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Aaron P. VillanuevaBSECE 4-1

ERROR DETECTIONError detection is most

commonly realized using a suitablehash unction !or chec"sumalgorithm#. A hash unction adds a$%ed-length tag to a message&'hich enables receivers to veriythe delivered message byrecom(uting the tag andcom(aring it 'ith the one (rovided.

)here e%ists a vast variety odi*erent hash unction designs.+o'ever& some are o (articularly

'ides(read use because o eithertheir sim(licity or their suitabilityor detecting certain "inds o errors!e.g.& the cyclic redundancy chec",s(erormance in detecting bursterrors#.

ERROR DETECTION METHODSRepetition Codes

A re(etition code is a codingscheme that re(eats the bits across

a channel to achieve error-reecommunication. iven a stream odata to be transmitted& the dataare divided into bloc"s o bits. Eachbloc" is transmitted some(redetermined number o times.or e%am(le& to send the bit(attern /1011/& the our-bit bloc"can be re(eated three times& thus(roducing /1011 1011 1011/.+o'ever& i this t'elve-bit (attern

'as received as /1010 1011 1011/ 'here the $rst bloc" is unli"e theother t'o it can be determinedthat an error has occurred.

Parity BitsA (arity bit is a bit that is

added to a grou( o source bits to

ensure that the number o set bits!i.e.& bits 'ith value 1# in theoutcome is even or odd. 2t is a verysim(le scheme that can be used todetect single or any other odd

number !i.e.& three& $ve& etc.# oerrors in the out(ut. An evennumber o 3i((ed bits 'ill ma"ethe (arity bit a((ear correct eventhough the data is erroneous.

E%tensions and variations onthe (arity bit mechanism arehorizontal redundancy chec"s&vertical redundancy chec"s& and/double&/ /dual&/ or /diagonal/(arity !used in A25-5P#.

ChecksumsA chec"sum o a message is

a modular arithmetic sum omessage code 'ords o a $%ed'ord length !e.g.& byte values#. )hesum may be negated by means oa ones,-com(lement o(eration(rior to transmission to detecterrors resulting in all-zeromessages.

Chec"sum schemes include(arity bits& chec" digits& andlongitudinal redundancy chec"s.Some chec"sum schemes& such asthe 5amm algorithm& the 6uhnalgorithm& and the Verhoe*algorithm& are s(eci$cally designedto detect errors commonlyintroduced by humans in 'ritingdo'n or remembering identi$cationnumbers.

Cyclic Redundancy ChecksCRCs!

A cyclic redundancy chec"!CC# is a non-secure hash unctiondesigned to detect accidentalchanges to digital data in com(uternet'or"s7 as a result& it is not

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suitable or detecting maliciouslyintroduced errors. 2t ischaracterized by s(eci$cation o'hat is called a generator(olynomial& 'hich is used as the

divisor in a (olynomial long divisionover a $nite $eld& ta"ing the in(utdata as the dividend& such that theremainder becomes the result.

A cyclic code has avorable(ro(erties that ma"e it 'ell suitedor detecting burst errors. CCs are(articularly easy to im(lement inhard'are& and are thereorecommonly used in digital net'or"sand storage devices such as hard

dis" drives.Even (arity is a s(ecial case

o a cyclic redundancy chec"&'here the single-bit CC isgenerated by the divisor % 8 1.

Crypto"raphic Hash #unctions)he out(ut o a cry(togra(hic

hash unction& also "no'n as amessage digest& can (rovide strongassurances about data integrity&

'hether changes o the data areaccidental !e.g.& due totransmission errors# or maliciouslyintroduced. Any modi$cation to thedata 'ill li"ely be detected througha mismatching hash value.

urthermore& given some hashvalue& it is ineasible to $nd somein(ut data !other than the onegiven# that 'ill yield the same hashvalue. 2 an attac"er can change

not only the message but also thehash value& then a "eyed hash ormessage authentication code!9AC# can be used or additionalsecurity. :ithout "no'ing the "ey&it is ineasible or the attac"er tocalculate the correct "eyed hashvalue or a modi$ed message.

Error$correctin" CodesAny error-correcting code can

be used or error detection. A code'ith minimum +amming distance&d& can detect u( to d ; 1 errors in acode 'ord.