Cryptography in Modern Communication Systems

Cryptography in Modern
Communication Systems
DSPS Fest ‘99
August 5th
by
Daniel Bailey 1 , William Cammack 2 , Jorge Guajardo 1 , and Christof Paar 1
1
Cryptography and Information Security (CRIS) Laboratory
WPI - ECE Department, Worcester MA 01609
2
DSP R&D Center
Texas Instruments Inc., P.O. Box 655303, MS 8374, Dallas, TX 75265

Overview
• Why Cryptography?
• Providing Information Security
• Secret-key Cryptography
• Public-key Cryptography
• Cryptography and DSPs
• State of the Art
• The SecuriTI Library
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Why Cryptography?
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Why Cryptography?
Our Information society relies increasingly on
technologies such as
•Internet (email, home shopping, … )
•wireless applications
•electronic commerce and data transfers …
Unprotected information systems pose a major threat
to individuals and society
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Providing Information Security
• Major tool for information security
Cryptography
Cryptography
secret-key
public-key
(BC … 1976) (Diffie-Hellman, 1976)
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Secret-key Cryptography
x
e
y=e k (x)
d
x
Alice
key k
key k
Bob
Oscar
Classical Problem: How to get the secret key to the other party?
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Secret-key Cryptography
• Until 1998, DES
– Optimized for hardware.
– Designed in secret.
• Now AES
– Many candidate algorithms optimized for
software.
– Designed in the open.
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Secret-key Cryptography
• AES history:
– Summer 1998 AES1, initial candidates
– April 1999, AES2 ends Round 1
comment period
– April 2000, AES3
• Example of AES Candidates’ Performance (200 MHz Pentium clock cycles,
128 bit encryption, in C)
Algorithm Company NIST Gladman
CAST-256 Entrust Technologies 2169 633
MARS IBM 807 369
RC6 RSA 636 270
RIJNDAEL J. Daemen & V. Rijmen 809 374
SAFER+ Cylinc Corporation 2095 1722
TWOFISH B. Schneier et. Al. 973 376
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Remember this?
x
e
y=e k (x)
d
x
Alice
key k
key k
Bob
Oscar
Classical Problem: How to get the secret key to the other party?
DSPS Fest '99 Cryptograhy in Modern Communication Systems 9

Public-key Cryptography
x
e
y=e PubK (x)
d
x
Alice
PubK Bob
PrivK Bob
Bob
Oscar
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Public-key Cryptography
• Based on hard mathematical problems
– Beware! Not easy to find
• 3 different families of algorithms
– Integer Factorization (RSA)
– Discrete Logarithm (Diffie-Hellman, DSA)
– Elliptic Curves (ECDSA)
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Public-key Cryptography
• Equivalent bit lengths of different algorithms
RSA DL ECC
512 512 106
1024 1024 163
2048 2048 211
• Computational Challenges
– Complicated Algorithms
– Most common operation: x e mod n
– Computationally expensive
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Did we solve the problem?
Given
: large
prime
p
and
an integer α
Alice
Bob
random private key
random private key
a ∈(1,2,
K , p −1)
a ∈ (1,2, K,
p −1)
b
A
public - key
A
b A
b B
a A a
= α mod p
b = α B
mod p
B
public - key
B
K =
b
a
B
A
= ( α
= α
a
a
B
B
a
A
a
a B
A
)
K = bA
= ( α
a
mod p
= α
y
y = eK ( x)
x = d
K
( y)
a
A
A
a
B
)
a
B
mod
p
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DSPs and Cryptography
• 1986, Barret: RSA on the TI TMS320
– 2.6 sec for a 512-bit exponentiation at 20 MHz.
• 1990, Dusse and Kaliski: RSA and DES on the
Motorola DSP56000
– 11.6 kbits/s (4.6kbits/s) for a 512-bit exponentiation.
– 350 kbits/s for DES.
– Both results at 20 MHz.
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State of the Art
Op 1024-RSA 2048-RSA 192-ECDSA
CHES’99 on the sign 11.7 ms 84.6 ms 1.67 ms
TI TMS320C6201 ver 1.2 ms 4.5 ms 6.28 ms
Point mult ------ ------ 4.64 ms
ANT 3rd Int. Symp sign 43.3 ms ------ 6.3 ms
Pentium 200 MHz ver 0.65 ms ------ 26 ms
Point mult ------ ------ 21.1 ms
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The SecuriTI Library
• Comprehensive cryptographic library for the TI
TMS320C6201 and TMS320C54x
• Includes
– High Speed multi-precision library
– Public-key library (RSA, DSA, ECC)
– Block cipher library (DES and AES)
– Hash function library (SHA-1, MD5)
• Modular design
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Any Questions?
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