Crate octavo_crypto

Cryptosystems primitives

Cryptosystem is a suite of algorithms that describe particular security service, in most cases used for achieving confidentiality. Typically this is set of three algorithms: key generation, encryption function and decryption function.

Mathematically it can be described as tuple (P, C, K, E, D), where:

• P is a set called “plaintext space”
• C is a set called “ciphertext space”
• K is a set called “key space”
• E is a set of functions e :: k -> p -> c called “encryption functions”
• D is a set of functions d :: k -> c -> p called “decryption functions”

For each ke ∈ K there is kd ∈ K such that d(kd, e(ke, p)) = p. If kd = ke then we call that “symmetric cipher” otherwise we call it “asymmetric cipher”.

In practise we use “asymmetric ciphers” for which computing kd from ke is computationally hard or impossible.

Kerckhoff’s Principle

A cryptosystem should be secure even if everything about the system, except the key, is public knowledge.

This is basic law for moder cryptography. Unfortunately many of people understand this as “keeping cryptosystem hidden is bad”. That is big misunderstanding of what that principle states. It is nothing bad to keep cryptosystem in secret, it is yet another obstacle to overcome by eavesdropper, just don’t rely on secrecy.

Key lengths

According to ECRYPT II Yearly Report on Algorithms and Keysizes this table presents key-sizes equivalence between types of algorithms:

Symmetric	Factoring Modulus	Discrete Logarithm	Elliptic Curves
48	480	480/96	96
56	640	640/112	112
64	816	816/128	128
80	1248	1248/160	160
112	2432	2432/224	224
128	3248	3248/256	256
160	5312	5312/320	320
192	7936	7936/384	384
256	15424	15424/512	512

Security table

Levels of security according to ECRYPT II Yearly Report on Algorithms and Keysizes

Security Level	Security (bits)	Protection	Comment
1.	32	Attacks in “real-time” by individuals	Only acceptable for auth. tag size
2.	64	Very short-term protection against small organizations	Should not be used for confidentiality in new systems
3.	72	Short-term protection against medium organizations, mediumterm protection against small organizations
4.	80	Very short-term protection against agencies, long-term prot. against small organizations	Smallest general-purpose level, <= 4 years protection
5.	96	Legacy standard level	2-key 3DES restricted to ~10^6 plaintext/ciphertexts, ~10 years protection
6.	112	Medium-term protection	~20 years protection
7.	128	Long-term protection	Good, generic application-indep. recommendation, ~30 years protection
8.	256	“Foreseeable future”	Good protection against quantum computers unless Shor’s algorithm applies

We recommend at least 128-bit security for general purpose.

Modules

asymmetric

Public-key (asymmetric) cryptosystems

block

Block cryptosystems

prelude

stream

Stream cryptosystems