Cryptography by the Numbers

NIST Recommendations
  • Modes of operation for block ciphers approved by NIST (source, updated February 12, 2018)
    • Encryption:  6
    • Authentication:  1
    • Encryption with Authentication:  5
    • Format-Preserving Encryption:  2
  • Minimum key sizes approved by NIST (source, published January 2016)
    • AES:  128 bits
    • Diffie-Hellman:  2048 bits (617 digits)
    • RSA:  2048 bits (617 digits)
    • Digital Signature Algorithm:  2048 bits (617 digits) for public key, 224 bits (68 digits) for private key
    • Elliptic Curve Cryptography:  224 bits (68 digits)
Record-Breaking Computations
  • Record for finding a discrete logarithm modulo a prime (source, announced June 16, 2016):

p = \lfloor 2^{766} \pi \rfloor + 62762 =1219344858334286932696341909195796109526657386154251328029273656175766870980306505584577389125860826715201547225794072935883258868036433287217994721542199148182841505800433148410869683590659346847659519108393837414567892730579162319 (768 bits, 232 digits)

  • Record for finding a discrete logarithm in a finite field (source, announced January 31, 2014):  Finite field has 29232 elements; size of the field is 9232 bits (2779 digits).
  • Record for factoring a product of two large primes of general form (source, published January 6, 2010):

n=1230186684530117755130494958384962720772853569595334792197322452151726400507263657518745202199786469389956474942774063845925192557326303453731548268507917026122142913461670429214311602221240479274737794080665351419597459856902143413 (768 bits, 232 digits)

  • Record for finding a discrete logarithm on an elliptic curve of general form modulo p (source, published September 9, 2009):

p = (2128 − 3)/(11 × 6949) = 4451685225093714772084598273548427 (112 bits, 34 digits)

  • Record for finding a discrete logarithm on a “pairing-friendly” elliptic curve modulo p (source, published

p =  1957518425389075254535992784167879 (114 bits, 35 digits)

  • Record for finding the shortest vector in a randomly generated lattice (source, announced August 30, 2018):  A point in a lattice in 153 dimensions which is distance 3192 from the origin.
Quantum Computing Records
  • Largest number reported factored using Shor’s Algorithm for fast quantum computing:  21  (source, published October 21, 2012)
  • Largest number reported factored using quantum computation at any speed:  200099 (source, published February 21, 2017)
Post-Quantum Cryptography
  • Submissions to the NIST Post-Quantum Cryptography Standardization process (source, presented April 11, 2018)
    • Submissions received by NIST:  82
    • Submissions meeting minimum specified requirements:  69
    • Submissions still in contention as of the First PQC Standardization Conference:  64
    • Submitters involved: 278, from “25 Countries, 16 States, 6 Continents”
    • 2nd NIST PQC Standardization Workshop:  August, 2019
    • Select algorithms or start a 3rd Round:  2020/2021
    • Draft standards available:  2022-2024
Quantum Cryptography Records
  • Fastest quantum key agreement systems:
    • Medium-distance:  1.02 Mbit/s over 20 km of optical fiber (source, published October 30, 2008)
    • Long-distance:  12.7 kbit/s over 307 km of optical fiber (source, published
  • Longest quantum key agreement systems:
    • Fiber-optic:  404 km (source, published
    • Ground-to-ground: 144 km (source, published January 5, 2007)
    • Air-to-ground: 20 km (source, published
    • Ground-to-air:  10 km (source, published June 6, 2017)
    • Satellite-to-ground:  1200 km (source, published September 7, 2017)