text" This is a multipart message in MIME format. --XXXXboundary text Content-Type: text/plain this is the body text --XXXXboundary text Content-Type: text/plain; Content-Disposition: attachment; filename="test.txt" this is the attachment text --XXXXboundary text-- Mr. Gopal Sakarkar
149. 149. • The "MIME-Version:" header tells the receiving UA to treat this as a MIME message. • The"Content-Type: “header specifies Mr. Gopal Sakarkar "multipart/mixed". • The message has parts separated by the string argument defined in "boundary=" • The "Content-Type:" header identifies it as "text/plain", meaning US-ASCII characters are used exclusively and any UA should be able to display this body part. • The "Content-Disposition: attachment" header has a parameter, "filename=", which specifies a suggested name for the file.
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151. 151. • SMTP (Simple Mail Transfer Protocol) is the procedure by which email data packets are transferred from one networked machine to another. • SMTP defines the message format and the message transfer agent (MTA), which stores and forwards the mail. • SMTP is a relatively simple, text-based protocol, where one or more recipients of a message are specified and then the message text is transferred. Mr. Gopal Sakarkar
152. 152. • Transfer email between mail servers reliably and efficiently . • In order to send email, the client sends the message to an outgoing mail server, which in turn contacts the destination mail server for delivery. • For this reason, it is necessary to specify an SMTP server when configuring an email client. Mr. Gopal Sakarkar
153. 153. • SMTP uses persistent connections • SMTP uses TCP port 25. • SMTP requires message (header & body) to be in 7 - bit ASCII • SMTP server uses CRLF.CRLF to determine end of message • Unsecured against spam. Mr. Gopal Sakarkar
154. 154. • Mail client is configured with the name of a local mail gateway (SMTP server) • Mail client does not have to know how to deliver mail to everywhere Mr. Gopal Sakarkar
155. 155. Scenario: Alice sends message to Bob 1)Alice uses UA to compose message and “to” bob@someschool.edu 2)Alice’s UA sends message to her mail server; message placed in message queue 3)Client side of SMTP opens TCP connection with Bob’s mail server Mr. Gopal Sakarkar
156. 156. 4)SMTP client sends Alice’s message over the TCP connection 5)Bob’s mail server places the message in Bob’s mailbox 6)Bob invokes his user agent to read message Mr. Gopal Sakarkar
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158. 158. REPLY CODES MEANING 211 System status, or system help reply 214 Help message 220 <domain> Service ready 221 <domain> Service closing transmission channel 250 Requested mail action okay, completed 354 Start mail input; end with <CRLF>.<CRLF> 421 <Domain> Service not available, closing transmission channel Mr. Gopal Sakarkar
159. 159. REPLY CODES MEANING 450 Requested mail action not taken: mailbox unavailable 451 Requested action aborted: local error in processing 500 Syntax error, command unrecognized 501 Syntax error in parameters or arguments 503 Bad sequence of commands 550 Requested action not taken: mailbox unavailable 551 User not local; please try <forward-path> 554 Transaction failed Mr. Gopal Sakarkar
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161. 161. This SMTP example shows how mail is sent by Smith at host Alpha.ARPA, to Jones and Green at host Beta.ARPA S: MAIL FROM:Smith@Alpha.ARPA R: 250 OK S: RCPT TO:Jones@Beta.ARPA R: 250 OK S: RCPT TO:Green@Beta.ARPA R: 550 No such user here S: RCPT TO:Brown@Beta.ARPA R: 250 OK S: DATA R: 354 Start mail input; end with <CRLF>.<CRLF> S: Blah blah blah... S: ...etc. etc. etc. S: <CRLF>.<CRLF> R: 250 OK Mr. Gopal Sakarkar
162. 162. • HELLO: Sent by a client to identify itself, usually with a domain name • EHLO: Enables the server to identify its support for Extended Simple Mail Transfer Protocol (ESMTP) commands • MAIL FROM: Identifies the sender of the message; used in the form MAIL Mr. Gopal Sakarkar FROM: • RCPT TO: Identifies the message recipients; used in the form RCPT TO: • TURN: Allows the client and server to switch roles and send mail in the reverse direction without having to establish a new connection
163. 163. • ATRN: The ATRN (Authenticated TURN) command optionally takes one or more domains as a parameter. The ATRN command must be rejected if the session has not been authenticated • DATA: Sent by a client to initiate the transfer of message content • RSET: Nullifies the entire message transaction and resets the buffer • VRFY: Verifies that a mailbox is available for message delivery • HELP: Returns a list of commands that are supported by the SMTP Mr. Gopal Sakarkar service • QUIT: Terminates the session
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166. 166. • Simple Mail Transport Protocol (SMTP) is the network protocol used to send email across the Internet. • SMTP provides reliability as it uses TCP connection. • Current research focuses on the security issues of SMTP. Mr. Gopal Sakarkar
167. 167. Tutorial –6 last date of submission : 27/9/2013 • Briefly explain the POP, IMAP protocols. • What are the advantages and disadvantages of Mr. Gopal Sakarkar SMTP. • List and explain the various applications of SMTP.
168. 168. Pretty Good Privacy (PGP) The first version of PGP was programmed in 1991 by Phil R. Zimmerman, who later founded PGP Security Consulting. PGP is one of the most popular encryption and authentication algorithm world-wide. PGP is more widely used in electronic mail security than any other areas. Mr. Gopal Sakarkar Phil R. Zimmerman
169. 169. Pretty Good Privacy (PGP) "If all the personal computers in the world - 260 million - were put to work on a single PGP-encrypted message, it would still take an estimated 12 million times the age of the universe, on average, to break a single message.” - Deputy Director William Crowell Mr. Gopal Sakarkar National Security Agency 3/20/1997
170. 170. Mr. Gopal Sakarkar Notation Ks = session key used in symmetric encryption scheme PRa = Private key of user A. PUa = public key of user A. EP = public key encryption DP = public key decryption EC =symmetric encryption DC = symmetric decryption
171. 171. Notation cont… Mr. Gopal Sakarkar H = hash function || = concatenation Z = compression using ZIP algorithm R64 = conversion to radix 64 ASCII format
172. 172. PGP Working PGP offers 5 services: • Authentication • Confidentiality • Compression • E-mail compatibility • Segmentation Mr. Gopal Sakarkar
173. 173. PGP Authentication This is a digital signature scheme with hashing. 1. Alice has (private/public) key pair (Ad/Ae) and she wants to send a digitally signed message m to Bob. 2. Alice hashes the message using SHA-1 to obtain SHA(m). 2. Now the original message m is compressed to obtain Mr. Gopal Sakarkar M=ZIP(m) 3. Alice generates a session key k and encrypts the compressed message and the signature using the session key C=sk.encryptk(M,c) 4. The session key is encrypted using Bob’s public key as before.
174. 174. 3. Alice encrypts the hash using her private key Ad to obtain ciphertext c given Mr. Gopal Sakarkar by c=pk.encryptAd(SHA(m)) 4. Alice sends Bob the pair (m,c) 5. Bob receives (m,c) and decrypts c using Alice's public key Ae to obtain signature s s=pk.decryptAe(c)
175. 175. 6. He computes the hash of m using SHA-1 and if this hash value is equal to s then the message is authenticated. Bob is sure that the message is correct and that is does come from Alice. Furthermore Alice cannot later deny sending the message since only Alice has access to her private key Ad which works in conjunction with the public key Ae. Mr. Gopal Sakarkar
176. 176. Message authentication • based on digital signatures • supported algorithms: RSA/SHA and DSS/SHA m h s hash enc m h h s hash compare dec accept / reject Mr. Gopal Sakarkar Ksnd -1 Ksnd receiver sender
177. 177. PGP Confidentiality 1. Alice wishes to send Bob a confidential message m. 2. Alice generates a random session key k for a symmetric Mr. Gopal Sakarkar cryptosystem. 3. Alice encrypts k using Bob’s public key Be to get k’ = pk.encryptBe(k) 4. Alice encrypts the message m with the session key k to get ciphertext c c=sk.encryptk(m) 5. Alice sends Bob the values (k’,c) 6. Bob receives the values (k’,c) and decrypts k’ using his private key Bd to obtain k k=pk.decryptBd(k’)
178. 178. 7. Bob uses the session key k to decrypt the ciphertext c and recover the Mr. Gopal Sakarkar message m m=sk.decryptk(c) Public and symmetric key cryptosystems are combined in this way to provide security for key exchange and then efficiency for encryption. The session key k is used only to encrypt message m and is not stored for any length of time.
179. 179. PGP Authentication and Confidentiality (at the same time) The schemes for authentication and confidentiality can be combined so that Alice can sign a confidential message which is encrypted before transmission. The steps required are as follows: 1. Alice generates a signature c for her message m as in the Mr. Gopal Sakarkar Authentication scheme c=pk.encryptAd(SHA(m)) 2. Alice generates a random session key k and encrypts the message m and the signature c using a symmetric cryptosystem to obtain ciphertext C C=sk.encryptk(m,c) 4. She encrypts the session key k using Bob’s public key k’ = pk.encryptBe(k) 5. Alice sends Bob the values (k’,C)
180. 180. 6. Bob recieves k’ and C and decrypts k’ using his private key Bd to obtain the session key k k=pk.decryptBd(k’) 7. Bob decrypts the ciphertext C using the session key k to obtain m Mr. Gopal Sakarkar and c (m,c) = sk.decryptk(C) 8. Bob now has the message m. In order to authenticate it he uses Alice’s public key Ae to decrypt the signature c and hashes the message m using SHA-1. If SHA(m) = pk.decryptAe(c) Then the message is authenticated.
181. 181. Mr. Gopal Sakarkar Working flow of PGP
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183. 183. Tutorial-7 Last date of submission: 1/10/2013 Explain the detail working of PGP encryption and authentication algorithm and its real life applications. Mr. Gopal Sakarkar
184. 184. S/MIME is the de-facto industry standard for secure mail over the Internet. Secure MIME (S/MIME) was developed by an industry consortium, and is now appearing in a number of major products. MIME is an extencion to the RFC 822 addressing many limitations Mr. Gopal Sakarkar of the use of SMPT. MIME specification includes – new message headers – a number of content formats supproting multimedia electronic mail – transfer encodings S/MIME
185. 185. S/MIME Functionality (messages) The general functionality of S/MIME is very similar to PGP buth offering the ability to sign and/or encrypt messages. Mr. Gopal Sakarkar S/MIME Functions The S/MIME functions are implemented as new MIME content types. Enveloped data – This consists of encrypted content of any type and encrypted content encryption keys for one or more receipients. – An enveloped data entity is prepared as follows: 1) Generate the pseudo random session key. 2) Encrypt the session key with each recipients public RSA key. 3) For each recipient prepare a RecipientInfo block containing senders public key certifcate, an identifier of the encryption algorithm and the encrypted session key. 4) Encrypt the message content with the session key.
186. 186. S/MIME Functionality Mr. Gopal Sakarkar Signed data A digital signature is formed by taking the message digest of the content to be signed and encrypting that with the private key of the signer. 1) Compute the message digest with SHA or MD5. 2) Encrypt the message digest with senders private key 3) prepare SignerInfo block containing singer’s public key certificate, an identifier of the message digest algorithm, and identifier of the encryption algorithm and the encrypted message digest. A signed data message can only be read by a recipient having S/MIME capabilities Clear signed data Same as previous but now the message contents are readable without S/MIME, which is needed if the recipient wishes to verify the identity if the sender. Signed and enveloped data Signed-only and encrypted-only messages can be nested in both orderings.
187. 187. S/MIME Functionality Mr. Gopal Sakarkar Registration request An application or a user typically applies to a CA for a public-key certificate. This content format is used to transfer such request. Certificates-only message This is a message containing only certificates or a certificate revocation list. It is sent as a response to registration request
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