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 function is true only of the majority (two or three) of thearguments are truecircular right shift (rotation) of the 64-bit argumentbybitsa 64-bit word derived from the current 512-bit input blocka 64-bit additive constantaddition moduloTwo observations can be made about the round function.1.Six of the eight words of the output of the round function involve simply per-mutation (,,,,,) by means of rotation. This is indicated by shading inFigure 11.10.2.Only two of the output words (,) are generated by substitution. Wordis afunction of input variables (,, ,,), as well as the round wordand theconstant. Wordis a function of all of the input variables exceptd, as wellas the round wordand the constant.KtWtaKtWthgfedeeahgfdcb264=+=Kt=WtnxROTRn(x)=Aa5121eB=ROTR14(e)ROTR18(e)ROTR41(e)Aa5120aB=ROTR28(a)ROTR34(a)ROTR39(a)Maj(a,b,c)=(aANDb)(aANDc)(bANDc)
348CHAPTER 11 / CRYPTOGRAPHIC HASH FUNCTIONSabcdefghabcd512 bitsefghChKtWtMaj+++++++Figure 11.10Elementary SHA-512 Operation (single round)It remains to indicate how the 64-bit word valuesare derived from the1024-bit message. Figure 11.11 illustrates the mapping. The first 16 values ofaretaken directly from the 16 words of the current block. The remaining values aredefined aswherecircular right shift (rotation) of the 64-bit argumentbybitsleft shift of the 64-bit argumentbybits with padding byzeros on the rightaddition modulo 264+ =nxSHRn(x)=nxROTRn(x)=s1512(x)=ROTR19(x)ROTR61(x)SHR6(x)s0512(x)=ROTR1(x)ROTR8(x)SHR7(x)Wt=s1512(Wt-2)+Wt-7+s0512(Wt-15)+Wt-16WtWt1024 bits64 bitsWt–16W0W1W9W14W63W65W71W76Wt–15Wt–7Wt–2W0W1W15W16WtMiW79+σ0σ1σ0σ1σ0σ1++Figure 11.11Creation of 80-word Input Sequence for SHA-512 Processing of Single Block
11.5 / SECURE HASH ALGORITHM (SHA)349Thus, in the first 16 steps of processing, the value ofis equal to the corre-sponding word in the message block. For the remaining 64 steps, the value ofconsists of the circular left shift by one bit of the XOR of four of the precedingvalues of, with two of those values subjected to shift and rotate operations. Thisintroduces a great deal of redundancy and interdependence into the message blocks

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Term
Spring
Professor
Sandeep Joshi
Tags
Cryptography, 1984, Public key cryptography, Elliptic Curve, The Golden Bough, Elliptic curve cryptography, elliptic curves

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