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NUMT-L  January 2016

NUMT-L January 2016

Subject:

Extended examples of repeated-squaring

From:

"King,Jonathan L,F," <[log in to unmask]>

Reply-To:

NumThy & Math-Cryptography (Prof. King) MWF7 LIT239 MAT4930-2H22 MAT6932-21BH" <[log in to unmask]>

Date:

Fri, 29 Jan 2016 17:18:17 +0000

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (106 lines)

Dear Cryptoads

[1]{Zed} (setq Base 23 E 205 Modulus 100 )
100
[2]{Zed} (repeated-squaring Base E Modulus)

 /--------------------- Mod 100 ----\
  N:      2^N |     Accum |  23^[2^N]
---+----------+-----------+-------------
  0:        1 |         1 |        23 <<
  1:        2 |        23 |        29
  2:        4 |        23 |        41 <<
  3:        8 |        43 |       -19 <<
  4:       16 |       -17 |       -39
  5:       32 |       -17 |        21
  6:       64 |       -17 |        41 <<
  7:      128 |         3 |       -19 <<
All:     done |        43 |
 \--------------------- Mod 100 ----/

 So  23^{205}  is mod-100 congruent
 to the product of the << marked values.
 Their mod-100 product is 43.
43
[3]{Zed} (repeated-squaring Base E Modulus :symmod nil)

 /--------------------- Mod 100 ----\
  N:      2^N |     Accum |  23^[2^N]
---+----------+-----------+-------------
  0:        1 |         1 |        23 <<
  1:        2 |        23 |        29
  2:        4 |        23 |        41 <<
  3:        8 |        43 |        81 <<
  4:       16 |        83 |        61
  5:       32 |        83 |        21
  6:       64 |        83 |        41 <<
  7:      128 |         3 |        81 <<
All:     done |        43 |
 \--------------------- Mod 100 ----/

 So  23^{205}  is mod-100 congruent
 to the product of the << marked values.
 Their mod-100 product is 43.
43
[4]{Zed} (repeated-squaring Base E Modulus)

 /--------------------- Mod 100 ----\
  N:      2^N |     Accum |  23^[2^N]
---+----------+-----------+-------------
  0:        1 |         1 |        23 <<
  1:        2 |        23 |        29
  2:        4 |        23 |        41 <<
  3:        8 |        43 |       -19 <<
  4:       16 |       -17 |       -39
  5:       32 |       -17 |        21
  6:       64 |       -17 |        41 <<
  7:      128 |         3 |       -19 <<
All:     done |        43 |
 \--------------------- Mod 100 ----/

 So  23^{205}  is mod-100 congruent
 to the product of the << marked values.
 Their mod-100 product is 43.
43
[5]{Zed} (repeated-squaring Base E 67 :symmod nil)

 /--------------------- Mod 67 ----\
  N:      2^N |     Accum |  23^[2^N]
---+----------+-----------+-------------
  0:        1 |         1 |        23 <<
  1:        2 |        23 |        60
  2:        4 |        23 |        49 <<
  3:        8 |        55 |        56 <<
  4:       16 |        65 |        54
  5:       32 |        65 |        35
  6:       64 |        65 |        19 <<
  7:      128 |        29 |        26 <<
All:     done |        17 |
 \--------------------- Mod 67 ----/

 So  23^{205}  is mod-67 congruent
 to the product of the << marked values.
 Their mod-67 product is 17.
17
[6]{Zed} (repeated-squaring Base E 67 :symmod t)

 /--------------------- Mod 67 ----\
  N:      2^N |     Accum |  23^[2^N]
---+----------+-----------+-------------
  0:        1 |         1 |        23 <<
  1:        2 |        23 |        -7
  2:        4 |        23 |       -18 <<
  3:        8 |       -12 |       -11 <<
  4:       16 |        -2 |       -13
  5:       32 |        -2 |       -32
  6:       64 |        -2 |        19 <<
  7:      128 |        29 |        26 <<
All:     done |        17 |
 \--------------------- Mod 67 ----/

 So  23^{205}  is mod-67 congruent
 to the product of the << marked values.
 Their mod-67 product is 17.


Cheers,  Prof.K

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