Pre-1976 cryptography The revolution of 1976 Modern cryptography

Photo: V. Lee

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Cryptography

Simon R. Blackburn

Royal Holloway, University of London

26th January 2009

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

This talk

I Pre-1976 cryptography

I The revolution of 1976

I Modern cryptography

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Secrecy and scrambling

Cryptography used to be all about secrecy and was mainly used bygovernments.

I Secrecy: Shaving the head of a slave. (Histiaeus andAristagoras of Miletus, approx 500BC)

I Scrambling: The Caesar Cipher (approx 50BC) KHOOR!

I Keys: Leon Battista Alberti; the Argenti family (approx 1460- 1590)

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Secrecy and scrambling

Cryptography used to be all about secrecy and was mainly used bygovernments.

I Secrecy: Shaving the head of a slave. (Histiaeus andAristagoras of Miletus, approx 500BC)

I Scrambling: The Caesar Cipher (approx 50BC) KHOOR!

I Keys: Leon Battista Alberti; the Argenti family (approx 1460- 1590)

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Secrecy and scrambling

Cryptography used to be all about secrecy and was mainly used bygovernments.

I Secrecy: Shaving the head of a slave. (Histiaeus andAristagoras of Miletus, approx 500BC)

I Scrambling: The Caesar Cipher (approx 50BC) KHOOR!

I Keys: Leon Battista Alberti; the Argenti family (approx 1460- 1590)

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Secrecy and scrambling

Cryptography used to be all about secrecy and was mainly used bygovernments.

I Secrecy: Shaving the head of a slave. (Histiaeus andAristagoras of Miletus, approx 500BC)

I Scrambling: The Caesar Cipher (approx 50BC) KHOOR!

I Keys: Leon Battista Alberti; the Argenti family (approx 1460- 1590)

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

The science of cryptography

Auguste Kerckhoffs La Cryptographie Militaire, 1883.

Before Kerckoffs: security through obscurity

Kerckoffs’ Law: ‘Compromise of the system should notinconvenience the correspondents’ or:

Secrecy resides entirely in the key

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

The science of cryptography

Auguste Kerckhoffs La Cryptographie Militaire, 1883.

Before Kerckoffs: security through obscurity

Kerckoffs’ Law: ‘Compromise of the system should notinconvenience the correspondents’ or:

Secrecy resides entirely in the key

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

The science of cryptography

Auguste Kerckhoffs La Cryptographie Militaire, 1883.

Before Kerckoffs: security through obscurity

Kerckoffs’ Law: ‘Compromise of the system should notinconvenience the correspondents’ or:

Secrecy resides entirely in the key

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Perfect secrecy

Gilbert S. Vernam (1917): the one-time pad.

Claude E. Shannon (1948/49): The one time pad is perfectlysecure!

Problem: How do both sender and recipient know the key?

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Perfect secrecy

Gilbert S. Vernam (1917): the one-time pad.

Claude E. Shannon (1948/49): The one time pad is perfectlysecure!

Problem: How do both sender and recipient know the key?

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Perfect secrecy

Gilbert S. Vernam (1917): the one-time pad.

Claude E. Shannon (1948/49): The one time pad is perfectlysecure!

Problem: How do both sender and recipient know the key?

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Whit Diffie and Martin Hellman

Diffie and Hellman (1976) solved this problem!

I Two parties: Alice and Bob

I All communications monitored by Eve.

I Alice and Bob come to know the same key; Eve doesn’t knowthe key

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Whit Diffie and Martin Hellman

Diffie and Hellman (1976) solved this problem!

I Two parties: Alice and Bob

I All communications monitored by Eve.

I Alice and Bob come to know the same key; Eve doesn’t knowthe key

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Whit Diffie and Martin Hellman

Diffie and Hellman (1976) solved this problem!

I Two parties: Alice and Bob

I All communications monitored by Eve.

I Alice and Bob come to know the same key; Eve doesn’t knowthe key

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Whit Diffie and Martin Hellman

Diffie and Hellman (1976) solved this problem!

I Two parties: Alice and Bob

I All communications monitored by Eve.

I Alice and Bob come to know the same key; Eve doesn’t knowthe key

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Modular arithmetic

Suppose we only know about the numbers 0, 1, 2, 3, . . . , 10, 11, 12.

I 22 = 4

I 23 = 4× 2 = 8

I 24 = 8× 2 = 16 = 3 (subtract 13)

I Using 28 = 9, we calculate 29 = 9× 2 = 18 = 5.

i 1 2 3 4 5 6 7 8 9 10 11 12 13 14

2i 2 4 8 3 6 12 11 9 5 10 7 1 2 4

If we are just given 2i , it is difficult to find i .If we are just given i , it is easy to find 2i .

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Modular arithmetic

Suppose we only know about the numbers 0, 1, 2, 3, . . . , 10, 11, 12.

I 22 = 4

I 23 = 4× 2 = 8

I 24 = 8× 2 = 16 = 3 (subtract 13)

I Using 28 = 9, we calculate 29 = 9× 2 = 18 = 5.

i 1 2 3 4 5 6 7 8 9 10 11 12 13 14

2i 2 4 8 3 6 12 11 9 5 10 7 1 2 4

If we are just given 2i , it is difficult to find i .If we are just given i , it is easy to find 2i .

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Modular arithmetic

Suppose we only know about the numbers 0, 1, 2, 3, . . . , 10, 11, 12.

I 22 = 4

I 23 = 4× 2 = 8

I 24 = 8× 2 = 16 = 3 (subtract 13)

I Using 28 = 9, we calculate 29 = 9× 2 = 18 = 5.

i 1 2 3 4 5 6 7 8 9 10 11 12 13 14

2i 2 4 8 3 6 12 11 9 5 10 7 1 2 4

If we are just given 2i , it is difficult to find i .If we are just given i , it is easy to find 2i .

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

How to exchange keys

Alice Eve Bob

Pick i andcalculate 2i −→ 2i

Pick j and2j ←− calculate 2j

Calculate (2j)i Calculate (2i )j

The common key: the secret number 2ij

Eve only knows 2i and 2j . How can she calculate 2ij from this?

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

How to exchange keys

Alice Eve Bob

Pick i andcalculate 2i −→ 2i

Pick j and2j ←− calculate 2j

Calculate (2j)i Calculate (2i )j

The common key: the secret number 2ij

Eve only knows 2i and 2j . How can she calculate 2ij from this?

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Photo: D. Spisak

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

What else can you do?

Modern cryptography is about authenticity as well as secrecy, andis now used by business as much as government.

I Public key cryptography: RSA (1977) ElGamal (1984)

I Digital signatures: RSA (1977)

I Zero knowledge: Goldwasser, Micali, Rackoff (1985)

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

What else can you do?

Modern cryptography is about authenticity as well as secrecy, andis now used by business as much as government.

I Public key cryptography: RSA (1977) ElGamal (1984)

I Digital signatures: RSA (1977)

I Zero knowledge: Goldwasser, Micali, Rackoff (1985)

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

What else can you do?

Modern cryptography is about authenticity as well as secrecy, andis now used by business as much as government.

I Public key cryptography: RSA (1977) ElGamal (1984)

I Digital signatures: RSA (1977)

I Zero knowledge: Goldwasser, Micali, Rackoff (1985)

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

What else can you do?

Modern cryptography is about authenticity as well as secrecy, andis now used by business as much as government.

I Public key cryptography: RSA (1977) ElGamal (1984)

I Digital signatures: RSA (1977)

I Zero knowledge: Goldwasser, Micali, Rackoff (1985)

S.R. Blackburn Royal Holloway

Cryptography

Pre-1976 cryptography The revolution of 1976 Modern cryptography

Many thanks

The slides of this talk will be available on my home page:

http://www.ma.rhul.ac.uk/sblackburn

S.R. Blackburn Royal Holloway

Cryptography