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Cryptography and Residue Arithmetic

Cryptography and Residue Arithmetic is a research topic within Information Systems. Science Explorer counts 9.8k research works in it since 1956. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers explores the applications, algorithms, and implementations of elliptic curve cryptography, with a focus on pairing-based cryptosystems, efficient algorithms for finite fields, quantum-resistant cryptosystems, and protection against side-channel attacks. It also covers hardware implementations and the use of elliptic curves in public key encryption.

  • Elliptic Curves
  • Cryptography
  • Pairing-Based Cryptosystems
  • Efficient Algorithms
  • Quantum-Resistant Cryptosystems
  • Finite Fields
  • Modular Multiplication
  • Side-Channel Attacks
  • Public Key Encryption
  • Hardware Implementations
Research works
9.8k
fractional, since 1956
In the world top 10%
979
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+16%
the tick is no change
Largest producer
China
28% of the 10 largest, 2022-now
Cryptography and Residue Arithmetic

Which countries lead Cryptography and Residue Arithmetic research?

By volume, China and India publish the most (361 and 296 works in 2022-now).

By volume, 2022-now

  1. 1 China 361 works
  2. 2 India 296 works
  3. 3 United States 219 works
  4. 4 Japan 93 works
  5. 5 France 92 works
  6. 6 Germany 59 works
  7. 7 South Korea 58 works
  8. 8 Russia 47 works
  9. 9 United Kingdom 41 works
  10. 10 Canada 39 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 27.7%India: 22.7%United States: 16.8%Japan: 7.1%6 others listed: 25.8%28%largest
China361 · 27.7%India296 · 22.7%United States219 · 16.8%Japan93 · 7.1%6 others listed337 · 25.8%

Shares of the rows listed above, not of the whole node.

Which institutions lead Cryptography and Residue Arithmetic research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Cryptography and Residue Arithmetic research, followed by Chinese Academy of Sciences and The University of Tokyo.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 31 works
  2. 2 Chinese Academy of SciencesChina 26 works
  3. 3 The University of TokyoJapan 16 works
  4. 4 State Key Laboratory of CryptologyChina 11 works
  5. 5 Vellore Institute of Technology UniversityIndia 10 works
  6. 6 Sun Yat-sen UniversityChina 9 works
  7. 7 SRM Institute of Science and TechnologyIndia 9 works
  8. 8 KU LeuvenBelgium 9 works
  9. 9 University of Chinese Academy of SciencesChina 9 works
  10. 10 Inha UniversitySouth Korea 9 works

Who are the leading researchers in Cryptography and Residue Arithmetic?

The most-cited researchers publishing on Cryptography and Residue Arithmetic include Lei Jiang, Mehdi Hosseinzadeh and Hywel C Williams.

  1. 1 Lei Jiang China 214k citations
  2. 2 Mehdi Hosseinzadeh Iran 137k citations
  3. 3 Hywel C Williams United Kingdom 126k citations
  4. 4 Hao Chen China 118k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Cryptography and Residue Arithmetic?

The most cited paper in Cryptography and Residue Arithmetic is "How to share a secret" (Adi Shamir, 1979), with 13,673 citations. Next come "A public key cryptosystem and a signature scheme based on discrete logarithms" (8,095) and "Identity-Based Encryption from the Weil Pairing" (7,095).

Most cited papers
#PaperReleasedCitations
1 How to share a secret Adi Shamir · Communications of the ACM Open access Nov 1979 13,673
2 A public key cryptosystem and a signature scheme based on discrete logarithms Taher ElGamal · IEEE Transactions on Information Theory Jul 1985 8,095
3 Identity-Based Encryption from the Weil Pairing Dan Boneh, Matthew K. Franklin · Lecture notes in computer science Conference paper 2001 7,095
4 Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems Paul C. Kocher · Lecture notes in computer science Conference paper 1996 4,361
5 Use of Elliptic Curves in Cryptography Victor S. Miller · Lecture notes in computer science Conference paperOpen access 28 Feb 2007 3,968
All 97 most cited papers, with filters and sorting

Where is Cryptography and Residue Arithmetic research done?

The largest centres of Cryptography and Residue Arithmetic research in 2022-now are Beijing (China), Tokyo (Japan), Paris (France) and Seoul (South Korea).

Largest cities, 2022-now

  1. 1 BeijingChina 98 works
  2. 2 TokyoJapan 42 works
  3. 3 ParisFrance 28 works
  4. 4 SeoulSouth Korea 28 works
  5. 5 GuangzhouChina 27 works
  6. 6 ChennaiIndia 23 works
  7. 7 ShanghaiChina 23 works
  8. 8 BengaluruIndia 21 works
  9. 9 Xi'anChina 21 works
  10. 10 NanjingChina 18 works
See Cryptography and Residue Arithmetic on the map

Where is the best place to study Cryptography and Residue Arithmetic?

Among universities, judged by research, Inha University, KU Leuven and The University of Tokyo score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 14.05%fractional works in this field (log) →share of work in the world top 10% →Inha UniversityKU LeuvenUniversity of WaterlooThe University of To…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Inha UniversitySouth Korea 66.744.1%25.8×9 +504.3%
2KU LeuvenBelgium 65.031.8%5.7×9 +30.0%
3The University of TokyoJapan 53.03.4%7.7×16 +27.9%
4University of WaterlooCanada 35.814.8%9.0×8 -19.2%
5University of Chinese Academy of SciencesChina 29.315.3%3.3×9 +52.8%
6Sun Yat-sen UniversityChina 29.212.5%2.8×9 +32.0%
7SRM Institute of Science and TechnologyIndia 28.47.5%5.6×9 +415.0%
8Sidi Mohamed Ben Abdellah UniversityMorocco 25.53.2%19.3×9 +95.6%
9Vellore Institute of Technology UniversityIndia 23.30.7%6.1×10 -1.5%
10National University of Defense TechnologyChina 22.07.2%6.7×8 +279.2%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Cryptography and Residue Arithmetic, country by country

Is Cryptography and Residue Arithmetic research growing?

Output in 2022-2025 was 16% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Cryptography and Residue Arithmetic.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Cryptography and Residue Arithmetic as a percentage of every work published that year, 0.0060% in 2024.

still counting0.010%0.020%Cryptography and Residue Arithmetic0.0093% in 202519801990200020102020

Fractional works of Cryptography and Residue Arithmetic over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Cryptography and Residue Arithmetic10.4% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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