The Cracking of the Cipher Challenge

10 steps to £10,000

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“The most incomprehensible thing about the universe is that it is comprehensible.”

Albert Einstein

Front cover & quotes

We are 12 billion light-years from the edge,

That’s a guess,

No one can ever say it’s true,

But I know that I will always be with you.

We are 13.7 billion light-years from the edge of the observable universe,

That’s a good estimate with well-defined error bars,

And with the available information, I predict that I will always be with you

The Cracking of the Cipher Challenge

10 steps to £10,000

www.simonsingh.net

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THE 10 STAGES

6. Playfair cipher 7. ADFGVX cipher 8. Enigma cipher 9. DES encryption 10. RSA

1.  Simple substitution 2.  Caesar cipher 3.  Homophonic cipher 4.  Vigenère cipher 5.  Book cipher

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STAGE 1 CIPHERTEXT

BT JPX RMLX PCUV AMLX ICVJP IBTWXVR CI

M LMT’R PMTN, MTN YVCJX CDXV MWMBTRJ

JPX AMTNGXRJBAH UQCT JPX QGMRJXV CI

JPX YMGG CI JPX HBTW’R QMGMAX; MTN JPX

HBTW RMY JPX QMVJ CI JPX PMTN JPMJ

YVCJX. JPXT JPX HBTW’R ACUTJXTMTAX YMR

APMTWXN, MTN PBR JPCUWPJR …..

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The start of the first page of Al-Kindi’s

manuscript c. 850 AD

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LETTER FREQUENCIES

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UNUSUAL MESSAGE

Today, by radio, and also on giant hoardings, a rabbi, an admiral notorious for his links to masonry, a trio of cardinals and a trio, too, of politicians inform us all of how our country now risks dying of starvation.

STAGE 5: BOOK CIPHER TEXT 109 182 6 11 88 214 74 77 153 109 195 76 37 188 166 188 73 109 15 208 42 5 217 78 209 147 9 80 169 109 22 96 169 3 29 214 9 198 77 112 8 30 117 124 86

73 124 86 96 73 177 50 161

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How does a book cipher work?

1. Pick a book and number the letters in it. It was the best of times it was the worst of times … 12 345 678 9… … 17 …

2. Substitute each letter in a message with matching number M e e t m e a t m i d n i g h t … 8 2 … 17 10

STAGE 8: ENIGMA CIPHER

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Rotor order 3! = 6 Rotor orientations 263 = 17,576 Rotor turnover points 262 = 676 Plugboard options = 1011 Total no. of keys = 1019

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STAGE 9: DATA ENCRYPTION STANDARD

Formally published on 15 January, 1977 56‑bit key ‑ 1017 keys, less than Enigma. How does it work? 64 bit blocks split into 2 x 32 bits, L0 & R0. RO is 'mangled' added to LO to create R1. RO becomes L1. Repeat 16 times, to give L16 & R16, the ciphertext. Each round of mangling is different, according to key* No publicly known shortcuts. Must search key space. Even invulnerable against differential cryptanalysis.

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CIPHER CHALLENGE CALENDAR

Stage 1 Sept 1999 The first 4 stages fell within a matter of days. A medical researcher and a schoolgirl (age 14) simultaneously crack stages 1-4 and head the

leader board.

Stage 2 Sept 1999

Stage 3 Sept 1999

Stage 4 Sept 1999

Stage 5 Dec 1999 Stages 6-8 are cracked within a couple of weeks, but nobody can crack stage 5.

Eventually, a Cambridge mathematician discovers the key text and claims stages 1-8.

Stage 6 Dec 1999

Stage 7 Dec 1999

Stage 8 Dec 1999

Stage 9

Apr 2000 Jim Gillogly cracks 1-4 & 6-9 early, but has to team up with John Palagyi to get stage 5.

Stage 10 Oct 2000 ?

STAGE 10: THE RSA CIPHER

What is RSA? •  Public key cryptography solves the key distribution problem. •  A technique for sharing a secret between remote strangers. How does RSA work? •  A mathematical padlock based on ease of multiplying versus the

immense difficulty of factoring. •  In this case you need to factor: 10742 78829 12665 65907

17841 12799 42116 61266 39217 94753 29458 88778 17210 35546 41509 80121 87903 38329 26235 28109 07506 72083 50494 19964 33143 42555 83344 01855 80898 94268 92463.

•  Would be the toughest cipher to be cracked in public.

How do you factor giant numbers?

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THE AMAZING JUGGLING SWEDES (a.k.a. the stealth Swedes: Fredrik Almgren, Gunnar Andersson,

Torbjorn Granlund, Lars Ivansson, Staffan Ulfberg)

•  Set to work on stage 10, succeed in generating dependencies

•  No access to expensive supercomputers •  Rewrite programme for Compaq quad

processor ES40 system •  Oct 5 they discover the two factors!!!!!!

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Triple Des

Key 1 encrypt Key 1 encrypt

Key 2 decrypt

Key 1 encrypt

Key 1 decrypt

Key 2 encrypt

Single Des !