Advanced Analogue and Digital Encryption Methods. Presented by: Dr. S. Sarpal

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Transcription:

Advanced Analogue and Digital Encryption Methods Presented by: Dr. S. Sarpal

Background Term given to a mathematical algorithm OR a set of known sequences. Mixed with message to hide the meaning of content. Needed for personal privacy or security applications. Many analogue and digital encryption methods available. Earliest Ciphers Vedic scriptures, the Egyptians, Julius Caesar. Infamous example: Military communications (Enigma). Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 2

Cryptographic Jargon Crypto system. Plaintext (data to be encrypted). Ciphertext (encrypted data). Key. Alice, Bob, Carol and Dave. Eve (the eavesdropper!) Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 3

Types of analogue crypto systems Spectrum inversion: AM modulation concept (inverted lower sideband) Variable split band (VSB) and rolling codes used for greater security. Spectrum shift (AM concept, upper sideband). Cut and rotate (much more effective!) General comments : Cheap to implement, does not require specialised hardware but offers limited security. Encrypted speech is discenable in some configurations. Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 4

Spectrum Inversion Example Using trigonometric identities Analogue multiplier used. Hilbert transform can be used to remove upper sideband (DSP or computer implementation). Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 5

Audio VSB Spectrum Inversion Example Magnitude Rolling code used to determine split point frequency (VSB). Split point frequency updated every 500ms. Freq Original Encrypted Increased security than single carrier frequency. Low cost ASIC implementation available. Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 6

Types of digital crypto systems Symmetric (or secret key) encryption: Same key used for encryption and decryption. Fast operation on computer, DSP or micro-controller. Examples: PRBS, DES, triple DES, RC2, IDEA, Blowfish, CAST-128, Skipjack, AES Asymmetric (or public key) encryption: Different keys for encryption and decryption. Slow operation, best suited to a DSP or ASIC. Examples: PGP, RSA, Diffie-Hellman, DSA, Elgamal General comments: Usually more expensive to implement than analogue methods. High level of security at much greater computation expense. Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 7

Simple digital encryption (PRBS) 1 0 1 0 1 0 = xor A B Q 0 0 0 0 1 1 1 0 1 1 1 0 Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 8

Asymmetric encryption (the RSA algorithm) Introduced in 1977. Named after its creators Rivest, Shamir and Adleman. Used for secure encryption and digital signatures. Patented in 1983, but released into the public domain in September 2000. Commonly used PGP, SSH, SSL, SET (Visa, Mastercard). Gets its security from the difficulty of factorizing large numbers. 1024-bit key is considered as the smallest key for secure communication. Many references have demonstrated that 300-bit or shorter keys can be broken in few hours using a simple laptop and freely available software! Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 9

Overview of the RSA algorithm Key Generation Two random large prime numbers, p and q are chosen. For maximum security, p and q should be of equal length. Calculate product n=p q Calculate random encryption key, e such that e and (p-1) (q-1) are relatively prime. Finally, extended Euclidean algorithm is used for computing the decryption key d, such that: e d = 1 mod (p-1) (q-1) PUBLIC KEY: e, n PRIVATE KEY: d Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 10

Overview of the RSA algorithm Encryption/decryption Encryption To encrypt our plaintext message m using our public key, e: c = m e mod n Example: m = 123, p = 29, q = 31, e = 13, d = 517 c = 123 13 (mod [29 31]) = 402 Decryption To decrypt the ciphertext c using our private key, d: m = c d mod n m = 402 517 (mod [29 31]) = 123 Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 11

Thank you for your attention, please feel free to ask any questions. Copyright Advanced Solutions Nederland 2009. ASN09-PPT001 Page: 12

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