Shamir’s attack on RSA with low decryption exponent
E195493
Shamir’s attack on RSA with low decryption exponent is a cryptanalytic method that exploits unusually small private exponents in RSA to efficiently recover the secret key and break the encryption.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Shamir’s attack on RSA with low decryption exponent canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1762035 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Shamir’s attack on RSA with low decryption exponent Context triple: [Adi Shamir, knownFor, Shamir’s attack on RSA with low decryption exponent]
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A.
New Directions in Cryptography
New Directions in Cryptography is a landmark 1976 paper that introduced the concepts of public-key cryptography and digital signatures, fundamentally reshaping modern cryptography and secure communications.
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B.
Blum–Blum–Shub pseudorandom number generator
The Blum–Blum–Shub pseudorandom number generator is a cryptographically secure generator based on the hardness of factoring large composite numbers, widely studied in theoretical computer science and cryptography.
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C.
Secrecy, Authentication, and Public Key Systems
"Secrecy, Authentication, and Public Key Systems" is Ralph Merkle's influential doctoral thesis that helped lay the foundations of modern public-key cryptography and secure communication protocols.
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D.
Merkle puzzles
Merkle puzzles are an early cryptographic protocol that introduced the concept of public-key exchange by allowing two parties to establish a shared secret over an insecure channel using computationally asymmetric “puzzle” problems.
-
E.
Probabilistic Encryption
Probabilistic Encryption is a cryptographic technique that uses randomness in the encryption process so that the same message encrypts to different ciphertexts, enhancing security against attackers.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Shamir’s attack on RSA with low decryption exponent Target entity description: Shamir’s attack on RSA with low decryption exponent is a cryptanalytic method that exploits unusually small private exponents in RSA to efficiently recover the secret key and break the encryption.
-
A.
New Directions in Cryptography
New Directions in Cryptography is a landmark 1976 paper that introduced the concepts of public-key cryptography and digital signatures, fundamentally reshaping modern cryptography and secure communications.
-
B.
Blum–Blum–Shub pseudorandom number generator
The Blum–Blum–Shub pseudorandom number generator is a cryptographically secure generator based on the hardness of factoring large composite numbers, widely studied in theoretical computer science and cryptography.
-
C.
Secrecy, Authentication, and Public Key Systems
"Secrecy, Authentication, and Public Key Systems" is Ralph Merkle's influential doctoral thesis that helped lay the foundations of modern public-key cryptography and secure communication protocols.
-
D.
Merkle puzzles
Merkle puzzles are an early cryptographic protocol that introduced the concept of public-key exchange by allowing two parties to establish a shared secret over an insecure channel using computationally asymmetric “puzzle” problems.
-
E.
Probabilistic Encryption
Probabilistic Encryption is a cryptographic technique that uses randomness in the encryption process so that the same message encrypts to different ciphertexts, enhancing security against attackers.
- F. None of above. chosen
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
attack on RSA
ⓘ
cryptanalytic attack ⓘ mathematical attack ⓘ |
| appliesWhen | RSA private exponent d is unusually small relative to modulus N ⓘ |
| assumes |
RSA modulus is known
ⓘ
public exponent is known ⓘ |
| basedOn |
Diophantine approximation techniques
ⓘ
lattice-based methods ⓘ |
| complexity | polynomial time under its parameter assumptions ⓘ |
| countermeasure |
choose sufficiently large private exponent d
ⓘ
follow recommended RSA key-size and exponent guidelines ⓘ |
| describedIn | research on attacks against low-exponent RSA ⓘ |
| developedBy | Adi Shamir ⓘ |
| exploits |
low RSA decryption exponent
ⓘ
small private exponent in RSA ⓘ |
| field |
cryptanalysis
ⓘ
public-key cryptography ⓘ |
| goal |
break RSA encryption
ⓘ
recover RSA private key ⓘ |
| improvesOn | Wiener’s attack on RSA ⓘ |
| input | RSA public key (N,e) ⓘ |
| involves |
continued fractions and lattice techniques
ⓘ
number theory ⓘ |
| output |
RSA private exponent d
ⓘ
factorization of RSA modulus N ⓘ |
| relatedTo | Wiener’s attack on RSA ⓘ |
| riskFactorFor | RSA implementations using small private exponents for efficiency ⓘ |
| securityImplication |
RSA key generation must avoid low decryption exponents
ⓘ
RSA with very small private exponent is insecure ⓘ |
| targets |
RSA
ⓘ
surface form:
RSA cryptosystem
|
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Shamir’s attack on RSA with low decryption exponent Description of subject: Shamir’s attack on RSA with low decryption exponent is a cryptanalytic method that exploits unusually small private exponents in RSA to efficiently recover the secret key and break the encryption.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.