Cryptography

Algorithms, Digital Signatures, and Pragmatics

Arun A Tharuvai

CSC8530

November 25, 2003

Introduction

• Cryptographic Algorithms

• Digital Signatures

• Cryptography Pragmatics

Cryptographic Algorithms

• Convert plaintext message M to ciphertext {M}K using an encryption algorithm E, and a key K

• E(K,M) = {M} K

• Secrecy should lie in the key, not the algorithm

Cryptographic Algorithms

• Symmetric Algorithms (Secret key)– Same key is used for encryption and decryption, and

shared by both parties

• Asymmetric Algorithms (Public key)– A public key, used by anyone for encryption

– A corresponding private key is used for decryption.

Cryptographic Algorithms

• Block Ciphers– Operate on fixed-size blocks of data. 64 bits is a common size.

Useful for non-realtime data, including email and data.

• Stream Ciphers– Operate on single bits of data. A stream of bits is used by a function

known as a keystream generator. In practice very similar to block ciphers.

• CBC mode– Each plain text block is combined with the preceding ciphertext block

using XOR before it is encrypted

– Prevents similar blocks from encrypting to the same result.

Design Techniques

• Confusion– Use of reversible mathematical operations

like XOR and bitshifting to combine each block of plaintext with a key

• Diffusion– Use of techniques like transposing portions

of each plaintext to reduce regular patterns in plaintext

Secret-key Algorithms

• TEA

• DES

• IDEA

• AES (Rijndael)

DES

• Data Encryption Standard

• Designed to be fast in hardware and slow in software. 56-bit key is used to encrypt 64 bit blocks

• Bit permutation, combined with 16 rounds of performing the XOR operation with different 48-bit subsets of the key.

• Chosen in 1977. In 1998, the EFF showed that it was possible to build a machine to crack DES keys in < 3 days for under $250,000, including design costs.

• Triple DES (3DES) – applies DES three times using 2 keys, as follows: E3DES(K1,K2,M) = EDES (K1,DDES (K2,EDES (K1,M))) and is effectively as strong as a 112-bit private key. However, it’s very slow.

Public-key Algorithms

• RSA

• Diffie-Helman

• El-Gamal

• Elliptic curve algorithms

RSA

• Most widely used public key encryption standard.

• Based upon the difficulty of factoring the product of two very large numbers.

• To generate a key-pair

• Choose two large prime numbers, P and Q. N = P * Q Z = (P-1)* (Q-1) d is any number relatively prime to Z. e is a number, such that e*d = 1 mod Z The encryption key is e,N and the decryption key is the pair d,N To encrypt plaintext M, E(e,N,M) = Me mod N To decrypt ciphertext c, D(d,N,C) = cd mod N

Hybrid Protocols

• SSL/TLS

– Negotiable encryption and authentication algorithms.

• SSH

• PGP/GPG

– Uses RSA to encrypt a secret key which is then used for encrypting a document via IDEA, or 3DES

Properties of Digital Signatures

• Authentic

• Unforgeable

• Non-repudiable

Digital Signatures

• Digital Signing

• Digest Functions

Public Key Signatures

• A computes a digest of M, H(M), and encrypts it with his private key.

• A then sends it along with M to B

• B then uses A’s K_pub to decrypt

Secret Key signatures

• Useful when two participants have already agreed upon shared key via a different channel, or public key cryptography.

• A concatenates M with K, and computes the digest, H(M+K) = h, sending M,h

• B concatenates M with K, H(M+K) = h’ comparing with h. If they’re equal the message was sent by someone with K.

Secure digest Functions – properties

• Ease of computing hash

• Difficulty of generating message from hash

• Difficulty of finding another message that maps to the same hash value

Secure Digest Functions

• MD5

• SHA

• Symmetric algorithm using CBC

Secure Digest Functions

• Birthday attack

I am writing {this memo | } to { demand | request | unform you} that {Fred | Mr. Fred Jones} {must | } be { fired | terminated} {at once | immediately}. As the {July 11| 11 July} {memo| memorandum} {from | issued by} {personnel| human resources} states, to meet {our | the corporate} {quarterly | third quarter} budget {targets | goals}, {we must eliminate all discretionary spending | all discretionary spending must be eliminated.}

{Despite | Ignoring } that {memo | memorandum | order }, Fred { ordered | purchased } {PostIts | nonessential supplies} in a flagrant disregard for the company’s {budgetary crisis | current financial difficulties}.

Certificate standards, Authorities

• X.509

• SPKI

Cryptography Pragmatics

• Performance

• Legal Issues

• Key sizes and speed

Cryptographic PerformanceKey/hash size

Speed (kb/s)

Secret

TEA 128 700

DES 56 350

3DES 112 120

IDEA 128 700

Public

RSA 512 7

RSA 2048 1

Message Digest

MD5 128 1740

SHA 160 750

Legal and Political Issues

• Until recently, there were severe restrictions on cryptography, especially export controls, including teaching of such knowledge to foreign nationals in the US.

• The FBI and NSA wanted restrictions for ease of decrypting both foreign and domestic communications.

• Algorithms approved for export were limited to 40-bit encryption. Easily breakable with modern technology.

• Proposals in the mid-90s called for mandatory key-recovery for products exported, and even those used internally.

• Currently, export controls now only exist on the T-7 countries.

• As of 2000, Cryptographic source code can be exported as long as copies are sent to the Bureau of Industry and Security of Commerce department.

Conclusion

• The end

References

• Charlie Kaufman, Radia Perlman, Mike Speciner, Network Security: Private Communication in a Public World, Prentice Hall, Inc, Upper Saddle River, New Jersey, 1995 505pp.

• Schneier, B., Applied Cryptography, 2nd ed., John Wiley & Sons, New York, 1996, 675 pp.

• Electric Frontier Foundation, Cracking DES: Secrets of Encryption Research, Wiretap Politics, and Chip Design, O’Reilly & Associates, Sevastopol, California, 1998, online at http://cryptome.org/cracking-des.htm

• George Coulouris, Jean Dollimore, Tim Kindberg, Distributed Systems: Concepts and Design 3rd ed, Addison-Wesley, New York, 2001, pp 272-291.