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Act of performing an initial computation before run time
In algorithms, precomputation is the act of performing an initial computation before run time to generate a lookup table that can be used by an algorithm
Precomputation
Password cracking dataset
random and stored with the password hash. A large salt value prevents precomputation attacks, including rainbow tables, by ensuring that each user's password
Rainbow_table
Security vulnerability in Diffie–Hellman key exchange
and reused. The researchers calculated the cost of creating logjam precomputation for one 1024-bit prime at hundreds of millions of USD, and noted that
Logjam_(computer_security)
Method of exchanging cryptographic keys
estimated by the authors behind the Logjam attack, the much more difficult precomputation needed to solve the discrete log problem for a 1024-bit prime would
Diffie–Hellman_key_exchange
Method of calculating ray-triangle intersections in 3D space
intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. Among other
Möller–Trumbore intersection algorithm
Möller–Trumbore_intersection_algorithm
Open problem on 3x+1 and x/2 functions
17, 2, 2, 20, 20, 8, 22, 8, 71, 26, 26, 80, 242 }. This requires 2k precomputation and storage to speed up the resulting calculation by a factor of k,
Collatz_conjecture
Problem of inverting exponentiation in groups
authors of the Logjam attack estimate that the much more difficult precomputation needed to solve the discrete log problem for a 1024-bit prime would
Discrete_logarithm
In databases, cached query results
languages, and it is sometimes described as a form of precomputation. As with other forms of precomputation, database users typically use materialized views
Materialized_view
Algorithm to solve the discrete logarithm problem
\alpha _{P}\deg(P)} . The Function Field Sieve algorithm consists of a precomputation where the discrete logarithms of irreducible polynomials of small degree
Function_field_sieve
Technique for defeating password protection using lists of likely possibilities
the hash dictionary to be recomputed for each password sought, making precomputation infeasible, provided that the number of possible salt values is large
Dictionary_attack
intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. Ray-Polygon
Badouel intersection algorithm
Badouel_intersection_algorithm
Algorithm in modular arithmetic
et al. showed that the full product is unnecessary if we can perform precomputation on one of the operands. We call a function [ ] : R → Z {\displaystyle
Barrett_reduction
2.71828...; base of natural logarithms
"Fast Multiple Precision exp ( x ) {\displaystyle \exp(x)} with Precomputations" (PDF). Proceedings of the 2024 IEEE 29th Symposium on Computer Arithmetic
E_(mathematical_constant)
Augmented password-authenticated key exchange protocol
showing subtle weaknesses; it is not UC‑secure, lacks resistance to all precomputation attacks, has weaker formal proofs, and offers no protection against
Secure Remote Password protocol
Secure_Remote_Password_protocol
Term in computer science
{\displaystyle S} against any triangle in L ( T ) {\displaystyle L(T)} . As a precomputation, take each physical body (represented by a set of triangles) and recursively
Collision_detection
Number whose cube is a given number
assuming that 1/3a is precomputed, so three iterations plus the precomputation require seven multiplications, three additions, and three divisions
Cube_root
Array that replaces runtime computation with a simpler array indexing operation
applications that require it. Depending on the values being precomputed, precomputation with interpolation can also be used to shrink the lookup table size
Lookup_table
Block cipher
in hardware for Twofish. An example of such a tradeoff would be the precomputation of round subkeys or s-boxes, which can lead to speed increases of a
Twofish
Group of rendering algorithms used in 3D computer graphics
2002 Conference Proceedings. Microsoft Research. Ramamoorthi, Ravi. "Precomputation-Based Rendering" (PDF). Foundations and Trends in Computer Graphics
Global_illumination
Stream cipher
known plaintext. The attack requires 32 GB of data storage after a precomputation stage of 238. Ekdahl and Johansson published an attack on the initialisation
A5/1
Algorithm for fast exponentiation
xn when the base is fixed and the exponent varies. As one can see, precomputations play a key role in these algorithms. Yao's method is orthogonal to
Exponentiation_by_squaring
Measure of cryptographic strength
June 2012). "Non-uniform cracks in the concrete: the power of free precomputation" (PDF). Advances in Cryptology - ASIACRYPT 2013. Lecture Notes in Computer
Security_level
Attempts to limit access to strong cryptography
primes in Diffie–Hellman implementations, and that NSA having done precomputation against those primes in order to break encryption using them in real
Crypto_Wars
1996 video game
games that followed Doom and concluded that extending the visibility precomputations would allow the game to render a larger number of polygons. Following
Crash_Bandicoot_(video_game)
Algorithm for fast modular multiplication
only place where a direct reduction modulo N is necessary is in the precomputation of R2 mod N. Most cryptographic applications require numbers that are
Montgomery modular multiplication
Montgomery_modular_multiplication
Image segmentation algorithm
eigenvector precomputation". In IEEE Conf. CVPR, pp. 1–8, 2008 S. Andrews, G. Hamarneh, A. Saad. Fast random walker with priors using precomputation for interactive
Random_walker_algorithm
On short connecting nets with added points
1986, Wu et al. improved dramatically on the running time by avoiding precomputation of the all-pairs shortest paths. Instead, they take a similar approach
Steiner_tree_problem
Brand of smart and proximity cards
MIFARE Classic, has instant running time, and does not require a costly precomputation. The new attack allows recovering the secret key of any sector of the
MIFARE
{\displaystyle {\text{GF}}\left(2^{128}\right)} for AES). With some precomputation, only a single multiplication per sector is required (note that addition
Disk_encryption_theory
Computer graphics method
around corners, and other types of bias. Reuse algorithms based on precomputation and caching may not respond quickly enough to lighting changes during
Path_tracing
Mathematical operation on points on an elliptic curve
doubling and 2 w − 2 − 1 {\displaystyle 2^{w-2}-1} point additions for precomputation. The algorithm then requires n {\displaystyle n} point doublings and
Elliptic curve point multiplication
Elliptic_curve_point_multiplication
Cryptanalytic attacks using a system of multivariate equations
plaintext in fraction of a second. This was further improvement from the precomputation algorithms that were the fastest known to break the Bluetooth cipher
Algebraic_attack
Tree connecting given points by short paths
points can also be tested in O ( n ) {\displaystyle O(n)} , after a precomputation step in which, for each point, the other points are sorted by their
Minimum-diameter spanning tree
Minimum-diameter_spanning_tree
this problem. Input enhancement is often used interchangeably with precomputation and preprocessing. Although they are related, there are several important
Input enhancement (computer science)
Input_enhancement_(computer_science)
Set of problems solved by small circuits
BPP, this also admits the possibility that adversaries can do heavy precomputation for inputs up to a certain length, as in the construction of rainbow
P/poly
and ambient occlusion at interactive framerates without the need for precomputation. Anisotropic filtering Sampling (signal processing) Spatial anti-aliasing
Cone_tracing
Method of cryptanalysis
input bits will exist with high probability, and can be discovered in a precomputation phase by "black box probing" of the relationship between input and output
Cube_attack
Stream cipher
about 240 operations. The attack was improved to 237 operations for precomputation and 239 for the actual key search. In 2005, Lu, Meier and Vaudenay published
E0_(cipher)
Computer image rendering software
using the path tracing engine gives an unbiased result, while using precomputations with a secondary engine increases processing time while making outcomes
Chaos_Corona
Best results achieved to date
1607. Joux, Antoine; Pierrot, Cécile. "Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms" (PDF). Archived
Discrete_logarithm_records
Concept in cryptography
2011-07-16. Retrieved 2025-10-20. "Breaking Diffie-Hellman with Massive Precomputation (Again)". Schneier on Security. 2015-10-16. Retrieved 2025-10-20. Bergsaker
Custom_hardware_attack
Type of cryptographic statistical attack
can be found with a complexity of 28 round transformations due to the precomputation step. The outbound phase completes the differential characteristic in
Rebound_attack
Encryption system for FreeBSD
a significant CPU overhead, as most block ciphers use key-specific precomputations, and makes disk updates non-atomic since the keys are written separately
GBDE
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Biblical
son of Noah|Ham, hot; heat; brown
Girl/Female
Christian & English(British/American/Australian)
Beautiful One
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Indian, Punjabi, Sikh
Everywhere
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Hindu
Praising Allah, Holy
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Hindu, Indian
Patience
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French
An Old French surname meaning pilferer or ferret.
Girl/Female
Hindu
Beautiful, Capable
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British, English
Traveler
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Indian
Having a face like a fairy, Beautiful
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Arabic, Muslim, Sindhi
Name of a Black Slave who Fought in the Early Wars of the Islam
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