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16 results for “cryptography”

Formulae (16)

Modular Exponentiation

c = m^e \bmod n

Core operation of RSA encryption — raise a message to a power, modulo n.

Cryptography & SecurityAdvanced

RSA Decryption

m = c^d \bmod n

Recovers the message using the private exponent d.

Cryptography & SecurityIntermediate

Euler's Totient

\varphi(n) = (p-1)(q-1)

Counts integers below n coprime to it, for n = pq — used to make RSA keys.

Cryptography & SecurityAdvanced

Shannon Entropy

H = -\sum_i p_i \log_2 p_i

Average information content — and the theoretical strength of a random source.

Cryptography & SecurityIntermediate

Password Entropy

H = L \log_2 R

Bits of security from password length and character-set size.

Cryptography & SecurityIntermediate

Key Space Size

K = 2^b

Number of possible keys for a b-bit key.

Cryptography & SecurityAdvanced

Birthday Bound

n \approx 1.177\sqrt{2^b}

Collisions become likely after about √ of the hash space.

Cryptography & SecurityBasic

Hamming Distance

d(x,y) = \sum_i [x_i \ne y_i]

Number of positions at which two strings differ.

Cryptography & SecurityAdvanced

Hamming Code Parity Bits

2^r \ge m + r + 1

Minimum parity bits r needed to protect m data bits.

Cryptography & SecurityBasic

XOR Cipher

c = m \oplus k

Bitwise XOR of message and key; XOR again with k to decrypt.

Cryptography & SecurityAdvanced

Diffie–Hellman Shared Secret

s = B^a \bmod p

Two parties derive the same secret over a public channel.

Cryptography & SecurityIntermediate

Brute-Force Time

t = \frac{K}{r}

Time to try every key at a given guess rate.

Cryptography & SecurityAdvanced

Avalanche Effect Target

E[\Delta] = \frac{n}{2}

A good hash flips about half its output bits when one input bit changes.

Cryptography & SecurityBasic

Caesar Cipher Shift

c = (m + k) \bmod 26

Shift each letter forward by k positions.

Cryptography & SecurityAdvanced

Collision Probability

P \approx \frac{n^2}{2N}

Approximate chance of a collision among n items in space N.

Quantum ComputingAdvanced

Shor's Factoring Complexity

O((\log N)^3)

Time complexity for Shor's algorithm to factor an integer N on a quantum computer.