L03_publickeycrypto

# Ciphertext block can be as big as the key length

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Unformatted text preview: lowed by public key by private key Result is the same! Ciphertext block can be as big as the key-length => digital signature can be as big as the key-length How secure is RSA ? Brute force attack: try all possible keys – the larger the value of d the try more secure more The larger the key, the slower the system ; Alternatively, one can break RSA by finding p and q, and thus d by Alternatively, and knowing n and e and However, for large n with large prime factors, factoring is a hard However, problem problem Cracked in 1994 a 428 bit key; \$100 \$100 Currently 1024-bit key size (no. of bits in n ) is considered strong Currently enough, for now for http://www.rsasecurity.com/rsalabs/node.asp?id=2218 \$100 RSA Scientific American Challenge Martin Gardner publishes Scientific American column about RSA Martin in August ’77, including the RSA \$100 challenge (129 digit , or about 430-bit n ) and the infamous “40 quadrillion = 40*10 15 years” about estimate required to factor RSA-129 = RSA-129 114,381,625,757,888,867,669,235,779,976,146,612,010,218,296, 114,381,625,757,888,867,669,235,779,976,146,612,010,218,296, 721,242,362,562,561,842,935,706,935,245,733,897,830,597,123, 563,958,705,058,989,075,147,599,290,026,879,543,541 (129 digits) or to decode encrypted message. RSA-129 was factored in 1994, using thousands of computers on Internet, using 5000 MIPS-years (1GHz Pentium PC ~= 250 MIPS) Internet, “The magic words are squeamish ossifrage.” Cheapest purchase of computing time ever! Gives credibility to difficulty of factoring, and helps establish key Gives sizes needed for security. sizes Other Factoring milestones ’84: 69D (D = “decimal digits”) (Sandia; Time magazine) ’91: 100D = 332 bits (using Quadratic Sieve techniques) ’94: 129D = 428 bits (\$100 challenge number) (Distributed QS, 94: 8 months, 5000MIPS-year) ; [ Ref: 1GHz Pentium PC ~= 250 MIPS] MIPS] ’99: 155D = 512 bits; (Generalized Number Field Sieve 99: techniques, 2 months and 10 days, 8000-MI...
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