New Directions in Cryptography
1976 · paper · Computer science
Examines new developments in cryptography, proposing ways to reduce the need for secure key-distribution channels and to provide the equivalent of a written signature. It also discusses how communication and computation theory can help solve long-standing cryptographic problems.
Checked: PDF from ee.stanford.edu, fetched 4 Oct 2026. Page numbers are those of that PDF.
2 findings
Substance "this adds kn = 5000 authentication bits to the message. It thus entails only a 5 percent data expansion during transmission (or 15 percent if the initial exchange ... is included)" with N = 10^6: 5000 bits is 0.5 percent of the message, and 15000 bits is 1.5 percent.
- p. 8 Section IV, first paragraph, left column
It thus entails only a 5 percent data expansion
- p. 8 Section IV, left column, first paragraph
It thus entails only a 5 percent data expansion during transmission (or 15 percent if the initial exchange
- p. 8 same sentence
(or 15 percent if the initial exchange
Judge's note: Page 8 shows N = 10^6, n = 50, k = 100 and kn = 5000, as printed. Page 7 shows that the y vectors are k-dimensional. So the initial exchange of 2n images is 2nk = 10000 bits, and the total is 15000 bits. Both printed percentages are ten times the values that follow from the paper's own parameters. The 3:1 ratio between 15 and 5 matches 2nk extra bits, so this is a single scaling slip, and this cluster covers both figures. The paper offers no other base for the percentages.
Second check: another model agreed
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Wording In the modified (hashed) scheme the initial exchange is written "of y1,Y1, ··· ,yN,YN is included", but only the n-bit vector m' is sent by the previous scheme. The exchange should be y1,Y1,…,yn,Yn.
- p. 8 Section IV, first paragraph, left column
of y1,Y1, ··· ,yN,YN is included
Judge's note: Page 8 image: the subscripts are capital N. Page 7 defines the unmodified scheme over N vectors. In the modified scheme the Lamport method is applied to m', which has n bits, so 2n images are needed. With N, the exchange would be 2*10^6*100 bits, which cannot match the printed overhead figure. That figure's 3:1 ratio to the 5 percent figure matches 2nk bits. The subscript appears to have been carried over from p. 7.
Second check: another model agreed
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8 minor (typos and the like; most checked by the judge only)
Wording "which can be checked by the system by applying f^t(X)": the system does not hold X; it applies f^t to the received authenticator f^{T-t}(X) and compares with the stored f^T(X).
- p. 8 Section IV, one-way user authentication paragraph
which can be checked by the sys- tem by applying f t(X)
Judge's note: The crop confirms the wording. Since f^t(f^{T-t}(X)) = f^T(X), the check is clear, but 'f^t(X)' read literally names the operand as the secret X. This is loose notation, not an error in the method.
Second check: another model agreed
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Wording "codified by Kerchoffs [2, p. 235] who wrote in 1881 that the compromise of a cryptographic system should cause no inconvenience": the date of Kerckhoffs's statement is usually given as 1883.
- p. 11 Section VII
who wrote in 1881 that
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: Kerckhoffs's 'La cryptographie militaire' was published in 1883. The page 11 crop confirms that the paper prints '1881'. The files contain nothing that settles the date. Checking Kahn [2, p. 235] would settle it.
Second check: another model agreed
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Typo Misspelling on p. 3 (journal p. 646): "which are unwieldly to use" should be "unwieldy" (spelled correctly on p. 10: "too unwieldy for most purposes").
- p. 3 Section II, left column
which are unwieldly to use
- p. 10 Section VI, left column
too unwieldy for most purposes
- p. 3 Sec. II, provably secure cryptosystems paragraph
which are unwieldly
Judge's note: The page 3 crop shows 'unwieldly'. The page 10 image shows 'unwieldy'. This is a plain misspelling.
Second check: none (judge only)
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Typo Reference [8] title reads "An improved algorithm for computing algorithms in GF(p) and its cryptographic significance"; "logarithms" is evidently meant.
- p. 11 References, [8]
An improved algorithm for com- puting algorithms in GF(p)
- p. 6 Section III, after Eq. (6)
using the best known algorithm [7, pp. 9, 575–576], [8]
Judge's note: The reference crop shows 'computing algorithms'. [8] is cited on p. 8 for the discrete exponential function of Section III and on p. 6 for the best known algorithm for computing logarithms. 'Computing algorithms' makes no sense in that context. This is a one-word slip in a citation title; the reference itself is identifiable.
Second check: none (judge only)
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Typo Misspelling on p. 10 (journal p. 653): "a known vector of n in-tergers" should be "integers".
- p. 10 Section VI, knapsack paragraph, right column
a known vector of n in- tergers
Judge's note: The page 10 image, right column, shows 'in-tergers' across the line break.
Second check: none (judge only)
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Typo Misspelling on p. 10 (journal p. 653): "certification via crypanalytic assault" should be "cryptanalytic".
- p. 10 Section VI, first paragraph, left column
certification via crypanalytic assault
Judge's note: The page 10 image, left column, first paragraph, shows 'crypanalytic'. The paper spells the word correctly elsewhere on the same page.
Second check: none (judge only)
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Typo Number disagreement on p. 11 (journal p. 654): "The one-wayness of this functions has already been discussed in Section III" should be "this function".
- p. 11 Section VI, end, left column
The one-wayness of this functions has already
- p. 11 Section VI, last paragraph
The one-wayness of this functions has already been discussed in Section III.
Judge's note: The page 11 image, left column, end of Section VI, shows 'this functions'.
Second check: none (judge only)
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Typo The name is printed "Kerchoffs" twice ("codified by Kerchoffs [2, p. 235]" and "set down by Kerchoffs [2, p. 234]"); the standard spelling is Kerckhoffs.
- p. 11 Section VII, left column
ciple was codified by Kerchoffs [2, p. 235]
- p. 11 Section VII, right column
set down by Kerchoffs [2, p. 234]
- p. 11 Section VII
This prin- ciple was codified by Kerchoffs [2, p. 235]
- p. 11 Sec. VII
codified by Kerchoffs
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the cryptographer's name is spelled Kerckhoffs. The page 11 image shows 'Kerchoffs' in both places, so this is not an extraction artefact. The spelling is consistent within the paper.
Second check: none (judge only)