Modulo arithmetic
Modulo arithmetic is arithmetic in which values are identified as equivalent when they differ by a multiple of a fixed modulus.
Hacking Cryptography
Arithmetic in which values are identified according to their remainders modulo a specified integer.
- How it is used
- Uses modular reduction to implement linear congruential generator state transitions and recover their hidden parameters.
- How deep it goes
- Explains recurrence, inverses, negative remainders, and recovery equations, then stops short of broader modular-arithmetic theory.
- Examples
- Demonstrates clock wraparound, 7’s inverse modulo 12, Go’s negative remainder, and LCG parameter-recovery code.
- What you can do after
- Diagnose/debug with it by implementing modular state updates and handling inverses and negative remainders correctly.
Real-World Cryptography
Modular arithmetic is arithmetic in which values are identified according to their remainders after division by a fixed modulus.
- How it is used
- Uses wrapped arithmetic and modular multiplication as foundations for Diffie–Hellman key exchange.
- How deep it goes
- Defines remainders, demonstrates multiplication and inverses, and connects the operation to multiplicative groups.
- Examples
- Uses a clock analogy, division by 5, and the product 3 × 2 modulo 5.
- What you can do after
- Apply modular reduction to simple divisions and multiplications, and identify multiplicative inverses modulo 5.
Read how Real-World Cryptography explains modulo arithmetic →
Grokking Data Structures
Modular arithmetic is arithmetic in which values are considered equivalent when they have the same remainder under a specified modulus.
- How it is used
- Uses remainders to map virtual circular-queue positions back to valid array indexes.
- How deep it goes
- Defines remainders through an eight-element array example and stops short of broader mathematical treatment.
- Examples
- Uses 8 % 8 = 0, 9 % 8 = 1, and virtual index 8 wrapping to array index 0.
- What you can do after
- Apply it via the modulo operator to convert virtual circular-queue indexes into safe array positions.
Read how Grokking Data Structures explains modulo arithmetic →
Related concepts
- size_timplemented by · size_t is an unsigned integer type in C and C++ used to represent object sizes and related counts.
- dataset splitused by · A dataset split is the division of a dataset into distinct subsets assigned different purposes, such as training, validation, or testing.
- integer wraparoundimplemented by · Integer wraparound is arithmetic behavior in which an out-of-range fixed-width integer result cycles or is reduced modulo the type’s representable range.
- elliptic curve point additionused by · Elliptic-curve point addition combines two curve points according to the curve's group law to produce another curve point.
- unsigned integerimplemented by · An unsigned integer is an integer type or representation whose values are nonnegative, with its representable range determined by its bit width and applicable rules.
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