1、Cryptography and Network Security(Various Hash Algorithms)Fourth Editionby William StallingsLecture slides by Lawrie Brown(Changed by Somesh Jha)1Birthday Attacks might think a 64-bit hash is secure but by Birthday Paradox is not birthday attack works thus:opponent generates 2m/2 variations of a val
2、id message all with essentially the same meaning opponent also generates 2m/2 variations of a desired fraudulent message two sets of messages are compared to find pair with same hash(probability 0.5 by birthday paradox)have user sign the valid message,then substitute the forgery which will have a va
3、lid signature conclusion is that need to use larger MACs2Hash Function Properties a Hash Function produces a fingerprint of some file/message/datah=H(M)condenses a variable-length message M to a fixed-sized fingerprint assumed to be public3Requirements for Hash Functions1.can be applied to any sized
4、 message M2.produces fixed-length output h3.is easy to compute h=H(M)for any message M4.given h is infeasible to find x s.t.H(x)=hone-way property5.given x is infeasible to find y s.t.H(y)=H(x)weak collision resistance6.is infeasible to find any x,y s.t.H(y)=H(x)strong collision resistance4Block Cip
5、hers as Hash Functions can use block ciphers as hash functions using H0=0 and zero-pad of final block compute:Hi=EMi Hi-1 and use final block as the hash value similar to CBC but without a key resulting hash is too small(64-bit)both due to direct birthday attack and to“meet-in-the-middle”attack othe
6、r variants also susceptible to attack5Hash Algorithms similarities in the evolution of hash functions&block ciphers increasing power of brute-force attacks leading to evolution in algorithms from DES to AES in block ciphers from MD4&MD5 to SHA-1&RIPEMD-160 in hash algorithms likewise tend to use com
7、mon iterative structure as do block ciphers6MD5 designed by Ronald Rivest(the“R”in RSA)latest in a series of MD2,MD4 produces a 128-bit hash value until recently was the most widely used hash algorithm in recent times have both brute-force&cryptanalytic concerns specified as Internet standard RFC132
8、17MD5 Overview1.pad message so its length is 448 mod 512 2.append a 64-bit length value to message 3.initialise 4-word(128-bit)MD buffer(A,B,C,D)4.process message in 16-word(512-bit)blocks:using 4 rounds of 16 bit operations on message block&buffer add output to buffer input to form new buffer value
9、 5.output hash value is the final buffer value 8MD5 Overview9MD5 Compression Function each round has 16 steps of the form:a=b+(a+g(b,c,d)+Xk+Ti)s)a,b,c,d refer to the 4 words of the buffer,but used in varying permutations note this updates 1 word only of the buffer after 16 steps each word is update
10、d 4 times where g(b,c,d)is a different nonlinear function in each round(F,G,H,I)Ti is a constant value derived from sin10MD5 Compression Function11MD4 precursor to MD5 also produces a 128-bit hash of message has 3 rounds of 16 steps versus 4 in MD5 design goals:collision resistant(hard to find colli
11、sions)direct security(no dependence on hard problems)fast,simple,compact favors little-endian systems(eg PCs)12Strength of MD5 MD5 hash is dependent on all message bits Rivest claims security is good as can be known attacks are:Berson 92 attacked any 1 round using differential cryptanalysis(but cant
12、 extend)Boer&Bosselaers 93 found a pseudo collision(again unable to extend)Dobbertin 96 created collisions on MD compression function(but initial constants prevent exploit)conclusion is that MD5 looks vulnerable soon13Secure HashAlgorithm(SHA-1)SHA was designed by NIST&NSA in 1993,revised 1995 as SH
13、A-1 US standard for use with DSA signature scheme standard is FIPS 180-1 1995,also Internet RFC3174 note:the algorithm is SHA,the standard is SHS produces 160-bit hash values now the generally preferred hash algorithm based on design of MD4 with key differences 14SHA Overview1.pad message so its len
14、gth is 448 mod 512 2.append a 64-bit length value to message3.initialise 5-word(160-bit)buffer(A,B,C,D,E)to(67452301,efcdab89,98badcfe,10325476,c3d2e1f0)4.process message in 16-word(512-bit)chunks:expand 16 words into 80 words by mixing&shifting use 4 rounds of 20 bit operations on message block&buf
15、fer add output to input to form new buffer value 5.output hash value is the final buffer value 15SHA-1 Compression Function each round has 20 steps which replaces the 5 buffer words thus:(A,B,C,D,E)-(E+f(t,B,C,D)+(A5)+Wt+Kt),A,(B30),C,D)a,b,c,d,e refer to the 5 words of the buffer t is the step numb
16、er f(t,B,C,D)is nonlinear function for round Wt is derived from the message block Kt is a constant value derived from sin16SHA-1 Compression Function17SHA-1 verses MD5 brute force attack is harder(160 vs 128 bits for MD5)not vulnerable to any known attacks(compared to MD4/5)a little slower than MD5(
17、80 vs 64 steps)both designed as simple and compact optimised for big endian CPUs(vs MD5 which is optimised for little endian CPUs)18Revised Secure Hash Standard NIST has issued a revision FIPS 180-2 adds 3 additional hash algorithms SHA-256,SHA-384,SHA-512 designed for compatibility with increased s
18、ecurity provided by the AES cipher structure&detail is similar to SHA-1 hence analysis should be similar19Keyed Hash Functions as MACs have desire to create a MAC using a hash function rather than a block cipher because hash functions are generally faster not limited by export controls unlike block
19、ciphers hash includes a key along with the message original proposal:KeyedHash=Hash(Key|Message)some weaknesses were found with this eventually led to development of HMAC 20HMAC specified as Internet standard RFC2104 uses hash function on the message:HMACK=Hash(K+XOR opad)|Hash(K+XOR ipad)|M)where K
20、+is the key padded out to size and opad,ipad are specified padding constants overhead is just 3 more hash calculations than the message needs alone any of MD5,SHA-1,RIPEMD-160 can be used 21HMAC Overview22HMAC Security know that the security of HMAC relates to that of the underlying hash algorithm a
21、ttacking HMAC requires either:brute force attack on key used birthday attack(but since keyed would need to observe a very large number of messages)choose hash function used based on speed verses security constraints23Summary have considered:some current hash algorithms:MD5,SHA-1,RIPEMD-160 HMAC authentication using a hash function2425
