Cryptography-Digest Digest #940, Volume #12      Mon, 16 Oct 00 22:13:00 EDT

Contents:
  Re: pseudo random test (=?ISO-8859-1?Q?Jacques_Th=E9riault?=)
  Re: pseudo random test (=?ISO-8859-1?Q?Jacques_Th=E9riault?=)
  DNA encoding ("binary digit")
  Re: CRC vs. HASH functions (Mack)
  Re: Public Key Algorithms and Analysis (John Savard)
  Re: Basic skills and equipment... ("Joseph Ashwood")
  Re: Optimisation of SHA-256 (Stephan Eisvogel)

----------------------------------------------------------------------------

Subject: Re: pseudo random test
From: [EMAIL PROTECTED] (=?ISO-8859-1?Q?Jacques_Th=E9riault?=)
Date: Tue, 17 Oct 2000 01:37:40 GMT

maybe this is still not enough, but a little bit more substantial than
the previous

followin are 20,000 character from a set of 94 ( ie: printable )

ymuPC\RdWHa^w?aVCE1Ca]w&vq*V>]0s5-"gpcC~-,?N2^-(SeC(Z~w(?Wd`1*YtG{TCw'*I
x5xy%3/%bpZ*QVno8'`{:mGxw.04:r(jyt3bS1EkF:m?+mfTB#R5AP{&I/7VClLG&V1Wq2t+
4mJ50Q3(gt47%Qnk&}6>M73o&n'RSWkI%AnFyZCr;4UnLNJEV;tZ'4w<Jp"!0:,=e`fm[7ar
Q02oRq2hj8<KNQ_>'\%,,<+6XLEJw~$nI(gAQ{f<^xPI#snX;(M=(=pxJn6+y(sT77UOS70*
I})>u:I(0a[\F27m[:ql_3DV{sR<eq|u0cM.G%w[RK5pt&]:;KnZiJ6UW~$a~A^HQlSNYvgO
=Fsd*HBB:jiQ%^/xF!mx/fkh]y^a$$%<0ZTcy*?Eu;%KdR$?T*q[6hc?B`Q@i>c"[^.@fR(9
r_I+6b9Bopn\hu)%uz-N|}H(k#.otpLZVSAD_IM#@)c!Lf@O&>*yc)-NYa.[N)i{*x5P3?\W
rs9+l*TwGPWiT\hn'y#YR3p4Ra%cup_w4$ALyQ1hD:|W/j-Sdac<y}k8)M\%=MI]j*z}uqyq
aB)NO>Sxd*=P^?GsHV<+,<$@+3:v`A0CsWSf]|k;v#e}[Asi&L;wJLKd1;:'oSa7,v+;GHdG
es([$c:6scTJmu4$u10n;tD.xb}&.m#VJ4$JEa;A<*'o$s;t+q"f/i9)p\e^-?Z~bb3QhzB$
50#\J_Q`x%@P8pFt#5_{W!>n"*5\upv-~&XTl:29:Sxx?#ZpEYbtwB-0"r#gwsFmp}>Kq_O7
Q[M'uf!ky&,>a!-g{D_)vix2V;Mz:OY\^Kdb?j?ICLU.lMc5x2tSTg22P^pRblRBay:{<AU1
^m.HF$qj!HY0GrQqj=lfC]FhK:X_lYqOY,a1gMsm;{)j.]^`M<4Bb}H8fl,>,{R#uS"Vteu0
cVuzO\LYgON5XGbQB=,V!_{#Xsh8uO%5`cu?7?%e%u+~%L*!r.V~a>.qt2=M0%Z2>;s/Ub$y
!N2^"Na>]6I8;3)c/jJb,oCqaM4AY`+,v`GHoSo\~IM3}I:gD>^mG7.(>}{_"|C_"|nrLaRF
:d7|LR"6_r&i|uI9v!uB235P[d;p&vQ:XBKB[UF%i:(I&`9.iv05\,"$:,xNMn03^eJs7Jz/
3=8<M[p3F>M~RDnXP:UIiK&RLd<`#tO_]UF`t&/X{Og[F42tEayWc2u0aX9GRC]\0!RS$fL/
sFoJF>h5W:WN?9n*i#B`'p-B68*{++F>~TgGmwz=sbnm1*S6EI]:Qd{Pyd7{/R1OH(,KE8#n
Z$gH!;&D-4`dh4)E|Ld./s(QU#@Xs&"H!A'-ep3rG]0c7v4@|F2)e"NrdKdZ3p:~Z%mM,nim
YWb}p$7icOu3=Wj%J*"{'"Ed%\9zs8Jr'lA+8"?Q7<:=oUJo}Sun^g.S.2sH07eM;yb%edw.
:8!P\gAx"qX<ruo+Y:Tj>o>ftJu:{EUF5]_Wlq>^C)*(v[/(d*Odl*Stp[7?Tv=R,>x|uV9f
Oqd_7a;b6E,*ty>jiK)-+`"8naCUc2ubS5^Ofx^Gib11&evl|='9}ADamUuJH}-<fS&fk91d
SC+^M}*tFE6T/v<C1s2E}?5fV:kFb7ED|fsJWEKC;-?kh1Y25j9N_,r^PSoA5N,E)5>-CK"z
1a5$<2F;!S_ssQHuH&\?d';1gl[@D1UfLE=qp~nohv%J86oah9oUdfe!r!Gg_UG?_@d~AW2>
IDkRU>5i~^(8sgn*|>9zP}PFgQ:A\}Jm1P.qavi&%C_iy]pO~.H@[EMAIL PROTECTED]>72Bw#&
]xxj^@)plG7q54r_"wx,KEV1HTk]>^pqdZMDZz}@P_j=-ts2c=*=tzsI=Y5b<^#>>mB#&^G@
D%F4&ls`D*[POUJm_&1ek?DGYyl:0B&iR#z|N:Jy.W]=OM[hA#\H2[!afgS$!`Lm/+X_{N1y
5`tXy7Bf^-Fq!t`~u`/0bxn8EB'L}PW+X+v=g{`",DD\5j*hYG@o@V?HZ6f(cu[)fT}QU5eN
1RO*lBA}@5_^cl}NBCDVeFjt]CGdcC4g_nzmL+:2#gkU&ye7G]3hwU^wtAyhbD4Ri=t2fzea
<cz%.y=!`4s'>&{q<#X5vJ"Ud>G'uZdG#6aBoL-.JRRWx/yJV6]BPDTV(7Ft%yE9BHUPZUb=
8]/Uj:&N3oShRPDtNg?"P!"\}/&O)uo#~/VT>iZ<+Ih{bCZGmL-sd+h%v61@;:r?(^q-%:MB
V?LF{w!`W/ape2j)-vKP0wrIJ$^u<+)Fr_Xmjy8(&K2_3S]jh83>IIj)KVb[<]:*@jMni;9&
E0I50?4iQuHQ"x@_%L)Un26QA0SA@*U@BR'F0_uf4K'@L$X*b]kqBuFINzP8x_RX[k?{SHW"
[|c)Bq$z"0uq!C"`SMU}kTpL[2A"DYl&?.`ZG-/v5BB4MaOB~6e]t$ESDWS76DfDr~qK#fs(
JtE1Hwe@J2rL]SVk,O4#8wUj,M_HCC}v3UJ&yUPtk@*M6[870r~ocS36f9&gRjrQSul{4sIF
~0z,|HoL&C#7-Si`0JW}!V?k)8U84mvc^<O:#K~sW&/Bq}`~z5bn/MPC?>2P7y2A*kwQ~'nI
}nMCj`K$bEILIPGr@?~#JvY(\:%i(u~I`iH>%8l)z.bNk]gGMb*?e52O4O=k9A$b.w8:nA,Q
2zZ!zBv_kih4L"8ck}]_3K6sf3t>"za7C/$TmHsFDl?INO"2.>S_S|?@d?fREZ;\8U_X]aJP
T5&:'pywu[fQr[p%6'7-5IHr'I/qh12bzMmD{+Yle#5y&AhWi:P)gSKR2FPWl\.]OZaLe}.$
)MQf(ux4J5#q/0L7{sJ(->,->G/66#f(MzRX@,zikt:c31i|?gU^!li;un$j)9iq/01^dQ)^
?'6.UTk)%AgaSpJJ+,({@DIe6)Z7r13VP61lQ%TBCoL@NSl'0YcGc$Un!q`!hYw=V[3WI%de
*^PO;S8L?x8F4H$tH,1:lVgx})m0ry;,mmN:*pu+nk-|M&GMo?)^Klt<,^#naDs%m-a+"W(V
`#PN2|Y>v!1fY2;5v94~O@"5qa&I?JUZ*8g))=i2KH$W4$>_cdYcf:NHB^lA:{foH5zPD#mD
Jz`Gupuv6gxM<u\<3N[h_@nxC7)?S/|@wK?T."8Exl:a\zWgc6Kf}7@^z:._CwNs7f:aoXE=
r`fv|zL}ls/(&OcgL{IVSgt<g%yU>=HYgXCpW$ZbW7GZPN]%%kZg,jTBc~2mv'#V"%Zzz$>>
M"_K.K%yj~<#?!8)A=A'|k"DT1<!"1/u"b`EOHocv<&h^@;|&9H,al[|w<4hjS'Df%zc,@K5
RMh@NOZQLg91?3HM*4jD*?Gd:I;]RZ=b3FH?}l8'm|<b%(Qla(lqVnksfzM[CHXlBR8xzZGV
iLXs3!1CDA`F6]t=!>QYM^kQ]%k]Zd#*!w8={m$Qhe[=X9(n=$h%S\nFf*T[~g#B$'@&p7[6
vffcw<sGMi^oE@fb1!5v.4S~Yw3El[P,cX)]](;~/)!Exr}T=6&Zj07]#Yyy73#Vy77S|aT7
h0>zO9}_GIB8!HoYu>/;ub?Ar%wX+|'XnwkgmE3k{E&0!~C`,^.~fog!_L_b4)\:^4`'JDPe
~]#}i+pxF*v|op_z4h(#P1jO0]\~=Syt1mY<jD*[7T073k)Gzl4"(F,WkpP?6&q<y5-LGwlw
Uh{;$,~=F8]g$,r9~GT=%5"e7's!B)N]`xd)SHcH`$/B<{JK!s.0Y.BRz+7txZK[g,-[^#Lg
O`>5/WBLD93atQ8Rv$85-4cY[UA;<STE|4h)hJM;2/"%wjl#:w!JA<bi=1PA>"/$er.u(yk:
9Hk6T8#iz.hIa09u@X2SQNqFnhSqzkNX(jkcD7a{r\iV{H#Ify+!89OKbCPr#HEDv71,Hd@:
`_e]AkwzKXL3hu<Xo1bK?;6h\tyr^:MZ+>=x~[13nBL0Ckhy<m7JcuKW2%^:1=VaNg2hQkLu
o]!D$ryxeCYsfZx|N>a.5_(3@u(whS+m~NTc/GSG!_nlTqzCaYW<[}l6_iU9$lQd_}?YF_H!
M8G53AK1i>SX%It?$t~HBPc|7bW:[Z#T[c(\==!.b3pusP~n#}kW4;?2P7W3s#/^#=n66!C|
L`9m[0rd>lZ"kZho1CzZ%s+^ub_-cQ}io|L;l*;P0/}0.xu]O[5?G9sOG@}0d%;SHuU5uC:V
@e~{1(kgh#|0;-'l].\?}3D#$^T0p<!FJq@HfAL"Y*V[mWDB}Br/80*rgij/Q9)l7Zg(doNE
oW#HoStj?-0s7u|DW#f5.%7K@'Hx5n&u}kUAr){IJ%$^!6HwtII?3o$8$dG=_&tGEmoK*)NL
,M}m5dKY`uZbT[mV]R53A5*<ayLSGj:D<B3z')),@J}H]05.xh|DBPR-R^8.z$a9Cuy$ij:t
IQ)l-P=c$n6BFAQp87y.}J8cq9#UVEJ5%Kvs!JvcZzz_*0<eaq<]sqbaQVk'em0W-/\D~*0>
KNXJ9kB*vN/?oH(xgx7pbwR6N<@h+"Zxra{.J!G|&uW<LK(gbFp#i.aTpGNHu{e?aDN!1P(r
^>R$esT\_<-x8kK,UvCS`&?P!mc'.?mOPJ$8G}/a7JOP[qC<[1#Pv+CmR|]6l{?q0t-,C5|z
BB1=&9-|lqp0``8b{"OH.Wh^^zkctj;;fslbt"7)1^?Jc{|Xk65B}87c^-cMr%X$64%}eUEN
_`;^1h0"a}JgQdSu+5%:T^KmJZsi<}~)KOc;<&-v`$T"]$[TD/9S:=|'^?g):$^lD-|\~]'~
<*F=^RM*jr~)5ATl:GuM-7>`J%9;Kd&'OG8(k\!7i:QaZ!.fUn<HLoNwk3X2bUmZGW]{s<f.
!t``zZh~U#m^#|XO%,n~<w!fY4Xo8ZBmixl62o%\Y}>UYu+5nGVbq:luL6EKw5PfW@G,ZVMu
n=c<],M^~I|`6GG$<rx[0G9WS;e1p'fQCE;+of4/Ci!n{XK^:AK-ZJWLVFa@Q)[LD*Az_2dZ
LY?/i+~*E\oqW;Q|6snT`erX)M)\pWU~p<9x\SMh1`U2Z@cU$Ep0jbn9`UyBLC=(C19ymq!u
y>V}|"`bd=y7M=*KW*ocqAe0kCun+vDhF{oex;UC_;xAQR.E|I6jzpn:I{VgTIN1WY#G+>1&
n+|&6ajJ^>wAZ21<;;:Z^3@ye0j@avq*',VAI#Z:X3>L}x#bQ|1"u+1WN4wR[c)>^V45`vp|
U%cCj5+mgRqKgG^#`:t9K-/E2oy|s/I9<uHFh[=^zuR<#k,8mrI?-NEL=5uJ=SCgOrYpF.c9
5sFXL9jf(U3b5SI-=WHsXC!0.95}-L!Vu4v/D4k:\;Q/yuuPeCvN>-b=FjkJ{jFA_IY9VGC[
w#={^+@3eCd#hIn&WyeXm,V[eocYuK(q*DW|*[@d{>Sz,u;AQ@=aH'RD;]$b*Z/aPW{pvhss
(^>LQW1]GWul^K#{WXFb|%a{lWezi9T!F8":`WGE&GGy+^:.#>!<JFD1=I*U$c,&@D+O{5+!
t];&-r.Oc^[Z_izf;~sx>B4lqdIM}v1q)_p,12{Z>t9f,>4.2O}}U,XPN~9`5<|]J6<]h<pu
O9MH1[>PZ$vS8SA!uKX3<47x4Nd}'zn~%<%xF2DE/;-zw?R1c_RUK[J3&5mX;3QywS+8riyf
GV"9mO~ZJD|c*EZ\j{~NEnWG#IlH/3di<Sb($q4I&Uc`{.'eav^A-"IgQ.@dQ/.|m;"T!4Ig
kELO||x/IZ2:=i0|m|Z=in(;M<A}|4Y<~1DuJX\,nF+sn3$[#BnQGRbc}e|"PA"oq>ho0Rw'
&7A^09`f|ZO^3y8Qm&=_i;Q*xBOUQw-1xZb|*K{&I<N:FenW}4XPn_|lcz:pdRL;]UT6[,j4
@!f6qF@k[!XPzHsn*q*R){}KLv`X7h1-z+ifJ"ulXX*cWo.R</?^GHCEt-*_%T7a4e#@JjjL
3j]uZO`,LlDYnGv2qD|@tnF3SCx7<Z3@83uG=@]15vFo;HG+Vr8UAhBR}o*lcxw[>7t3#F$}
<Z[m]BHNJg^$0{^Y+g@]!r"U/b53+k~s4RC=")9;hPfiJ_eOI&R7)O73U$E6jF^7o"(<U/i+
m1|<DOFd;<.7E,zicyO\P;t-!]sp/1&m]DZ?>AJF~KO|:gSGWU~ch1GoDP.3E|]U(-?$B1r,
JjCm0%V3cq{B`zL^Ms~ufWJZ$|2b|EZ3EQM8J0xF,TD~kN&0`T0D?O@,Nfs;<V{NiL>i?P)a
ZeINVZ}l|Vk#F.c^=UD[woh^=V5"&(~pWCzt;oxh(^(5w,}$CB_mi8sIg`]grC^iG'\]>)3d
.y)~v{G1p=72j/GF7()uP~"B}p0sypiT:SU{%4ezsmM0#(rTjI[V-EKUcD"u5,B=,5MF}B6e
0nxwOGomW1SGE+]YLX#Be4<'{d%A/*7zD%%M#v,-)R)v<n&WX7xKZI%rTwnC9A^w&Kv!T9KR
`05(n`EdOD)@P}wh0!A,Gbr7wsX)=@JuN0(m[2ZgE0#A4<\gw%$tq39@ng\Sf%RaqdILIiN1
y]},?z-l@g3h_u$Z<G\by{#[l=)4m#rDRLAWG,N=jgD@[9kg*rhb{cd@,Xe$0\QNJC*MRrwv
!@~)B[F{xi$!o)}z~}lSqQ0qW`.W)Z'*&i#rCQJy+!v^!y4Yor#mU`1pCUsWBL2is_,{.hS@
LF3B\|78LH73F&R5N&f5;_l7!'DY8|B(Im1laF[;$E4$q)WL1Am5I533sVc_Y;=p,7i_&f2]
3Y(x\{vW7j0H9<A1Zx5}8{~-Ss(y:z1uO|u}(VQ$$E\'0hg0^K}GbDosQ4oa;{x~&nBbYtGG
9+,mJ3.s-Nyle<LG;2Gqxoj1)f'e{2x(Da}]nC4WYF#N(7e}Su_uC_QCa%uy/C/|>wL'0sr4
7^7wV[BoG@ip[D'LqfoMhp^,[q0{ceZ~J4d:_);So[6dV06$D8CQ,k;~D/FQ&>:u$LImA*VM
.$?dxA!ebl,gx[A.W,5YK2v*vO!76^xX&Q#K,M'%>~(JLq<wYW@9P7js+YX?KsQ.l`pCK+IH
/!z\VmC4&sS&3Uw15'Tj~4CpUsqCGb.rnX<{Z|+x#'uB9<M#ya(nwf`5a?*IS>EQB`d9Um:Y
(Vp@i'y!vn0vRCe.@)~KY_0}&wRtP=8HuK[*mt=4[R|v%$@e7T{RT4t5/%KMH<cNh1nLb@O$
O'gZp=>Y$L{:;%@y!n_vZiWRYF`.'aIE}FnA44u+:_CC6e-5i%2T@JO0DIGT0u=8qNE7dVgr
'w]Pf$~m$N;[>kSOu;rd&D&rD;%1uc(Q-BnFW<c'G.l0tdvVslxqQaWY@Uui4uTdA|$6%ydn
vgtK+~S'L2zouw#mTJ\%8V4ToOoD>'z,r]+a}#0.?ed%.SRl+:HhvWG{Yi`5L$)`O?3j`Z49
yKS`$V"=Nuf$U2|,;r-M9iX0"|cZ%C=t+<GQx"gk?E#MhedW6o9R.g-A5{TK0k#|p>f,)hKp
p?o,D^94g1;fga'rRmAf?obE)Yp-Fa^odxM&u{|_{3#+`c|amyOV^G(DKGqZ>&TStyl%m]$L
CyP(r?Yqy^[JRj"Hw)UL3)c]7d&d/D*uj$N5!vOZKP*`T!A1:RldaKa_33!9Brkl'1iZVq)e
'Z9/?#UCh2lNBT/c3CQ.\p;xu7{*a>NQDmy0l7N(X2BJ{Xf*_%$hZF|j<j@C6SxVG0OpBXDo
G^a2$/gD'9WRUck\kiaWQ/!K{14MnMR<p"PT:NmGLa3$,0\eq^u%nOFZ-L+'Ph`Zan)BJ&Zi
E'XP8350C\`*Vk3#V9ja%{G,!wkc~BD"M51.NvBsAS:/H_.Vh:I.#Mw|UBa5x`W@jR^'M(p;
"rv9S^X+g$3*`4VS,R_c8r6<f'OYrN'g(5gR#{HEU3]rd/:k({_+;Tl5[~>`BY_O[flbLl2X
ZEg';*d78$,sP)?mERoN_^V(g1C+jN'f(\]nT"4;O4-GeiBpT.5R.w1O<HI"3z&(<m"Gan-f
8^MSvE1s<i4.#8&P>5"CY4NbQcKD~AL=l">W.^X9,`lB/86Ay.K)[c;B^?*47kz/Wu@kCc([
:x-1$GQRt{5eq1H2e)_Ko|om)}Kp{sV[z,)r1QrY_H7[Vd\Brghat'Dw>7W69^E/0_oCT5;^
3/ZQ0LXF@<OQ%lC6Li+7)vG2G?hNj@t1rA{;?T8W5,d.YQ`&;+]0PphON-~2]^buz8-C25vY
?`ex]oh+slQf"^@v#7Yj0HE`#0[G<sz36D^9nC~[5~j6PJ^6S|>GYKk3sUg2/IoBVu__t5EN
kIoHU-0g[R2wV#@X'v1qG_Z"HS?R\{'Ldh*cRGfkj=#F}fvQVjB]e_nRQTAxtfLSq8]9F&Hq
e^~Du9[2WFnmF&H&3J;P7xc-#-%&.KVrfP_0VVw0^irE&&kp7IGi{nN|B5eBp)f'@vg/f@ML
9&k9;(+*&.BhE+j)yL}:]&~B.5'D";C*z6PX9L-"s|6\hsBliqx$ZhI4*D$]yV|RLn{uk|0i
D6)}2cQ:p8;:&OSN3[-n|r+1ejp]@dD0N.ZDH7jsS;y=IL,_}Vvj)r~aN(k|)MfwGl?ExlDb
hmPIk|j<Y)'v([.#*+i{H]N@%EenA-Q8Mt+;SeL(?uczHzT`R7=Rb;@eK\aV{I<'0CswW>MM
U<WaojuY[a'o#H1u."Eh!9GK~]qag<h'oCB]6xX(Vr%[=OD_$}Wg3FB^WZns)8o2wYrQe5IT
lC^80RD*:k\P2es_d`_Q$g-JPJf)ny9F~\{P%*+Akj0VBuOG[{rP"iPcv2URsLK`5+yF(c<S
!ij>zN:j&O$8|E3Y(0|a5_A4FEy+_9f5_[mW/)CMmIZpP'vdb=V#QQS%'l1Z}JZ1Mn`;F5X|
:$f#{E'ub@ps-+V;ge;=RCy6fnH|U124-@YpdSM6lp"!jASP5k>l&VP/"P4Ii/Av#}07k!z1
XO;A>["6R3v5XPi4QhXLJeI!9vZOV>uuv&/M#fM)i}XbXr{Uk^{9XtiL.L`-|j<\nc:f-q*p
\}11/=Set)C}Ap-gBe(`COz;f\.b@1{G5eLOl1kn{D^`$Q]RlRD}<bvUToL9,v.,Zn*ww/xE
=n\{k$P>^fqkLV<4obxqa]lS!6dlO%+!t`2koTywP8vpZX$izLf9+]+e~,;lD*_/gtm4}@Kw
)'t?v$PWH4A'E29uR{x4>C`DV!SaJ&r.9V}//OaG?$i+S.Bc[KI\Yt&D>_Jl;uBeWMvn@<=2
}.1\K+'Mo}M4$T^_};kCGML@kve#\oXYe#*%@tWq-Ity*,&?$l=K.2N}f/ZKKxS%=g9V~&S7
=RBv#Ex0/:X`_)UBOHuQu/)*'!]0\|W+u5CZxH/:4ra0w>u].I;u6NUjvvy@PcHa"%nhp\-}
S'rI,tYzt@1T#8A217flxaF9#?4"2ka}gK7v)tv6<OAUWp^)i5)f2)=@F]m\MnP^l8>^z+;3
hsP|"O6{\sG<[Y;7)7Tq[lP1E2TCu0x[[Af?i3v7ySoX{2YP;8`iRleL+)^L8cgm'0I%}[k\
pE.n>;c=SoP6I."xf-;<N6HAZ]+lA|R3dilz~[4DLhP.7%+96fC*-;r;wE&1@?+MW5}XMz9x
G0OZy/-^wN=|1slg'tt?KjONwn>:t05V_=}HQU9.gh'Md=V4&D'\bmWg5/ZL}[$b(\7B>D@|
)a!QO=|m]Z5|-ht,rYX1a7NS5qJgEZ#f[mr4'87a3XyFR(0P"4@-d^w,|+Wc3L*{?g!9f8&Y
N<DO?BNu^pzimt&*OBDGTx*mo9;KceMJ%*Fs(WBMpRsB}*?S"7E(mDbT4\g\h7shNi[.m8>Q
NiXb;sd7V&biIy+51,h@eE.%"PyciyaX7TU>|sggTMisaPr-o5S3KFH6`Qf<5lLv0<>/TvTz
flxVN[y#upEK6R*^jJK\!W9cinBU0fQ#\xufT)rIy`c`LUfC6n]Q$cAnPf*TU/Mox0:{iRT~
8eQ,|]=}f]zYQt1*:\G2_rSP&*1.ja25$+Y"u|,dr$/|~K(Jf3d=zUCkEn`N2[R4=0lsb-zr
O-WoU>{Ku>,LOmy"mp1qh1cuw?q_{Ii,eO/Pk{2W0T(ybKI0,ox_z8{]f^i~sJHKUDKVTF+D
l%dGDfS{Jc5awf$&ldS&uIe,+=fVD)P{mE}+!^RVbb[@:,OzRww)T3k).vrQ2<jD9QtDTJBS
M@wsb)HIs8*yxNjzd+'G@</5Fx}h6<nZl,Sf:(Isrowv|_RYs]^'F!D7[1lQ#|/$?vH{tmjO
@7!%wMVZ(\O+D.{kCN_4qAko--d'eBMJdf$Yx_y15vP2KfNE*j+'nqnv=^][DKA/gc}/"c!3
W=f6cn=eg%4rYnVMJ-AR8[['F"'B9?/6jSB15EPN^>cI72jmGpvl_l_6]Zs]]xP*[EMAIL PROTECTED]"["
<~}(#2RAkexorXC'h\X%i`n<r'I\[t*5SK0Zl}r?:^fw%.5j{m`Pr&g/p9HLrT"@{<tVRL`I
8}%y$H|dpS{7>cgwaS!gziXod*tZ-*r3O_8\*,x%:E.d)}g".VN/GrG`U1.q3&!LQzGaVgrc
Ai%.Yh@8~UuO*-!#ZnqNi$0oe~8k-be:y1ehE@L6x"Bd^y00Wq$IEUQOkd`/chZi~=rr9LxP
jbv'gwLX=`<ZH4(Q9eX]<HlUVL7<ce->u@%!_x["6Sf=4U'Fv'_ZRo}W"XcIazsxVn7?F7/m
$f\)nj=ENkET=K"FTkLm:)yi@;*F%y<{KL8i37'0Uls"X#+YC$|d{;!n>Ga#=0B}5Zu&iZt@
rz)OVl!/,`rxB:uSZpmv",O*1#VYTD#p/1S(wIk}LVGRaFaXq'pgF&%i?#t)=$eY:MP\^762
bX#]^?w>`H]GV8KdVPJW-B|<_vz?l?h4AAh[zSOd6%^GB>D,~gQ63]-@Ft4C,Vlu,L+TLEHf
8~&+hSsb4+xZ?2w_;!ZD^({6vsMoECaceneJV-I\E#b;@1\O.^P"Ix,.L=b&s1fqq$\)2mn`
~juyq-eJlz3H@n'b0tHANbv%1Us7`t|b)Yb(t?b`gLtYOn&A5[[[|g>wM:Zp]C'lFm&?J056
n4`\PKGr%5[k`EE|jz25%0P@>+\U??ITPwH#>AM/k/v}L\W6~[<'}?~-Xu=o*Xr@TJ#!?n3_
3Az"z/I2K@uJVMFS|f:u}V<+9:;xY9B'L#3ZgaUAgh'cANq&AbS&*``E3ru/p|>vG4z{(Q_,
dtbtz;j^gyw!-<l\AjtV['qP+(~u@cdj7HLbR=dsC=B:jA"eJyn{-1m{nc^#+&]sl}{1P+sT
T>38bb*~8j-3oV7@0g3e&[S(/n+\WaddkH<,YUD&;{CZ"gM~7t:|VaE})Zl}J="S1(Ho6'A%
}<o/[d-'=h>35mWZCWE&Yv}g6Z/1FB;hih&?|]rbs[gm[jOX<=-;f^C7'lvP5O3_zp5o8.p:
sq'?GL.h(k_#mb;ocR)YHVd)tN^J"Jf\s%vz]h-#'8Rvu_?hn>8<hfedu~^8cb>69z]MB_3/
A8}=.3Se4Sk>/4;0;mtw9{`=2:w|4&hL"jQi|krQRg&G3MNcW?*G-M"7.X^a-WLnm;<|v[IC
BeOM&wZO$kg)Oy<Tjk]`##4ZK""#0cmRd[k+%P,`Zw)Bd|esw5/oj(Fks&`63#-ZEOc:WqY"
kL|mgTfs3u/1R5PvT3!>A.'H*\Tbf#6|a@*EK)`SkEFQw;6#M55)X[/`M(r>i:U}fw]rJ4(o
qgf&:;.ry{*@C#l6$-I~DL?DV,5/1'IdK|g#}O5;T?^=-igM'(Ii>Q,O]3^aJFHj.[C@$u}3
zLGoT!pNJL-*Xhr)0rG{V-C4;?=)~8XUu4CQx4AN4-<vWlnxmRUk{[dn)<4=3n^>)Iu.Hteh
k<]<fjf:\X6QhsN:WV?Y,T2*^v>*z/7mT0<6Jf\w-GfD-{py(YY2|Ear=ZPqU<QT^{=@Maum
'--8C.[uY*Wxnqf-)oO[*NrgUWi7+sFF'>-0:Ff`yY[p6CMhKAk:5a4;w;6Gui1<IcO|71R>
ug#682hDOj41*+)jQlE,6Egid9ajs@+h~.-Y'q9/<C_B%whi5xn5]ymkpk7\t28"Xs(8q[#5
I007@.,"q>jW4Rimr,&je:y]xZ#:e/F]Qs@.lPBmoY%a|a^#ir`WnQEP>l3pHyHK:aM@m~we
csG*$){aK8sX\I]|<?Z*"po8TS\Z^5$"z@~uNmT^ST7w!,x.Ldj26g>,@6znX@V(U-\gFL&T
k$0+k,5SLX,=[g@=.@>NVQ56w}_-}-WuohrFA?LSgRk;{T"N<=K~#k+d|crN`}1Mu%zO,\iZ
>78wId'<_Q2+7O,#GW]\~S1vGp{%Nl4K;jRe,kG"f}l;J98%}:L]IcgBOm]G#mZ9Z1O`s1}{
5oR'K{deWi8idRlm3]W7Il~[kEG!W-L#ZMj`%zCgVbW~FHG.JS/6|%JRb_,<?z_@l8<1nDS3
H/gd.Lnb9:Bujue}E/Ra\eWvBV_9<rS(Wq;p6N?w$W$VDTlyQ=zCO}O0)EM^w)qo)_:$~Mf7
3y"A&U+pub3Dx&iJ|(RM)]@za^i]_YbTk5{,_f%`+X|nRCdD>ft"(U1Fh<YshN8G=b1i|~&>
9J63f2hs:9v-ty.Rz[BogNe1B@@[^SG>>b1]a1ZA)%86eYwi)N3L?'E0H_b3ls>=9#[;aMt1
:++,-<Qk[S-j`|1uJmDD5Nk3VCc:o{}"N#6)5h`%K"bgA|)}~^K:Pyaf31hld3Mo;~7T\'+|
83N$(\pwGk'"^2)<>*yQ4GQ95v5^othj)mKi/ZQ&r~GTa6aSPw7$F4z0n@);K4@AOu6zn:T@
+f8Lyjw{I(]XKv%iK72C:h5E1]F{luD+ETR-M0/oeHqR$i`/^gGdGU%`G|M7Ur)lJg]5JOty
hA#L|#!xJAb7]so2sQCC\u)H$Vy!FhFC8/}!3>box&doeh4}lul|\Tqo[rv~4KZaP#$6}9N4
5H$LM3e>b0]~s]O;(=K=d"9"s=n*vCZ.!82Z?LV[YO;`)O#L]O.HY=e*{8]E|0lt5>Pz2iWY
=F08paBh~"[txHSRPEhs/wGK*9BKKF'\./}sx;BXBg^Tw1*xtgF.0)m$m1]5Yyy~IS.^{;XX
:xC>vOq=+9l'Naujfqu3Io<|eo}!=pZblr)_(Z,9}_Ug?nZRgh'w9a>MgCEc`Ni>}J!:,5{U
MV?NQduYmFFF+!U@RHW[Nsk7q/NB9tGp:&.p[\|!%E%FS}UP1@gKe)SilaElD>4#fhE[$0Ki
(uyz<kV\6y,u:=l%t\3b@4*YO#uh8uPd8VjWrd%`jkNzW9pR0'K%<K1r1Ypyg#{|8me9CBc(
[SH;+B\c%];G7]RM3JJs0H2M?q3i,VLM;^zcZ,wSF~sm#q^d5MqOi(8sH3S`oxo?:;xb,s2V
(qIt(G3Zh)Lq,B-?X$G/8^_RJl\6.iTQ^k6b^6=o{{u~Vn;ooOqnndt:cav=Q9Uh.Yp_f>9x
[]p.paDA";q@A<*]f,R>IHbdfs$}p#xJ\uBrLN%i6tqO0,9#-6OYL&bz@Ky}}-r$EK8VWA=X
h_;=3z[#S,g=sStqaT.-!)-E4iyEje,.lEJizy0jCsbG1w}kOuH*YwGKW0For>mhZ'=,O]gH
b|0"13ci4q0`EjYbL%ep9oMPPY+86@CWO\KS]Qr-KUrBO[vzg\8]y*0-2(IR/LETg\UNk@hz
i0Hi}3@X+7P^Z9AEJ2>svD`.*:C>uwko]lV-CQ]zi#LL@}H66n'VsKlE4oL(a|[/'/])*QAM
1Xll@?~owKyn8kNOU}=y&GL$>Kzu}HHk|d5Ie7Ci(dT{yKQVU_`JUc>]INaK7}*XI;Xrp0`0
~yVrp?[8J\S].1;/A9dsMo_nMI#S6{&0~XcN|eV1F*f4z^dN4yxqGE"/{4sQC0/)MS?)0Q"{
t80\;RIgG1[aD00h\[AB9*z[iqN)X)g{Cu\"8?6u1;m6Ci=sZ1\udzQAinpJ0|$lp&P{tGbC
Q9[my+P741qkyfB1Jp41}P~uWWg;^l-B7npfMS(pM}'Pbw_ZLg4d(Pp#KyndX#lIp!qG'r>R
{ex|Kc!&Ahp.@YXJju0<s(XmUZ~%$.@FAL5bX/#d2yS$Rc;x}VQ{mo"@c)TWAO9W91e|1G<s
QGV>hhSSahY3dEr)c/{'NLOz8eEZ[U?FtEw|t!gK~55k<L+#PWL6d$d)~O]7hWF[}-sXF%GK
D;$NF'DUN=e3z6GL3,~QXE,mu6+da/?-#w=tMS]-5,l$i-nY7'o4tE;Z(?sH_!8h4c4?,Beu
zJ2@#cv+/me'g=W?0e^_O1*VGh}IX!gPc/iAjEc~^WXgA"R\11(\ls=K']A2-t\e!oi!o&iv
!1sNN(:5N#$rGney9wX?.tqtb;+5xO~dDa!t)'fs-,TH^4$0k4+LROMyDR/5:}6c7$1]~zdc
gq&NpZK^zoLLz!<jh_MJ2g6F`wkgM(KN00[mpiOL;=fOl%P*'^5j}80ss,.p+\[EMAIL PROTECTED]~F4
LKXhk?5e2H(M)Gz.i)oF\]GOy>lA;k).1/,Is=1EG3]B\s0IiWGqxMZ/bPn|lmM$,k>zKb/[
N#t,b.[oZehnf+.?,Y!jY}2aBCsGp6:y@Wv_W"^H4Uyc8,o5h.75w'3F-;@(~B{u;XH/;3In
zA]XfNJ@#[*Fe-ME3H9i^{zN1Cjc/G'nlLkHE'mX0kf\H6?9mccX`Xq"n!iLq`<B)c=%'a?p
tw_x87B?g!2"hG3gsWhzGQ)\F~\U~Q&c*?\$>OaB\>{bR#`5_nS8o:fykUm&g/$YIL?=Bm9E
'_B*-AM@lMUsW'-4}Fsd6T!<#|AdJ&FKmw9a'b}DgQ3W&$*2T|axk,5FI]n%38H8muXKW6u]
A0dOg;QDTQ%M%eM[pwc@wd?{G]5HY8A(is.AW#"S??+V"GJ-0\b;\FXU^Jr(*;gVZn>nbR/-
~4Afddpv3tBR~#HZqW3bE'u"W:`4jZjmvA0rH#,]%J=38oAZ+I/[I4JS_,\;;n4ZRA^W_e!{
pt`;GI%phv*JDGZ%5Cy4p0Q-?3+v]b?|_=ZX"~AD#^wlRseFrYz>-i010<6.fJ_y~,U,|6z]
j>AApYV!t_7$4fQy-CBP4-|V=&j(7T_hd-)SlMR2tU@ExTRoDPK0?'5iA/_{F^(.CL~y.zox
$ty)dcvpKv;7*=b!R!k1y~N&~M`4oqKBEM_T/qNUn%|dA8j]5^Itwm90^c\1|XqJ^%5#XVof
KgqcSGQZ7YF0Q>y%l@/&JdG>u%wq,Mx=+dBFUJL;G|3RFvv&CzqGv}5Y-ZHK:(hl{`FYB&'8
&N5-]@{:O?#jXvlX?oP~T[|R)gd*]V"zL:*le~c[?fS5|n)D_X>C4yV~NH}H$'NesTX/!j\@
I6M+N>a.01{mAa7OjN:Xo:\]o@D[y<(4.>l?Ylc[1e(dc(wDR)qF~UFQU?}*?sJ%YtrANOr#
W^Pm5w<RN2,#EN;s6IILApgZ"|5]CitFvuC5W`b$AtT>8);rFl.#vJWPb%iiA@,I$E(o9!D(
i5b.F<$su{f_v4:U@2\Meik-?>[DD#vO%lx<=pQ$h}xU/P_~/y'?Q&[)=%3b+{Iiu,NXAE[N
DR20b*adch4tAg.U)'_V&Y+"]/omNZR6E~gE9a>"=CV<UXp2c5r~l;[}K')zF,u'KH}84/mm
"+Ys|@i1@3ch=kC8s0!9|=+!VK5PyFm^3"]Z4eY(<Sw\^Dfp0JjE8)rUCJuZZ!:Vo(m467H0
?)?1G=@%e#3hg[>U{N(Y]//g>cKBx/Ojx`4w.$?I^RPXK{:JhcjMuvbe)nUQXY)Rm9<B!J2F
M\Lb2$u<v8M1>w$c{?amSjr@fEw5KX$[te%vLHr*xJ'S~J2bE$!?1RwA#}"kF-[VE9fKmJi\
7TSB+z)5HV<J7spX}Op`b$MV<$}dx-uRt)fHX\vJX/jbeP>GaU@M~H5ckPx89JMg5ifjN@Ol
+B;S;48{`Fj>]nksStfcHlDF}Co*v=P#Assz?;\6nFfAX;l:v-^@<e27)OStjS?TRHQL2'9Y
14S>wAu};P+UF8KEq1`Dhbp6o7.Jj.2O\8Z//"B|Gf,r=ipU`J9aZ68Tuuz^>]RstHT#-kh(
bki;zmY%g[:c@>$N>=[$Nm3x&Wckjvl]c]%Qc;f#SpwQax4VL}MI&s5n)cOO}";_V^^.-WHq
:}l`(I*5]4Xtjt)1.\)nbW,SX:%+-{J&QYtzpepa8TI{7Ync?u[6_}#2|`2M!r]!TctA`pGR
ho7c[|vcNS%AA/hTbYd;8BUVNA+.1P'1M.#P:WNv^l3x+Sy4uY.cl2To+F,YSQmM3o9l,HB-
>7T]?r<;%*`1;!|*yg0.CCo9uB=O>tu.Q?[IKEZ?acw5)[=X~%8nMT.HP,P/M~l[$Cq8neaN
BP}~e?=tUuhh5[:mxLMqJP[!7KS"dO.'s"z198#L!qVrC_R^A"u$6wgN]5Z)jnRS^{DRd8L;
jW8_w_|gbWtc<Eb'x@N<V%*->Tk?QQZgsos&|dr8X"9zoF!]M:vK<xp+M$E4=*;2B'N$ct(z
OBfL0UAV"xfD6fMB&(%<Y)boGPjfseKHC+T";0;l29=c((OJcr+ayNGk^FZy!MnKSz|>4jX#
9w`A_{qk;l))Mi1aQeJ{,EDP5#/I04#VhtPe\kV{Myq.m}.ajY]OWlw9N!WC3^\7'*=urwjz
Y|p[Dd^!BNnESUJL}`{0&<u[d#x^GG/U[,<kWEePU5yPGg\\29,eD{\=Ml:.^e9l=M[9nt[7
%/'<wY$Ku==L[L%BoiQNFY}l]`$?:(%t{D98OEl{O[}K<"bz&0Ria?<|$yj5BC.n#"x$2~96
U?XF;gz<}%FJ;e|eF]#yn#uVg[P3&ex'P~xFhoJ('"9-4Dt@S&r.MqHRSn#B6oHI$kWWZf^Q
iHk;XE=-wq`gk9G6:9;XP1}o/dm1B|f6wN#k`N-hrE2P}L6>|-~48$na=v7RY/fHH&rg~0(z
b%df$4(ObzPMQVu(v}(,d)#-N:X4KasYS]CMIY8a('gU2$r];As6gkIyM{fY_vAOa@M`0(<F
(!H3Wn<^RPm!^2qt?8GHq(RQPdQBx#W:{gwqN_"P.ya2PoM#c6z$~rqV.J]hLo!FWx~h14}j
dj3o69BM;C/\q<#"RSpl_b};C$NuZQ6s~\fmta~u%;EH'Ua7+,5U>.?!/B}|F@lyP+)+Z2C8
JfV)@u}BK9,e&?T{xx)&}i)Z0-*.Lfp7J@^~=,cw2VQVYCZ/0@d&0k,Pbo<ET3<7!NR7BN$,
AtblJZrYUK#&hB'4s%tv6]^,Sn1rkAT4pL<|q6yMl{:>8ydZ-B5Hxhb=}uB+q&G4XJ3Y:,dm
"?{rp';]*Au0'~b7bThO(&kDWE+4"/\oa?C3g/[IY"}/]kL!(_/E+8O\&l>62FzakW%OVP^R
^qiGJn?1w0O4Wma5K$_"V"{pUBvi0o~*FX%fn-3.74#*G[VY?Cesgrng_mV%)X@:]44#s|c}
lb0q#NB]DZeC8@w<;v$`OB[Wb?~C#XWs2W[r=Du7B3V\.7l.FbgUNcB:,+xYBK<0"0T50ZT?
pCGv"=^{oKM%=7_fiY2FI&"M|`,cRZ'6vzNFSW=L(Stj3j@Xo7PQv,Zo)z0u-]u`w.t-*HC<
Y``x+8g$08y,?(gEup,)Y"FBjUn!8+9DF'.'yF]Cq9RRH0G^0uJ[oGUa%'bjq4mVVS59H;M'
J[fj3VD;\rH!8L5I1N<*@)mbGpg>qC)$-,.I>/:0@.PTjl8@:Sa$2By)x8t{<Pg`fEjZ>uxx
t_z|oZ=]:x7QAN':+@?u:`p}CHZ0!#"P)<y\Y2!BmtV>~QzvJ/MGiL.1oG3:Cabicv=Q)(G*
gJO|yv!bI03MF.+00vG"\BqP8ya|w;,h~@a>i:2[DFPT~.iN)\@M/v+!pu*S]9E$dDIC@TZ5
xe(d'Rhgk;`PKMn4*QEHe6d,a0jkmEhRwLuAqQp_6_<@&n;r!!jOQ?uC2<\m,DC{8z6)(s."
}Oj4^2,WRpP*;&`WNxsy!lJ{QV87=@+^PaVfb82f$u>C|*wrsTfc5`jwc(e7fN">&#+^;a9j
UOg3,khQbjF]Ail?qG&SV-uY"tcA,iUvki"o`RxQG2*c;dv.~j0ZsF=K7YOp9T^Z0U%O<-R*
\Ft{.,PoS!]Q}[N[p)RLIspH}QACvu`AkV6(XG0riih.w2K^':=vMI5StAA0pIzk|q_?Hpsy
RpS78BuY|DFQ:g/nrVPosOB"g{K<KnD9H;"\&\/UC{8R'/T2%>o%-<*hFx5B$\r}C8Vs0Jf{
4,pX>l"*Sve(WW*_`QK'~pK8<t(<:LB>RJ~f\jbKu)6L2&5c2n;&9WnB!.#jIj.v;N|OZ381
W/57i"qSqGp.3GW}@'8(%xu9=7(S?LN$!!*]N/c#ofet;mO4o%i;Y~>3^NcQ&|A.YG7O+b-T
w?0YV@>=y"b!:~h%0AN)UERk`ft|SU{$/W&(uENrK)yF^&O6d_aaJ|_q3+?m\c/aSK)`]!q"
ti-*'v@\,j?25|:[4z=ydON^dMNc,fPx=xyp[@#b;Go1ykRMsm6@{dH)32r6w>1*T&?J9wVO
{}=|np'2Tc(F=-(<CAjT})h1~`4"7Q_>jN`jRMd]>S#8&l.JRv\zMi[A;[\/8()QcZT7P|Ns
=Vz*a85PCNj*rj{i4\Ye%%&@-M0B5^.!m)Yk}YH!AMy#qDbM*<Rk.gb[Jw^#gft`\+g3LNu#
MuWc),}8[Tq0e\@'n7r/R|`8Fd{=oEk}N//F#.SUEWR=.>FC^#Kggo^M>Q'H7[oicY%0pr+M
XZ}bOGZ6~U~a28#nkImP<8~;tazAi}Hd:6S<"l("/mJ$LOv=6&YS2`1xrHBC|8b-rC5t?Q"{
-YI:4",^tews"*y7Z6!FFp*P<m4{;K!t=u+1<',dc[0nF:qmgw!y`SoC~VW2^YXW9P}S*Qn|
>vU4hC|Q|3n,FG3N?w5/8$_7"m9\jrN]mmsdG(/H2j&r]>?*H1okd$;cLTdz.*XU/@s&sq>.
9+trcLJe!/-Fm7OYJ9$"j`:E:\[@D7M9Co,=!.b3;WHHm&9"*;><w3bBrJdl.@M{1u>8c@@6
Cg]~Ur^ai6AD9Kkx+mU%4&2.NY7"1h9kqc.gL{O[o^t=<q=yd_eCzt#OmaHUqo'16(yDUT0@
Z7kzR2sOG9wysKf[S}t99*bceX]z{n2^qF9T,A(<Jl~PJYs#I/8K^5go>e_u$=bIF'bpNj5l
c$^X2{e!IG"(VCIdVT"cCdo^i+@{fN!s[%-#*nz-3u~m=K'?(G*{Y|XKEu%x5px!9o<1H!<G
>p8(1<~!!N%bv?+lhuntxP%M_hRRq!u$)>D"eeYvt>RXu9YxS:/@D*VYgK&Kz(gqb4-Na?~H
=g"MDDiJFcq\nE+[ac#u^VfnK.<J%e]DUS#!~K6DE!)|D?wY"N('u6qI/h=\$o~w/pB4(LTT
:W_zb]bI*f~^pb+ErvR4"{ltPMij!NXuo:?@CEoW5`3wiiUy=G-&}hpHcE!^^/Iq$W]L{gPx
B4'e/m)5-]92Zq4HwE{\>pwLkRJ7L/|+*LtaBWC.|4[^[DOTR&tLMa*itV9p@7JNk]T5dFoZ
"YU3?<qBHU^IcIR},||tdRN-'&gHlz,G?\id8[J`9jBMK!8]#@Z-r<mz[_'pL4wNo5s;lh@'
Etj/%`r=+q\2;!N11Q:55pWPySFq9GFD!93uK\m=6c},nzpm[Ei5+YzB9Yg3ET[aHMc,Hv=N
<A<,U"k1Euw(|{7S$-oCigf"*dBJi]+W/G|$a3@S3\JnIF,M|k'"?|29yeNF]|$'zBsE}tPZ
Qm+^S[W\BoU%%3;}1=7$9.D>N$U1i[va-@b%Sx;8zeO+$.@oQ~'"`^~;:{e<R5Z}w|.E!2&}
Z>J3{lj5j7z0W&?xZ}8IdpJw6r<WZsU/:qG5hew%7i^t0:5*&cTf'GYb|4+.b]Dh^,f$x{{g
~guQ$1arFT!W/Np7eEXU[mXahy]m7{*Ajn*!g6S`+cVQuWg}M0eV[-0FN&zb!d8leJ\Ox[>>
\=$,*kKpw:qMa?K.nRRkq"O;5-FYIC]a*5mTXWmXWP=FGZ29IdKkGO\Ji:$nmExJ@`x|2,P~
NZNm2w[fsI-~-U5yPa{FRgH/O?xG~3=L8L+46%Ez$-EeMnW&Yv,$V#zNGL:}NlSt$N}5UTa&
mOBgqqX138J!t5U%dp:Hs(4KMVN0t*84yj9Sztwc3M"I&eiha29wmMRE

------------------------------

Subject: Re: pseudo random test
From: [EMAIL PROTECTED] (=?ISO-8859-1?Q?Jacques_Th=E9riault?=)
Date: Tue, 17 Oct 2000 01:37:42 GMT

>Mok-Kong Shen <[EMAIL PROTECTED]> wrote:

> NIST has a test suite. See a recent thread initiated by me.
> Passing the tests does not mean that it is cryptologically
> secure, but a PRNG that fails very probably not.
> 
> M. K. Shen

I took a look at what they have, unfortunately that runs on Unix ( .tar
) extension.

I have a Macintosh

I began to code some tests, but that is quite an undertaking, maybe more
than designing the RNG that I have now.

What would be the most important test for an PRNG to pass.

Jacques Thériault

------------------------------

From: "binary digit" <[EMAIL PROTECTED]>
Subject: DNA encoding
Date: Tue, 17 Oct 2000 01:55:54 GMT

Hey, if any of you heard last year the winner of the inetl science research
contest took a message and encoded it in DNA.  When I first heard this I was
skeptical on how she did this task.  I searched around to see if theer was
any explanatyion on how she did it and i found a video of her at the rewards
explaining how it worked.  She said she took a group of acids and made them
reprtesent a letter of the alphabet.  for ie 'ccc' = x and so on.  I also
read that she claimed her encryption to be 'unbreakable', which i giggled at
cause if thats the way she actually did her project, how did she win the
intel contest and how could she even claim that was unbreakable.  Can anyone
verify any of this, on how she actually encoded a message 'into' dna?



------------------------------

From: [EMAIL PROTECTED] (Mack)
Subject: Re: CRC vs. HASH functions
Date: 17 Oct 2000 01:58:17 GMT

>Mack wrote:
>[Mack]
>> >> Most MD style Hash functions use some sort of CRC type
>> >> polynomial on the front end so this is an issue there as well.
>> >
>[Bryan]
>> >Not true.  SHA-1 has the W buffer up front, but the effect
>> >is nothing like a CRC.  In particular, the W-buffer
>> >operations are reversible, so it alone never induces
>> >collisions.  MD-2 actually tacks on a checksum (good thing
>> >too), but it's not on the front end; it's appended in the
>> >back.
>> >
>>
>> The W buffer in SHA-1 acts very much like a CRC.
>
>Whether you choose to look at it as being like a CRC is not
>the issue.  It does not introduce collisions and does not
>produce the same problem.
>

Back in my original post I stated that if security was an issue
then a Secure Hash Function is necessary.  CRCs provide
no security against an opponent.

I also stated that if security was not an issue then a CRC is
superior.  The very fact that SHA-1 uses a CRC like function as
its first step backs this argument.

Choosing a polynomial for a particular function is an entirely
different issue.  Generally high density is best. But low density
may be ok for some uses.

>> The use of the W buffer however hides that fact.  The
>> addition of the S (rotate) only changes the actual polynomial
>> not the fact that it behaves like a CRC.
>
>The W buffer is inseparable from the use of the W buffer.
>Try it; add multiples of whatever you think is the polynomial,
>and see what happens to the digest.
>

Unraveling a secure hash function involves more than one phase.
I think my doubts are justified though.  In SHA-256 the totally
linear operation is replaced with a mildly non-linear one using a
combination of XOR and ADD mod 2^32.  It is possible to have
a collision free highly non-linear function in that location but it is
slower.

But that is another thread entirely.  In a situation where security
is needed a CRC will not work.  Otherwise a CRC is superior.

It is faster (and smaller).  The faster issue may be negated somewhat
in hardware.  But hardware only makes the secure hash function
larger.  That is more silicon area.

A properly chosen polynomial will meet the same requirements
as a secure hash for non-security uses and do so faster.

>
>--Bryan
>
>
>Sent via Deja.com http://www.deja.com/
>Before you buy.
>
>

Mack
Remove njunk123 from name to reply by e-mail

------------------------------

From: [EMAIL PROTECTED] (John Savard)
Subject: Re: Public Key Algorithms and Analysis
Date: Tue, 17 Oct 2000 01:44:13 GMT

On Mon, 16 Oct 2000 12:00:21 -0700, "Joseph Ashwood" <[EMAIL PROTECTED]>
wrote, in part:

>I looked they seem to be more focused on convincing people that it's
>completely and totally unbreakable than actually saying anything.

That may seem to be true after reading

http://www.arithmetica.com/encrypt/whatitis.html

but on another page, they give the names of the inventors, so one can
dig further.

U. S. Patent 5440640 seems to be the one they're talking about,
although 5577124 and 5751808 are the ones about zeta functions.

Thus, in the earlier 5577124, we are told that

"The method encompasses a new one-way function with trapdoor based on
Artin reciprocity in an algebraic number field."

and apparently the place to look for a good explanation is a paper
entitled "Zeta Functions, One-Way Functions, and Cryptogrphy", by the
inventors, Drs. Anshel and Goldfeld, in the April 1994 issue (v. 15,
no. 3) of _American Mathematical Society Abstracts_. (Apparently, the
paper was actually given at a conference - it is not clear what source
one is to go to to find the paper itself rather than just its
abstract.)

In the background to that patent, they note that keys are used once
and then discarded, and this acts as a solution to the problem of
authentication. If I understood that correctly, that means they claim
to have achieved what the interlock protocol is aiming at, and that,
if true, would be very significant in itself.

Since the keys are one-way functions, it may work conceptually - but
with different operations - something along the way that
Diffie-Hellman does, but that may be only one way of using it.

John Savard
http://home.ecn.ab.ca/~jsavard/crypto.htm

------------------------------

From: "Joseph Ashwood" <[EMAIL PROTECTED]>
Subject: Re: Basic skills and equipment...
Date: Mon, 16 Oct 2000 17:11:31 -0700

> What are the essential mathematics skills one should have?

Knowledge of various functions like AND, OR, NOT, XOR, addition,
subtraction, multiplication, division, are enough to understand most of it.
To understand the advanced information you need to understand the above
(where applicable) in polynomial bases.

> Moreover, which
> books/online text files would you recommend?

I would recommend you buy Applied Cryptography by Bruce Schneier. It is a
very good beginning text. Also you might want to grab something like
getright, or net vampire or whatever your favorite is and head on over to
the Counterpane library (http://www.counterpane.com/biblio) and grab every
document, start reading. Once you've got a better understanding of those you
should begin using google, or whatever your favorite search engine is and
search for keywords that sound interesting. You might also consider the
Handbook of Applied Cryptography.

> Any special
> (freeware/open-source) computer programs?

Pegwit is good for an understanding of elliptic curves.
                    Joe



------------------------------

From: Stephan Eisvogel <[EMAIL PROTECTED]>
Subject: Re: Optimisation of SHA-256
Date: Tue, 17 Oct 2000 04:03:39 +0200

Daniel Léonard wrote:
> With your last sentence "Loop unrolling was nice for 8086...", do you
> mean that we should stop unrolling loops and just let the compiler do it
> for us ?

Depends. If you have loops that are only very few instructions long, you
may want to unroll them and see if it makes a difference (timing aka
profiling your code is always a good idea). With P6 and better CPUs that
are available even at food chains nowadays, the effect may be nil though.

-- 
hawo bofh

------------------------------


** FOR YOUR REFERENCE **

The service address, to which questions about the list itself and requests
to be added to or deleted from it should be directed, is:

    Internet: [EMAIL PROTECTED]

You can send mail to the entire list (and sci.crypt) via:

    Internet: [EMAIL PROTECTED]

End of Cryptography-Digest Digest
******************************

Reply via email to