Deconstructing Columnar Transposition Ciphers
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The document presents a detailed explanation of columnar transposition ciphers, discussing how encryption and decryption processes work. It covers classical cipher systems, including substitution and transposition methods, as well as the mechanics of implementing a columnar transposition cipher, including key agreement and character positioning within a grid. Furthermore, it explores the mathematical aspects of the cipher, including orders and permutations, alongside examples to illustrate the concepts.
Editor's Notes
- #14: EXPLAIN SCYTALE
- #15: EXPLAIN SCYTALE
- #23: CTC IS A PERMUTATION -- ELEMENT OF A FINITE GROUP -- HAS A FINITE ORDER
- #24: CTC IS A PERMUTATION -- ELEMENT OF A FINITE GROUP -- HAS A FINITE ORDER
- #25: CTC IS A PERMUTATION -- ELEMENT OF A FINITE GROUP -- HAS A FINITE ORDER
- #26: CTC IS A PERMUTATION -- ELEMENT OF A FINITE GROUP -- HAS A FINITE ORDER
- #27: CTC IS A PERMUTATION -- ELEMENT OF A FINITE GROUP -- HAS A FINITE ORDER
- #28: CTC IS A PERMUTATION -- ELEMENT OF A FINITE GROUP -- HAS A FINITE ORDER
- #29: CTC IS A PERMUTATION -- ELEMENT OF A FINITE GROUP -- HAS A FINITE ORDER
- #32: CAN SEE THIS FROM THE GRID
- #33: CAN SEE THIS FROM THE GRID
- #34: CAN SEE THIS FROM THE GRID
- #35: GO TO TCPERM -- ILLUSTRATE (5,13) AND OTHERS
- #36: SOME CELLS IN THE BOTTOM ROW MAY BE EMPTY = TRICKY
- #38: CONTENT OF PLAINTEXT DOESN’T MATTER; NUMBER MESSAGE POSITIONS STARTING AT 0 THROUGH L-1
- #40: BOTTOM-RIGHT ALWAYS OCCUPIED NEXT ENTRY MIGHT BE EMPTY NEXT ENTRY OVER MIGHT BE EMPTY; IF SO THEN EITHER C|L-1 OR C|L-2. EITHER WAY
- #41: BOTTOM-RIGHT ALWAYS OCCUPIED NEXT ENTRY MIGHT BE EMPTY NEXT ENTRY OVER MIGHT BE EMPTY; IF SO THEN EITHER C|L-1 OR C|L-2. EITHER WAY
- #64: CYCLE DECOMPOSITION AND ORDER ARE UNAFFECTED BY FINAL CHARACTER IF L EVEN ASSUME L IS ODD AND POSSIBLY MISSING THE LAST CHARACTER
- #65: CYCLE DECOMPOSITION AND ORDER ARE UNAFFECTED BY FINAL CHARACTER IF L EVEN ASSUME L IS ODD AND POSSIBLY MISSING THE LAST CHARACTER
- #66: CYCLE DECOMPOSITION AND ORDER ARE UNAFFECTED BY FINAL CHARACTER IF L EVEN ASSUME L IS ODD AND POSSIBLY MISSING THE LAST CHARACTER
- #67: CYCLE DECOMPOSITION AND ORDER ARE UNAFFECTED BY FINAL CHARACTER IF L EVEN ASSUME L IS ODD AND POSSIBLY MISSING THE LAST CHARACTER
- #68: CYCLE DECOMPOSITION AND ORDER ARE UNAFFECTED BY FINAL CHARACTER IF L EVEN ASSUME L IS ODD AND POSSIBLY MISSING THE LAST CHARACTER
- #69: CYCLE DECOMPOSITION AND ORDER ARE UNAFFECTED BY FINAL CHARACTER IF L EVEN ASSUME L IS ODD AND POSSIBLY MISSING THE LAST CHARACTER
- #70: CYCLE DECOMPOSITION AND ORDER ARE UNAFFECTED BY FINAL CHARACTER IF L EVEN ASSUME L IS ODD AND POSSIBLY MISSING THE LAST CHARACTER
- #72: GO TO TCPERM TO LOOK AT THESE AND OTHER INITIAL CYCLES DO ONE WHERE L = 2^K-1 EXPLAIN PROOF OF THEOREM 5 USING RFC FORMULA
- #73: GO TO TCPERM TO LOOK AT THESE AND OTHER INITIAL CYCLES DO ONE WHERE L = 2^K-1 EXPLAIN PROOF OF THEOREM 5 USING RFC FORMULA
- #74: GO TO TCPERM TO LOOK AT THESE AND OTHER INITIAL CYCLES DO ONE WHERE L = 2^K-1 EXPLAIN PROOF OF THEOREM 5 USING RFC FORMULA
- #75: GO TO TCPERM TO LOOK AT THESE AND OTHER INITIAL CYCLES DO ONE WHERE L = 2^K-1 EXPLAIN PROOF OF THEOREM 5 USING RFC FORMULA
- #76: GO TO TCPERM TO LOOK AT THESE AND OTHER INITIAL CYCLES DO ONE WHERE L = 2^K-1 EXPLAIN PROOF OF THEOREM 5 USING RFC FORMULA
- #77: GO TO TCPERM TO LOOK AT THESE AND OTHER INITIAL CYCLES DO ONE WHERE L = 2^K-1 EXPLAIN PROOF OF THEOREM 5 USING RFC FORMULA
- #78: GO TO TCPERM TO LOOK AT THESE AND OTHER INITIAL CYCLES DO ONE WHERE L = 2^K-1 EXPLAIN PROOF OF THEOREM 5 USING RFC FORMULA
- #79: GO TO TCPERM TO LOOK AT THESE AND OTHER INITIAL CYCLES DO ONE WHERE L = 2^K-1 EXPLAIN PROOF OF THEOREM 5 USING RFC FORMULA
- #80: TCPERM -- LOOK AT 2,11 AND OTHERS WHERE LENGTH ≠ POWER OF 2 - 1 THM 6 PROOF USES ADDITIONAL MACHINERY FOUND IN PAPER; TOO LENGTHY TO PRESENT HERE TODAY log_2 L = largest power of 2 less than L = how many powers of 2 are in IC; must be at least 1 more than these
- #81: TCPERM -- LOOK AT 2,11 AND OTHERS WHERE LENGTH ≠ POWER OF 2 - 1 THM 6 PROOF USES ADDITIONAL MACHINERY FOUND IN PAPER; TOO LENGTHY TO PRESENT HERE TODAY log_2 L = largest power of 2 less than L = how many powers of 2 are in IC; must be at least 1 more than these
- #82: TCPERM -- LOOK AT 2,11 AND OTHERS WHERE LENGTH ≠ POWER OF 2 - 1 THM 6 PROOF USES ADDITIONAL MACHINERY FOUND IN PAPER; TOO LENGTHY TO PRESENT HERE TODAY log_2 L = largest power of 2 less than L = how many powers of 2 are in IC; must be at least 1 more than these
- #83: ILLUSTRATE WITH ANOTHER WHERE CYCLE LENGTHS ≠
- #84: ILLUSTRATE WITH ANOTHER WHERE CYCLE LENGTHS ≠
- #85: ILLUSTRATE WITH ANOTHER WHERE CYCLE LENGTHS ≠
- #86: ILLUSTRATE WITH ANOTHER WHERE CYCLE LENGTHS ≠
- #87: ILLUSTRATE WITH ANOTHER WHERE CYCLE LENGTHS ≠
- #88: ILLUSTRATE WITH ANOTHER WHERE CYCLE LENGTHS ≠
- #89: ILLUSTRATE WITH ANOTHER WHERE CYCLE LENGTHS ≠
- #90: ILLUSTRATE WITH ANOTHER WHERE CYCLE LENGTHS ≠
- #104: “ORBIT-STABILIZER THEOREM”
- #105: “ORBIT-STABILIZER THEOREM”
- #106: “ORBIT-STABILIZER THEOREM”
- #107: ALSO NOTE STABILIZER OF 5: {1, 22, 29, 8} o(1)/F_5 = {1, 18, 9} -> {5, 20, 10} MAPPING MULTIPLIES BY 5 mod 35 So orbits of non-1 elements are represented by cosets in o(1)/F
- #108: ALSO NOTE STABILIZER OF 5: {1, 22, 29, 8} o(1)/F_5 = {1, 18, 9} -> {5, 20, 10} MAPPING MULTIPLIES BY 5 mod 35 So orbits of non-1 elements are represented by cosets in o(1)/F