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RSA

https://en.wikipedia.org/wiki/RSA_(cryptosystem)

RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem that is widely used for secure data transmission. It is also one of the oldest. The acronym RSA comes from the surnames of Ron Rivest, Adi Shamir, and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly, in 1973 at GCHQ (the British signals intelligence agency), by the English mathematician Clifford Cocks. That system was declassified in 1997.

In a public-key cryptosystem, the encryption key is public and distinct from the decryption key, which is kept secret (private). An RSA user creates and publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers are kept secret. Messages can be encrypted by anyone, via the public key, but can only be decoded by someone who knows the prime numbers.

Explanation

GOST

https://en.wikipedia.org/wiki/GOST_(hash_function)

The GOST hash function, defined in the standards GOST R 34.11-94 and GOST 34.311-95 is a 256-bit cryptographic hash function. It was initially defined in the Russian national standard GOST R 34.11-94 Information Technology – Cryptographic Information Security – Hash Function. The equivalent standard used by other member-states of the CIS is GOST 34.311-95.

Larger key sizes increase security

https://en.wikipedia.org/wiki/Key_size

Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fastest known attack against an algorithm), since the security of all algorithms can be violated by brute-force attacks. Ideally, the lower-bound on an algorithm's security is by design equal to the key length (that is, the security is determined entirely by the keylength, or in other words, the algorithm's design doesn't detract from the degree of security inherent in the key length). Indeed, most symmetric-key algorithms are designed to have security equal to their key length. However, after design, a new attack might be discovered. For instance, Triple DES was designed to have a 168 bit key, but an attack of complexity 2112 is now known (i.e. Triple DES now only has 112 bits of security, and of the 168 bits in the key the attack has rendered 56 'ineffective' towards security). Nevertheless, as long as the security (understood as 'the amount of effort it would take to gain access') is sufficient for a particular application, then it doesn't matter if key length and security coincide. This is important for asymmetric-key algorithms, because no such algorithm is known to satisfy this property; elliptic curve cryptography comes the closest with an effective security of roughly half its key length.

Whitening

https://en.wikipedia.org/wiki/Key_whitening

In cryptography, key whitening is a technique intended to increase the security of an iterated block cipher. It consists of steps that combine the data with portions of the key.

The most common form of key whitening is xor-encrypt-xor -- using a simple XOR before the first round and after the last round of encryption.

The first block cipher to use a form of key whitening is DES-X, which simply uses two extra 64-bit keys for whitening, beyond the normal 56-bit key of DES. This is intended to increase the complexity of a brute force attack, increasing the effective size of the key without major changes in the algorithm. DES-X's inventor, Ron Rivest, named the technique whitening.

Explanation

Speed

Symmetric key systems are considerably faster than asymmetric key systems but have issues with proper key distribution, controlling keys as more users need to communicate, and cannot provide non-repudiation or authenticity.

Explanation

Password salting

https://en.wikipedia.org/wiki/Salt_(cryptography)#Benefits

Salts also combat the use of hash tables and rainbow tables for cracking passwords. A hash table is a large list of pre-computed hashes for commonly used passwords. For a password file without salts, an attacker can go through each entry and look up the hashed password in the hash table or rainbow table. If the look-up is considerably faster than the hash function (which it often is), this will considerably speed up cracking the file. However, if the password file is salted, then the hash table or rainbow table would have to contain "salt . password" pre-hashed. If the salt is long enough and sufficiently random, this is very unlikely. Unsalted passwords chosen by humans tend to be vulnerable to dictionary attacks since they have to be both short and meaningful enough to be memorized. Even a small dictionary (or its hashed equivalent, a hash table) is significant help cracking the most commonly used passwords. Since salts do not have to be memorized by humans they can make the size of the rainbow table required for a successful attack prohibitively large without placing a burden on the users.

Explanation

Elliptic Curve

https://en.wikipedia.org/wiki/Elliptic-curve_cryptography

For current cryptographic purposes, an elliptic curve is a plane curve over a finite field (rather than the real numbers) which consists of the points satisfying the equation:

SHA2

https://en.wikipedia.org/wiki/Collision_resistance

Collision resistance is a property of cryptographic hash functions: a hash function H is collision-resistant if it is hard to find two inputs that hash to the same output; that is, two inputs a and b where a ≠ b but H(a) = H(b). The pigeonhole principle means that any hash function with more inputs than outputs will necessarily have such collisions; the harder they are to find, the more cryptographically secure the hash function is.

Due to the Birthday Problem, for a hash function that produces an output of length n bits, the probability of getting a collision is 1/2^n/2.

So, just looking for a hash function with larger "n".

The SHA-2 family consists of six hash functions with digests (hash values) that are 224, 256, 384 or 512 bits: SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, SHA-512/256.