leksion 7 hashes and messsage digests

8/12/2019 Leksion 7 Hashes and messsage digests

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Hashes and MessageDigests

MsC, Ing. Ezmerina [email protected]



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Overview

HashesAuthentication

MD2MD5SHA



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How Many Bits forHash?

m bits, takes 2m/2 to find two with the same hash

64 bits, takes 232

messages to search (doable) Need at least 128 bits



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Using Hash forAuthentication

Alice to Bob: challenge r A Bob to Alice: MD( K AB|r A) Bob to Alice: r B Alice to Bob: MD( K AB|r B) Only need to compare MD results



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Using Hash to Compute MIC

Cannot just compute MD( m) – Why?MIC: MD( K AB|m )o Allows concatenation with additional message:

MD( K AB|m |m’)• MD through chunk n depends on MD through

chunks n-1 and the data in chunk n

Put secret at the end of message:o MD( m| K AB)o HMAC - MD( K AB|MD( K AB|m ))



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Using Hash to EncryptOne-time pad:o compute bit streams using MD, K , and IV

• b1=MD( K AB|IV), b i=MD( K AB|b i-1), …

o with message blockso Sender can generate the one-time pad in advance but receiver cannot. Why?

Or mixing in the plaintext to provide integrityo similar to cipher feedback mode (CFB)

• b1=MD( K AB|IV), c1= p1 b1

• b2=MD( K AB| c1), c2= p2 b2

o lose pre-computation capability, gain (some)integrity protection



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MD2128-bit message digest:o Arbitrary number of bytes of messageo First pad to multiple of 16 bytes

o Append MD2 checksum (16 bytes) to the end• The checksum is almost a MD, but notcryptographically secure by itself.

o Process whole message



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MD2 PaddingThere must always be paddingIf the message is multiple of 16 bytes, 16 bytes of padding are added

Otherwise the number of bytes (1-15) are addedEach pad byte specifies the number of bytes of padding that was added



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MD2 ChecksumOne byte at a time, k × 16 stepsmnk : byte nk of messagecn=π (mnk cn-1 ) cn

o C n = (n mod 16)th

byteπ : 0 → 41, 1 → 46, …o Substitution on 0-255

(value of the byte)



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MD5: Message DigestVersion 5



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MD5 Box



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MD5



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MD5 ProcessAs many stages as the number of 512-bit blocks inthe final padded messageDigest: 4 32-bit words: MD=A|B|C|D

Every message block contains 16 32-bit words:m0|m1|m2…|m 15o Digest MD 0 initialized to:

A=01234567,B=89abcdef,C=fedcba98,

D=76543210o Every stage consists of 4 passes over the message

block, each modifying MD



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MD5 Blocks



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MD5Every bit of the hash code is function of every bit inthe inputThe complex repetition of the basic functions F, G, H,

I produces results that are well mixed – It is veryunlikely that two messages chosen at random willhave the same hashMD5 is as strong as a 128-bit hash can be – birthday

attack 2 64



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Secure Hash Algorithm

Developed by NIST, specified in the Secure HashStandard (SHS, FIPS Pub 180), 1993SHA is specified as the hash algorithm in the DigitalSignature Standard (DSS), NIST



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General LogicInput message must be < 2 64 bitso not really a problem

Message is processed in 512-bit blocks sequentially

Message digest is 160 bitsSHA design is similar to MD5, but a lot stronger



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SHA-1



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Basic Steps...Step 4: the 80-step processing of 512-bit blocks – 4rounds, 20 steps each.

Each step t (0 <= t <= 79):o Input:• W t – a 32-bit word from the message• K t – a constant.

• ABCDE: current MD.o Output:

• ABCDE: new MD.



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Basic Logic Functions



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SHA Versus MD5SHA is a stronger algorithm:

Brute-force birthday attacks requires on the orderof 2 80 operations vs. 2 64 for MD5

SHA’s 80 steps and 160 bits hash (vs. 128) requires alittle more computation



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Revised SHA



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History of Hash Algorithms

AlgorithmsMD – proprietary, never published, not widely usedMD2 – first public algorithm, oriented towards 8-bit processing,little memory, good for embedded devices

MD3 – immediately superceded by MD4 (never published)MD4 – runs faster than MD2, uses 32-bit operations, becamesuspectMD5 – slightly slower, more conservative

SHA 1 NIST standard similar to MD5 even more conservativeEventually MD2 and MD4 are “broken” – two messages with thesame hash are foundMDs produce 128-bit digests, SHA-1 – 160-bit digest



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Summary

HashesAuthentication

MD2MD5SHA

leksion 7 hashes and messsage digests

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